@misc{GalliatDeuflhardRoitzschetal., author = {Galliat, Tobias and Deuflhard, Peter and Roitzsch, Rainer and Cordes, Frank}, title = {Automatic Identification of Metastable Conformations via Self-Organized Neural Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6197}, number = {00-51}, abstract = {As has been shown recently, the identification of metastable chemical conformations leads to a Perron cluster eigenvalue problem for a reversible Markov operator. Naive discretization of this operator would suffer from combinatorial explosion. As a first remedy, a pre-identification of essential degrees of freedom out of the set of torsion angles had been applied up to now. The present paper suggests a different approach based on neural networks: its idea is to discretize the Markov operator via self-organizing (box) maps. The thus obtained box discretization then serves as a prerequisite for the subsequent Perron cluster analysis. Moreover, this approach also permits exploitation of additional structure within embedded simulations. As it turns out, the new method is fully automatic and efficient also in the treatment of biomolecules. This is exemplified by numerical results.}, language = {en} } @misc{KoberSaderZeilhoferetal., author = {Kober, Cornelia and Sader, Robert and Zeilhofer, Hans-Florian and Prohaska, Steffen and Zachow, Stefan and Deuflhard, Peter}, title = {Anisotrope Materialmodellierung f{\"u}r den menschlichen Unterkiefer}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6574}, number = {01-31}, abstract = {Im Rahmen der biomechanischen Simulation kn{\"o}cherner Organe ist die Frage nach einer befriedigenden Materialbeschreibung nach wie vor ungel{\"o}st. Computertomographische Datens{\"a}tze liefern eine r{\"a}umliche Verteilung der (R{\"o}ntgen-)Dichte und erm{\"o}glichen damit eine gute Darstellung der individuellen Geometrie. Weiter k{\"o}nnen die verschiedenen Materialbestandteile des Knochens, Spongiosa und Kortikalis, voneinander getrennt werden. Aber die richtungsab{\"a}ngige Information der Materialanisotropie ist verloren. In dieser Arbeit wird ein Ansatz f{\"u}r eine anisotrope Materialbeschreibung vorgestellt, die es erm{\"o}glicht, den Einfluss der individuellen kn{\"o}chernen Struktur auf das makroskopische Materialverhalten abzusch{\"a}tzen.}, language = {de} } @misc{DeuflhardHegeSeebass, author = {Deuflhard, Peter and Hege, Hans-Christian and Seebass, Martin}, title = {Progress Towards a Combined MRI/Hyperthermia System}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5755}, number = {00-07}, abstract = {Regional hyperthermia, a clinical cancer therapy, is the main topic of the Sonderforschungsbereich Hyperthermia: Scientific Methods and Clinical Applications'' at Berlin. In recent years, technological improvements towards a better concentration of heat to the desired target region have been achieved. These include a rather sophisticated integrated software environment for therapy planning and a new hyperthermia applicator. In a next step, a detailed closed loop monitoring of the actual treatment is to be developed. For this purpose the hyperthermia applicator is combined with an MRI system, which will allow to check the positioning of the patients and to measure individual blood perfusion as well as the 3D temperature distribution. The measurements will then be employed for an on-line control of the whole treatment. In this intended setting, new fast feedback control algorithms will come into play.}, language = {en} } @misc{DeuflhardReich, author = {Deuflhard, Peter and Reich, Sebastian}, title = {2nd International Symposium Algorithms for Macromolecular Modelling}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5455}, number = {TR-97-03}, abstract = {The report contains the program and the collected abstracts of the 2nd International Symposium ``Algorithms for Macromolecular Modelling''.}, language = {en} } @misc{DeuflhardLouisSchlegeletal., author = {Deuflhard, Peter and Louis, Alfred and Schlegel, W. and Seebass, Martin}, title = {Workshop "Scientific Computing in der Medizin" SCMED '97}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5474}, number = {TR-97-05}, abstract = {Die Arbeitstagung \glqq Scientific Computing in der Medizin\grqq , kurz SCMED \grq 97, findet vom 22. - 23. September 1997 im neu errichteten Geb{\"a}ude des Konrad-Zuse-Zentrums auf dem Dahlemer naturwissenschaftlichen Campus der Freien Universt{\"a}t Berlin statt.}, language = {en} } @misc{Deuflhard, author = {Deuflhard, Peter}, title = {Adaptive Pseudo-transient Continuation for Nonlinear Steady State Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6814}, number = {02-14}, abstract = {Pseudo--transient continuation methods are quite popular for the numerical solution of steady state problems, typically in PDEs. They are based on an embedding into a time dependent initial value problem. In the presence of dynamical invariants the Jacobian matrix of the nonlinear equation system is bound to be singular. The paper presents a convergence analysis which takes this property into account -- in contrast to known approaches. On the basis of the new analysis adaptive algorithms are suggested in detail. These include a variant with Jacobian approximations as well as inexact pseudo--transient continuation, both of which play an important role in discretized PDEs. Numerical experiments are left to future work.}, language = {en} } @misc{Deuflhard, author = {Deuflhard, Peter}, title = {From Molecular Dynamics to Conformational Dynamics in Drug Design}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6878}, number = {02-20}, abstract = {Computational drug design studies molecular recognition in the {\em virtual lab}. The arising Hamiltonian dynamics is known to be chaotic and ill-conditioned already after picoseconds, whereas times are \$msec\$ up to \$min\$. Classical molecular dynamics with long term trajectory computation gives, at best, information about time and statistical ensemble averages. The present paper surveys a recent new modeling approach called {\em conformational dynamics}, which is due to the author and Ch. Sch{\"u}tte. This approach achieves information about the dy time scales by telescoping a short term deterministic model with a statistical model. Examples of small biomolecules are included.}, language = {en} } @misc{DeuflhardHochmuth, author = {Deuflhard, Peter and Hochmuth, Reinhard}, title = {Multiscale Analysis of Thermoregulation in the Human Microvascular System}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6985}, number = {02-31}, abstract = {The bio-heat transfer equation is a macroscopic model for describing the heat transfer in microvascular tissue. So far the deduction of the Helmholtz term in the bio-heat transfer equation is not co role. In view of a future numerical application of this new mathematical model to treatment planning in hyperthermia we derive asymptotic estimates for first and second order correctors.}, language = {en} } @misc{DeuflhardNowakWeiser, author = {Deuflhard, Peter and Nowak, Ulrich and Weiser, Martin}, title = {Affine Invariant Adaptive Newton Codes for Discretized PDEs}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7005}, number = {02-33}, abstract = {The paper deals with three different Newton algorithms that have recently been worked out in the general frame of affine invariance. Of particular interest is their performance in the numerical solution of discretized boundary value problems (BVPs) for nonlinear partial differential equations (PDEs). Exact Newton methods, where the arising linear systems are solved by direct elimination, and inexact Newton methods, where an inner iteration is used instead, are synoptically presented, both in affine invariant convergence theory and in numerical experiments. The three types of algorithms are: (a) affine covariant (formerly just called affine invariant) Newton algorithms, oriented toward the iterative errors, (b) affine contravariant Newton algorithms, based on iterative residual norms, and (c) affine conjugate Newton algorithms for convex optimization problems and discrete nonlinear elliptic PDEs.}, language = {en} } @misc{EhrigOfenlochSchaberetal., author = {Ehrig, Rainald and Ofenloch, Oliver and Schaber, Karlheinz and Deuflhard, Peter}, title = {Modelling and Simulation of Aerosol Formation by Heterogeneous Nucleation in Gas-Liquid Contact Devices}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6416}, number = {01-15}, abstract = {This paper describes a new simulation tool for the prediction of aerosol formation and behavior in gas--liquid contact devices such as absorbers, scrubbers, quench coolers, and condensers as well as multistage gas cleaning processes, respectively. Aerosol formation can impact severely the separation efficiency of gas cleaning processes. Aerosol or fog formation can arise by spontaneous condensation or desublimation in supersaturated gas phases. The rigorous description of the mass and energy transfer between the gas phase, the liquid phase, and the growing aerosol droplets leads to a system of partial differential and algebraic equations. For the solution of these systems we have developed the plant simulation tool AerCoDe. This program bases upon the linearly--implicit Euler discretisation, which in combination with extrapolation permits an adaptive step size and order control. Typical simulation results of a multistage industrial flue gas scrubbing process are presented. It is shown, that experimental data can be confirmed if the number concentration of condensation nuclei as an input parameter is roughly known.}, language = {en} } @misc{WeiserDeuflhard, author = {Weiser, Martin and Deuflhard, Peter}, title = {The Central Path towards the Numerical Solution of Optimal Control Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6380}, number = {01-12}, abstract = {A new approach to the numerical solution of optimal control problems including control and state constraints is presented. Like hybrid methods, the approach aims at combining the advantages of direct and indirect methods. Unlike hybrid methods, however, our method is directly based on interior-point concepts in function space --- realized via an adaptive multilevel scheme applied to the complementarity formulation and numerical continuation along the central path. Existence of the central path and its continuation towards the solution point is analyzed in some theoretical detail. An adaptive stepsize control with respect to the duality gap parameter is worked out in the framework of affine invariant inexact Newton methods. Finally, the performance of a first version of our new type of algorithm is documented by the successful treatment of the well-known intricate windshear problem.}, language = {en} } @misc{ErdmannKoberLangetal., author = {Erdmann, Bodo and Kober, Cornelia and Lang, Jens and Sader, Robert and Zeilhofer, Hans-Florian and Deuflhard, Peter}, title = {Efficient and Reliable Finite Element Methods for Simulation of the Human Mandible}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6403}, number = {01-14}, abstract = {By computed tomography data (CT), the individual geometry of the mandible is quite well reproduced, also the separation between cortical and trabecular bone. Using anatomical knowledge about the architecture and the functional potential of the masticatory muscles, realistic situations were approximated. The solution of the underlying partial differential equations describing linear elastic material behaviour is provided by an adaptive finite element method. Estimations of the discretization error, local grid refinement, and multilevel techniques guarantee the reliability and efficiency of the method.}, language = {en} } @misc{Deuflhard, author = {Deuflhard, Peter}, title = {A Comparison of Related Concepts in Computational Chemistry and Mathematics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7138}, number = {02-46}, abstract = {This article studies the relation of the two scientific languages Chemistry and Mathematics via three selected comparisons: (a) QSSA versus dynamic ILDM in reaction kinetics, (b) lumping versus discrete Galerkin methods in polymer chemistry, and (c) geometrical conformations versus metastable conformations in drug design. The common clear message from these comparisons is that chemical intuition may pave the way for mathematical concepts just as chemical concepts may gain from mathematical precisioning. Along this line, significant improvements in chemical research and engineering have already been possible -- and can be further expected in the future from the dialogue between the two scientific languages.}, language = {en} } @misc{WeiserSchielaDeuflhard, author = {Weiser, Martin and Schiela, Anton and Deuflhard, Peter}, title = {Asymptotic Mesh Independence of Newton's Method Revisited}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7352}, number = {03-13}, abstract = {The paper presents a new affine invariant theory on asymptotic mesh independence of Newton's method in nonlinear PDEs. Compared to earlier attempts, the new approach is both much simpler and more natural from the algorithmic point of view. The theory is exemplified at collocation methods for ODE boundary value problems and at finite element methods for elliptic PDE problems.}, language = {en} } @misc{HochmuthDeuflhard, author = {Hochmuth, Reinhard and Deuflhard, Peter}, title = {Multiscale Analysis for the Bio-Heat Transfer Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7302}, number = {03-08}, abstract = {The bio-heat transfer equation is a macroscopic model for describing the heat transfer in microvascular tissue. In [{\sl Deuflhard, Hochmuth 2002}] the authors applied homogenization techniques to derive the bio-heat transfer equation as asymptotic result of boundary value problems which provide a microscopic description for microvascular tissue. Here those results are generalized to a geometrical setting where the regions of blood are allowed to be connected. Moreover, asymptotic corrector results are derived.}, language = {en} } @misc{DeuflhardWeber, author = {Deuflhard, Peter and Weber, Marcus}, title = {Robust Perron Cluster Analysis in Conformation Dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7415}, number = {03-19}, abstract = {The key to molecular conformation dynamics is the direct identification of metastable conformations, which are almost invariant sets of molecular dynamical systems. Once some reversible Markov operator has been discretized, a generalized symmetric stochastic matrix arises. This matrix can be treated by Perron cluster analysis, a rather recent method involving a Perron cluster eigenproblem. The paper presents an improved Perron cluster analysis algorithm, which is more robust than earlier suggestions. Numerical examples are included.}, language = {en} } @misc{DeuflhardSchuette, author = {Deuflhard, Peter and Sch{\"u}tte, Christof}, title = {Molecular Conformation Dynamics and Computational Drug Design}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7427}, number = {03-20}, abstract = {The paper surveys recent progress in the mathematical modelling and simulation of essential molecular dynamics. Particular emphasis is put on computational drug design wherein time scales of \$msec\$ up to \$min\$ play the dominant role. Classical long-term molecular dynamics computations, however, would run into ill-conditioned initial value problems already after time spans of only \$psec=10^{-12} sec\$. Therefore, in order to obtain results for times of pharmaceutical interest, a combined deterministic-stochastic model is needed. The concept advocated in this paper is the direct identification of metastable conformations together with their life times and their transition patterns. It can be interpreted as a {\em transfer operator} approach corresponding to some underlying hybrid Monte Carlo process, wherein short-term trajectories enter. Once this operator has been discretized, which is a hard problem of its own, a stochastic matrix arises. This matrix is then treated by {\em Perron cluster analysis}, a recently developed cluster analysis method involving the numerical solution of an eigenproblem for a Perron cluster of eigenvalues. In order to avoid the 'curse of dimension', the construction of appropriate boxes for the spatial discretization of the Markov operator requires careful consideration. As a biomolecular example we present a rather recent SARS protease inhibitor.}, language = {en} } @misc{WeiserDeuflhardErdmann, author = {Weiser, Martin and Deuflhard, Peter and Erdmann, Bodo}, title = {Affine conjugate adaptive Newton methods for nonlinear elastomechanics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7768}, number = {04-01}, abstract = {The paper extends affine conjugate Newton methods from convex to nonconvex minimization, with particular emphasis on PDE problems originating from compressible hyperelasticity. Based on well-known schemes from finite dimensional nonlinear optimization, three different algorithmic variants are worked out in a function space setting, which permits an adaptive multilevel finite element implementation. These algorithms are tested on two well-known 3D test problems and a real-life example from surgical operation planning.}, language = {en} } @misc{DeuflhardChairs, author = {Deuflhard, Peter and (Chairs), Hyung Yong Ra}, title = {Korean-German Bilateral Symposium on Scientific Computing}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7778}, number = {04-02}, abstract = {Collection of abstracts of the Korean-German Bilateral Symposium on Scientific Computing, Berlin January 15/16, 2004}, language = {en} } @misc{KlapprothSchielaDeuflhard, author = {Klapproth, Corinna and Schiela, Anton and Deuflhard, Peter}, title = {Consistency Results for the Contact-Stabilized Newmark Method}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11164}, number = {09-06}, abstract = {The paper considers the time integration of frictionless dynamical contact problems between viscoelastic bodies in the frame of the Signorini condition. Among the numerical integrators, interest focuses on the contact-stabilized Newmark method recently suggested by Deuflhard et al., which is compared to the classical Newmark method and an improved energy dissipative version due to Kane et al. In the absence of contact, any such variant is equivalent to the St{\"o}rmer-Verlet scheme, which is well-known to have consistency order 2. In the presence of contact, however, the classical approach to discretization errors would not show consistency at all because of the discontinuity at the contact. Surprisingly, the question of consistency in the constrained situation has not been solved yet. The present paper fills this gap by means of a novel proof technique using specific norms based on earlier perturbation results due to the authors. The corresponding estimation of the local discretization error requires the bounded total variation of the solution. The results have consequences for the construction of an adaptive timestep control, which will be worked out subsequently in a forthcoming paper.}, language = {en} } @misc{WeiserErdmannDeuflhard, author = {Weiser, Martin and Erdmann, Bodo and Deuflhard, Peter}, title = {On Efficiency and Accuracy in Cardioelectric Simulation}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10934}, number = {08-41}, abstract = {Reasons for the failure of adaptive methods to deliver improved efficiency when integrating monodomain models for myocardiac excitation are discussed. Two closely related techniques for reducing the computational complexity of linearly implicit integrators, deliberate sparsing and splitting, are investigated with respect to their impact on computing time and accuracy.}, language = {en} } @misc{DeuflhardDoesselLouisetal., author = {Deuflhard, Peter and D{\"o}ssel, Olaf and Louis, Alfred and Zachow, Stefan}, title = {Mehr Mathematik wagen in der Medizin}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10776}, number = {08-25}, abstract = {Der Artikel gibt einen Einblick in das reiche Feld der Zusammenarbeit zwischen Mathematik und Medizin. Beispielhaft werden drei Erfolgsmodelle dargestellt: Medizinische Bildgebung, mathematische Modellierung und Biosignalverarbeitung im Bereich der Dynamik des Herzens sowie mathematische Modellierung und Simulation in der Krebstherapie Hyperthermie und der Mund-Kiefer-Gesichts-Chirurgie. In allen F{\"a}llen existiert ein Gleichklang der Interessen von Medizin und Mathematik: Beide Disziplinen wollen die Resultate schnell und zuverl{\"a}ssig. F{\"u}r die Klinik heißt das, dass notwendige Rechnungen in m{\"o}glichst kurzer Zeit, und zwar auf dem PC, ablaufen m{\"u}ssen und dass die Resultate so genau und belastbar sein m{\"u}ssen, dass medizinische Entscheidungen darauf aufbauen k{\"o}nnen. F{\"u}r die Mathematik folgt daraus, dass h{\"o}chste Anforderungen an die Effizienz der verwendeten Algorithmen und die darauf aufbauende Software in Numerik und Visualisierung zu stellen sind. Jedes Kapitel endet mit einer Darstellung der Perspektive des jeweiligen Gebietes. Abschließend werden m{\"o}gliche Handlungsoptionen f{\"u}r Politik und Wirtschaft diskutiert.}, language = {de} } @misc{KlapprothDeuflhardSchiela, author = {Klapproth, Corinna and Deuflhard, Peter and Schiela, Anton}, title = {A Perturbation Result for Dynamical Contact Problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10793}, number = {08-27}, abstract = {This paper is intended to be a first step towards the continuous dependence of dynamical contact problems on the initial data as well as the uniqueness of a solution. Moreover, it provides the basis for a proof of the convergence of popular time integration schemes as the Newmark method. We study a frictionless dynamical contact problem between both linearly elastic and viscoelastic bodies which is formulated via the Signorini contact conditions. For viscoelastic materials fulfilling the Kelvin-Voigt constitutive law, we find a characterization of the class of problems which satisfy a perturbation result in a non-trivial mix of norms in function space. This characterization is given in the form of a stability condition on the contact stresses at the contact boundaries. Furthermore, we present perturbation results for two well-established approximations of the classical Signorini condition: The Signorini condition formulated in velocities and the model of normal compliance, both satisfying even a sharper version of our stability condition.}, language = {en} } @misc{SchuetteFischerHuisingaetal., author = {Sch{\"u}tte, Christof and Fischer, Alexander and Huisinga, Wilhelm and Deuflhard, Peter}, title = {A Direct Approach to Conformational Dynamics based on Hybrid Monte Carlo}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3889}, number = {SC-98-45}, abstract = {Recently, a novel concept for the computation of essential features of the dynamics of Hamiltonian systems (such as molecular dynamics) has been proposed. The realization of this concept had been based on subdivision techniques applied to the Frobenius--Perron operator for the dynamical system. The present paper suggests an alternative but related concept that merges the conceptual advantages of the dynamical systems approach with the appropriate statistical physics framework. This approach allows to define the phrase ``conformation'' in terms of the dynamical behavior of the molecular system and to characterize the dynamical stability of conformations. In a first step, the frequency of conformational changes is characterized in statistical terms leading to the definition of some Markov operator \$T\$ that describes the corresponding transition probabilities within the canonical ensemble. In a second step, a discretization of \$T\$ via specific hybrid Monte Carlo techniques is shown to lead to a stochastic matrix \$P\$. With these theoretical preparations, an identification algorithm for conformations is applicable. It is demonstrated that the discretization of \$T\$ can be restricted to few essential degrees of freedom so that the combinatorial explosion of discretization boxes is prevented and biomolecular systems can be attacked. Numerical results for the n-pentane molecule and the triribonucleotide adenylyl\emph{(3'-5')}cytidylyl\emph{(3'-5')}cytidin are given and interpreted.}, language = {en} } @misc{DeuflhardHohmann, author = {Deuflhard, Peter and Hohmann, Andreas}, title = {Einf{\"u}hrung in die Numerische Mathematik.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4704}, number = {TR-90-06}, abstract = {Diese Vorlesung ist eine Einf{\"u}hrung in die Numerische Mathematik als einem der drei Bereiche (neben den Naturwissenschaften und der Informatik) des am besten mit dem Begriff Scientific Computing charakterisierten Forschungsgebietes. Aufgabe dieser relativ jungen Wissenschaft ist die Entwicklung von Rechenverfahren f{\"u}r Probleme aus den Naturwissenschaften mit Hilfe mathematischer Methoden.}, language = {de} } @misc{DeuflhardNowakLutzWestphal, author = {Deuflhard, Peter and Nowak, Ulrich and Lutz-Westphal, Brigitte}, title = {Bessel'scher Irrgarten}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9525}, number = {07-09}, abstract = {Dieser Artikel berichtet {\"u}ber eine erfolgreiche Sch{\"u}leraktivit{\"a}t, die seit Jahren am Zuse-Institut Berlin (ZIB) bei Besuchen von Sch{\"u}lergruppen erprobt und verfeinert worden ist. Das hier zusammengestellte Material ist gedacht als Basis f{\"u}r eine Unterrichtseinheit in Leistungskursen Mathematik an Gymnasien. Inhaltlich wird von einem zwar f{\"u}r Sch{\"u}ler (wie auch Lehrer) neuen, aber leicht fasslichen Gegenstand ausgegangen: der Drei-Term-Rekursion f{\"u}r Besselfunktionen. Die Struktur wird erkl{\"a}rt und in ein kleines Programm umgesetzt. Dazu teilen sich die Sch{\"u}ler selbstorganisierend in Gruppen ein, die mit unterschiedlichen Taschenrechnern "um die Wette" rechnen. Die Sch{\"u}ler und Sch{\"u}lerinnen erfahren unmittelbar die katastrophale Wirkung von an sich kleinen'' Rundungsfehlern, sie landen -- ebenso wie der Supercomputer des ZIB -- im Bessel'schen Irrgarten''. Die auftretenden Ph{\"a}nomene werden mathematisch elementar erkl{\"a}rt, wobei lediglich auf das Konzept der linearen Unabh{\"a}ngigkeit zur{\"u}ckgegriffen wird. Das dabei gewonnene vertiefte Verst{\"a}ndnis fließt ein in die Konstruktion eines klassischen Algorithmus sowie eines wesentlich verbesserten Horner-artigen Algorithmus.}, language = {de} } @misc{WeberWalterKubeetal., author = {Weber, Marcus and Walter, Lionel and Kube, Susanna and Deuflhard, Peter}, title = {Stable computation of probability densities for metastable dynamical systems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9331}, number = {06-39}, abstract = {Whenever the invariant stationary density of metastable dynamical systems decomposes into almost invariant partial densities, its computation as eigenvector of some transition probability matrix is an ill-conditioned problem. In order to avoid this computational difficulty, we suggest to apply an aggregation/disaggregation method which only addresses wellconditioned sub-problems and thus results in a stable algorithm. In contrast to existing methods, the aggregation step is done via a sampling algorithm which covers only small patches of the sampling space. Finally, the theoretical analysis is illustrated by two biomolecular examples.}, language = {en} } @misc{DeuflhardKrauseErtel, author = {Deuflhard, Peter and Krause, Rolf and Ertel, Susanne}, title = {A Contact-Stabilized Newmark Method for Dynamical Contact Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9361}, number = {06-42}, abstract = {The numerical integration of dynamical contact problems often leads to instabilities at contact boundaries caused by the non-penetration condition between bodies in contact. Even a recent energy dissipative modification due to Kane et al. (1999), which discretizes the non-penetration constraints implicitly, is not able to circumvent artificial oscillations. For this reason, the present paper suggests a contact stabilization which avoids artificial oscillations at contact interfaces and is also energy dissipative. The key idea of this contact stabilization is an additional \$L^2\$-projection at contact interfaces, which can easily be added to any existing time integration scheme. In case of a lumped mass matrix, this projection can be carried out completely locally, thus creating only negligible additional numerical cost. For the new scheme, an elementary analysis is given, which is confirmed by numerical findings in an illustrative test example (Hertzian two body contact).}, language = {en} } @misc{DeuflhardHuisingaJahnkeetal., author = {Deuflhard, Peter and Huisinga, Wilhelm and Jahnke, Tobias and Wulkow, Michael}, title = {Adaptive Discrete Galerkin Methods Applied to the Chemical Master Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9471}, number = {07-04}, abstract = {\begin{abstract} In systems biology, the stochastic description of biochemical reaction kinetics is increasingly being employed to model gene regulatory networks and signalling pathways. Mathematically speaking, such models require the numerical solution of the underlying evolution equat ion, also known as the chemical master equation (CME). Up to now, the CME has almost exclusively been treated by Monte-Carlo techniques, the most prominent of which is the simulation algorithm suggest ed by Gillespie in 1976. Since this algorithm requires an update for each single reaction event, realizations can be computationally very costly. As an alternative, we here propose a novel approach, which focuses on the discrete partial differential equation (PDE) structure of the CME and thus allows to adopt ideas from adaptive discrete Galerkin methods (as designed by two of the present authors in 1989), which have proven to be highly efficient in the mathematical modelling of polyreaction kinetics. Among the two different options of discretizing the CME as a discrete PDE, the method of lines approach (first space, then time) and the Rothe method (first time, then space), we select the latter one for clear theoretical and algorithmic reasons. First numeric al experiments at a challenging model problem illustrate the promising features of the proposed method and, at the same time, indicate lines of necessary further research. \end{abstract}}, language = {en} } @misc{ReineckeDeuflhard, author = {Reinecke, Isabel and Deuflhard, Peter}, title = {A Complex Mathematical Model of the Human Menstrual Cycle}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9112}, number = {06-18}, abstract = {This paper aims at presenting the complex coupled network of the human menstrual cycle to the interested community. Beyond the presently popular smaller models, where important network components arise only as extremely simplified source terms, we add: the GnRH pulse generator in the hypothalamus, receptor binding, and the biosynthesis in the ovaries. Simulation and parameter identification are left to a forthcoming paper.}, language = {en} } @misc{DeuflhardHerothMaas, author = {Deuflhard, Peter and Heroth, J{\"o}rg and Maas, Ulrich}, title = {Towards Dynamical Dimension Reduction in Reactive Flow Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2383}, number = {SC-96-27}, abstract = {The paper addresses the possibilities of reducing the overall number of degrees of freedom in large scale reactive flow computations. Attention focusses on the dimension reduction technique ILDM due to {\sc Maas and Pope}, which treats certain automatically detected fast dynamic components as algebraic equations (so-called slow manifold). In earlier papers, the dimension of the reduction had been kept constant throughout each computation. Recently, a mathematically sound and nevertheless cheap dimension monitor for the chemistry part only has been suggested by {\sc Deuflhard and Heroth}. The present paper reports about first steps taken towards the implementation of that monitor into a flame code. Moreover, a sparse grid storage scheme is advocated and analyzed in view of the construction of efficient table look--ups for nested manifolds.}, language = {en} } @misc{DeuflhardWeiser, author = {Deuflhard, Peter and Weiser, Martin}, title = {Local Inexact Newton Multilevel FEM for Nonlinear Elliptic Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2401}, number = {SC-96-29}, abstract = {The finite element setting for nonlinear elliptic PDEs directly leads to the minimization of convex functionals. Uniform ellipticity of the underlying PDE shows up as strict convexity of the arising nonlinear functional. The paper analyzes computational variants of Newton's method for convex optimization in an affine conjugate setting, which reflects the appropriate affine transformation behavior for this class of problems. First, an affine conjugate Newton--Mysovskikh type theorem on the local quadratic convergence of the exact Newton method in Hilbert spaces is given. It can be easily extended to inexact Newton methods, where the inner iteration is only approximately solved. For fixed finite dimension, a special implementation of a Newton--PCG algorithm is worked out. In this case, the suggested monitor for the inner iteration guarantees quadratic convergence of the outer iteration. In infinite dimensional problems, the PCG method may be just formally replaced by any Galerkin method such as FEM for linear elliptic problems. Instead of the algebraic inner iteration errors we now have to control the FE discretization errors, which is a standard task performed within any adaptive multilevel method. A careful study of the information gain per computational effort leads to the result that the quadratic convergence mode of the Newton--Galerkin algorithm is the best mode for the fixed dimensional case, whereas for an adaptive variable dimensional code a special linear convergence mode of the algorithm is definitely preferable. The theoretical results are then illustrated by numerical experiments with a {\sf NEWTON--KASKADE} algorithm.}, language = {en} } @misc{DeuflhardFrieseSchmidtetal., author = {Deuflhard, Peter and Friese, Tilmann and Schmidt, Frank and M{\"a}rz, Reinhard and Nolting, Hans-Peter}, title = {Effiziente Eigenmodenberechnung f{\"u}r den Entwurf integriert-optischer Chips}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2131}, number = {SC-96-02}, abstract = {{\bf Efficient eigenmode computation for the design of integrated optical chips.}The paper deals with adaptive multigrid methods for 2D Helmholtz eigenvalue problems arising in the design of integrated optical chips. Typical features of the technological problem are its geometric complexity, its multiscale structure, the possible occurrence of eigenvalue clusters, and the necessity of quite stringent required relative error tolerances. For reasons of sheer computational complexity, multigrid methods must be used to solve the discretized eigenvalue problems and adaptive grids must be automatically constructed to avoid an undesirable blow-up of the required number of nodes for these accuracies. In view of the problem specifications, an adaptive multigrid method based on Rayleigh quotient minimization, simultaneous eigenspace iteration, and conjugate gradient method as smoother is carefully selected. Its performance in the numerical simulation of a component of a rather recent optical chip (heterodyne receiver of HHI) is documented.}, language = {de} } @misc{EhrigNowakDeuflhard, author = {Ehrig, Rainald and Nowak, Ulrich and Deuflhard, Peter}, title = {Highly scalable parallel linearly-implicit extrapolation algorithms}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5405}, number = {TR-96-11}, abstract = {We present parallel formulations of the well established extrapolation algorithms EULSIM and LIMEX and its implementation on a distributed memory architecture. The discretization of partial differential equations by the method of lines yields large banded systems, which can be efficiently solved in parallel only by iterative methods. Polynomial preconditioning with a Neumann series expansion combined with an overlapping domain decomposition appears as a very efficient, robust and highly scalable preconditioner for different iterative solvers. A further advantage of this preconditioner is that all computation can be restricted to the overlap region as long as the subdomain problems are solved exactly. With this approach the iterative algorithms operate on very short vectors, the length of the vectors depends only on the number of gridpoints in the overlap region and the number of processors, but not on the size of the linear system. As the most reliable and fast iterative methods based on this preconditioning scheme appeared GMRES or FOM and BICGSTAB. To further reduce the number of iterations in GMRES or FOM we can reuse the Krylov-spaces constructed in preceeding extrapolation steps. The implementation of the method within the program LIMEX results in a highly parallel and scalable program for solving differential algebraic problems getting an almost linear speedup up to 64 processors even for medium size problems. Results are presented for a difficult application from chemical engineering simulating the formation of aerosols in industrial gas exhaust purification.}, language = {en} } @misc{Deuflhard, author = {Deuflhard, Peter}, title = {Numerik von Anfangswertmethoden f{\"u}r gew{\"o}hnliche Differentialgleichungen.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4580}, number = {TR-89-02}, abstract = {Das voliegende Skriptum entstand aus einer Vorlesung, die ich im WS 87/88 an der Freien Universit{\"a}t Berlin im Fachbereich Mathematik gehalten habe. Mein urspr{\"u}ngliches Vorlesungsmanuskript wurde von Herrn F. Bornemann in weiten Teilen {\"u}berarbeitet, reorganisiert und substantiell erg{\"a}nzt. Der Inhalt stammt gr{\"o}ßtenteils aus Originalarbeiten j{\"u}ngeren Datums. Dar{\"u}berhinaus finden sich zahlreiche Teile, die aus meiner jahrelangen Besch{\"a}ftigung mit dem Thema entstanden aber unpubliziert geblieben sind. Das Skriptum erhebt nicht den Anspruch, ein Lehrbuch zu sein. Es war zun{\"a}chst als Ausarbeitung f{\"u}r meinen studentischen H{\"o}rerkreis sowie als internes Arbeitspapier f{\"u}r das ZIB bestimmt. Die Kunde von der bloßen Existenz eines solchen Skriptums hat jedoch zu einer derart regen Nachfrage gef{\"u}hrt, daß es hiermit als Technischer Report des ZIB einer breiteren ffentlichkeit zug{\"a}nglich gemacht werden soll. In der vorliegenden Form richtet es sich in erster Linie an Mathematiker; es soll sich jedoch auch f{\"u}r Naturwissenschaftler und Ingenieure eignen, die sich einen Einblick in den theoretischen und algorithmischen Hintergrund der von ihnen verwendeten wissenschaftlichen Software verschaffen wollen.}, language = {de} } @misc{DeuflhardBoellingBott, author = {Deuflhard, Peter and B{\"o}lling, Reinhard and Bott, Raoul H.}, title = {Materialien zur Euler-Vorlesung in Sanssouci.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5029}, number = {TR-93-10}, abstract = {Aus dem Inhalt: Vorwort; Leonhard Euler - aus der Zeit seines Wirkens in Berlin; Introductory Remarks.}, language = {de} } @misc{DeuflhardHegeSedlmayred, author = {Deuflhard, Peter and Hege, Hans-Christian and Sedlmayr(ed.), E.}, title = {Scientific Computing in der Theoretischen Physik. Collected Abstracts.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5068}, number = {TR-94-01}, abstract = {Die von der DMV-Fachgruppe Scientific Computing in Kooperation mit dem gleichnamigen GAMM-Fachausschuss organisierte Tagung \glqq Scientific Computing in der Theoretischen Physik\grqq~fand vom 16. - 18. M{\"a}rz 1994 am Fachbereich Mathematik und Informatik der Freien Universit{\"a}t Berlin statt. Ziel des Workshops war, die Kontakte zwischen den Fachleuten der Gebiete {\em Computational Physics} und {\em Scientific Computing} zu intensivieren. Schwerpunkte des Workshops waren numerische Simulation von Transportmodellen der Astrophysik und Halbleiterphysik, Multilevel-Methoden f{\"u}r partielle Differentialgleichungen sowie Monte-Carlo-Methoden und molekulardynamische Verfahren f{\"u}r Probleme der Statistischen Physik und Quantenfeldtheorie. Der Workshop fand ein {\"a}usserst positives Echo und f{\"u}hrte {\"u}ber 70 Teilnehmer der verschiedenen Teilgebiete der Theoretischen Physik und ca. 50 Teilnehmer aus dem Bereich der Numerischen Mathematik zusammen. \originalTeX}, language = {en} } @misc{DeuflhardGottschewski, author = {Deuflhard, Peter and Gottschewski, J{\"u}rgen}, title = {Das Konrad-Zuse-Zentrum f{\"u}r Informationstechnik Berlin. Struktur, wissenschaftliches Konzept und Einbettung in die Region}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5274}, number = {TR-95-12}, abstract = {Die Arbeit beschreibt Konzept, Struktur und Ausstattung des ZIB. {\"U}bergeordnetes Ziel des ZIB ist die Beschleunigung des {\it Know-how Transfers} aus der mathematischen Grundlagenforschung {\"u}ber die Entwicklung von Algorithmen und Software bis hin zur tats{\"a}chlichen Nutzung in der Industrie. In der Tat ist Computational Mathematics inzwischen zu einer der wichtigsten {\it Schl{\"u}sseltechnologien} geworden, die nicht zuletzt im Zusammenhang mit der Standort-Diskussion eine wichtige Rolle spielt und vermehrt spielen wird. Dazu m{\"u}ssen Methodenentwicklung und Rechenzentrum auf h{\"o}chstem Niveau sowie interdisziplin{\"a}re Forschung m{\"o}glichst vereint in einer Institution mit enger Anbindung an ein universit{\"a}res Umfeld realisiert sein. Das Konrad-Zuse-Zentrum hat die wesentlichen Voraussetzungen als SC Zentrum bereits geschaffen; ein Ausbau zum HPSC Zentrum w{\"a}re eine nat{\"u}rliche Entwicklung - falls die Politik diese Chance rechtzeitig begreift!}, language = {de} } @misc{Deuflhard, author = {Deuflhard, Peter}, title = {Zuses Werk weiterdenken. (Vortrag)}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4717}, number = {TR-90-07}, language = {de} } @misc{BraessDeuflhardLipnikov, author = {Braess, Dietrich and Deuflhard, Peter and Lipnikov, Konstantin}, title = {A Subspace Cascadic Multigrid Method for Mortar Elements}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3954}, number = {SC-99-07}, abstract = {A cascadic multigrid (CMG) method for elliptic problems with strong material jumps is proposed and analyzed. Non--matching grids at interfaces between subdomains are allowed and treated by mortar elements. The arising saddle point problems are solved by a subspace confined conjugate gradient method as smoother for the CMG. Details of algorithmic realization including adaptivity are elaborated. Numerical results illustrate the efficiency of this CMG algorithm.}, language = {en} } @misc{DeuflhardHeroth, author = {Deuflhard, Peter and Heroth, J{\"o}rg}, title = {Dynamic Dimension Reduction in ODE Models}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1951}, number = {SC-95-29}, abstract = {The paper analyzes a splitting technique into fast and slow dynamical components of ODE systems as suggested by {\sc Maas and Pope} recently. Their technique is based on a real block -- Schur decomposition of the Jacobian of the right hand side of the ODE. As a result of the analysis, a computationally cheap monitor for the possible necessary recovering of the splitting is derived by singular perturbation theory. Numerical experiments on moderate size, but challenging reaction kinetics problems document the efficiency of the new device within a linearly-implicit stiff integrator.}, language = {en} } @misc{EhrigNowakDeuflhard, author = {Ehrig, Rainald and Nowak, Ulrich and Deuflhard, Peter}, title = {Massively Parallel Linearly-Implicit Extrapolation Algorithms as a Powerful Tool in Process Simulation.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3127}, number = {SC-97-43}, abstract = {We study the parallelization of linearly--implicit extrapolation codes for the solution of large scale PDE systems and differential algebraic equations on distributed memory machines. The main advantage of these algorithms is that they enable adapativity both in time and space. Additive Krylov--Schwarz methods yield high parallel perfomance for such extrapolation methods. Our approach combines a slightly overlapping domain decomposition together with a polynomial block Neumann preconditioner and a reduced system technique. Furthermore we get important advantages through the explicit computation of the matrix--products of the preconditioner and the matrix of the linear system. The parallel algorithms exhibit scalability up to 64 processors already for medium--sized test problems. We show that the codes are really efficient in large application systems for chemical engineering problems.}, language = {en} } @misc{DeuflhardLangNowak, author = {Deuflhard, Peter and Lang, Jens and Nowak, Ulrich}, title = {Adaptive Algorithms in Dynamical Process Simulation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1823}, number = {SC-95-16}, abstract = {Dynamical simulation of industrially relevant processes strongly advises the use of algorithms, which are {\em adaptive} both in time and in space discretization. The paper presents two alternatives: (a) a fully adaptive method of lines approach, which is based on finite difference methods and essentially applicable to 1D problems; (b) a fully adaptive Rothe method, which is based on a fast multilevel finite element method and applicable to 1D up to 3D.}, language = {en} } @misc{Deuflhard, author = {Deuflhard, Peter}, title = {Differential Equations in Technology and Medicine. Computational Concepts, Adaptive Algorithms, and Virtual Labs}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4223}, number = {SC-99-34}, abstract = {This series of lectures has been given to a class of mathematics postdocs at a European summer school on Computational Mathematics Driven by Industrial Applications in Martina Franca, Italy (organized by CIME). It deals with a variety of challenging real life problems selected from clinical cancer therapy, communication technology, polymer production, and pharmaceutical drug design. All of these problems from rather diverse application areas share two common features: (a) they have been modelled by various differential equations -- elliptic, parabolic, or Schr{\"o}dinger--type partial differential equations, countable ordinary diffential equations, or Hamiltonian systems, (b) their numerical solution has turned out to be real challenge to computational mathematics.}, language = {en} } @misc{SchuetteHuisingaDeuflhard, author = {Sch{\"u}tte, Christof and Huisinga, Wilhelm and Deuflhard, Peter}, title = {Transfer Operator Approach to Conformational Dynamics in Biomolecular Systems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4247}, number = {SC-99-36}, abstract = {The article surveys the development of novel mathematical concepts and algorithmic approaches based thereon in view of their possible applicability to biomolecular design. Both a first deterministic approach, based on the Frobenius-Perron operator corresponding to the flow of the Hamiltonian dynamics, and later stochastic approaches, based on a spatial Markov operator or on Langevin dynamics, can be subsumed under the unified mathematical roof of the transfer operator approach to effective dynamics of molecular systems. The key idea of constructing specific transfer operators especially taylored for the purpose of conformational dynamics appears as the red line throughout the paper. Different steps of the algorithm are exemplified by a trinucleotide molecular system as a small representative of possible RNA drug molecules.}, language = {en} } @misc{GalliatHuisingaDeuflhard, author = {Galliat, Tobias and Huisinga, Wilhelm and Deuflhard, Peter}, title = {Self-Organizing Maps Combined with Eigenmode Analysis for Automated Cluster Identification}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4279}, number = {SC-99-38}, abstract = {One of the important tasks in Data Mining is automated cluster analysis. Self-Organizing Maps (SOMs) introduced by {\sc Kohonen} are, in principle, a powerful tool for this task. Up to now, however, its cluster identification part is still open to personal bias. The present paper suggests a new approach towards automated cluster identification based on a combination of SOMs with an eigenmode analysis that has recently been developed by {\sc Deuflhard et al.} in the context of molecular conformational dynamics. Details of the algorithm are worked out. Numerical examples from Data Mining and Molecular Dynamics are included.}, language = {en} } @misc{LipnikovDeuflhard, author = {Lipnikov, Konstantin and Deuflhard, Peter}, title = {Domain Decomposition with Subdomain CCG for Material Jump Elliptic Problems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3057}, number = {SC-97-36}, abstract = {A combination of the cascadic conjugate gradient (CCG) method for homogeneous problems with a non-overlapping domain decomposition (DD) method is studied. Mortar finite elements on interfaces are applied to permit non-matching grids in neighboring subdomains. For material jump problems, the method is designed as an alternative to the cascadic methods.}, language = {en} } @misc{DeuflhardSeebass, author = {Deuflhard, Peter and Seebass, Martin}, title = {Adaptive Multilevel FEM as Decisive Tools in the Clinical Cancer Therapy Hyperthermia}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3739}, number = {SC-98-30}, abstract = {The paper surveys recent progress in a joint mathematical-medical project on cancer therapy planning. Within so-called regional hyperthermia the computational task is to tune a set of coupled radiofrequency antennas such that a carefully measured tumor is locally heated, but any outside hot spots are avoided. A mathematical model of the whole clinical system -- air, applicator with antennas, water bolus, individual patient body -- involves Maxwell's equations in inhomogeneous media and a parabolic bioheat transfer equation, which represents a simplified model of heat transfer in the human body (ignoring strong blood vessel heat transport). Both PDEs need to be computed fast and to medical reliability (!) on a workstation within a clinical environment. This requirement triggered a series of new algorithmic developments to be reported here, among which is an adaptive multilevel FEM for Maxwell's equations, which dominates the numerical simulation time. In total, however, the main bulk of computation time (see Table 3 in Section 4 below) still goes into segmentation -- a necessary preprocessing step in the construction a 3D virtual patient from the input of a stack of 2D computed tomograms (left out here).}, language = {en} } @misc{DeuflhardWeiserSeebass, author = {Deuflhard, Peter and Weiser, Martin and Seebass, Martin}, title = {A New Nonlinear Elliptic Multilevel FEM Applied to Regional Hyperthermia}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3785}, number = {SC-98-35}, abstract = {In the clinical cancer therapy of regional hyperthermia nonlinear perfusion effects inside and outside the tumor seem to play a not negligible role. A stationary model of such effects leads to a nonlinear Helmholtz term within an elliptic boundary value problem. The present paper reports about the application of a recently designed adaptive multilevel FEM to this problem. For several 3D virtual patients, nonlinear versus linear model is studied. Moreover, the numerical efficiency of the new algorithm is compared with a former application of an adaptive FEM to the corresponding instationary model PDE.}, language = {en} } @misc{SchoepfDeuflhard, author = {Sch{\"o}pf, R. and Deuflhard, Peter}, title = {OCCAL: A mixed symbolic- numeric Optimal Control CALculator.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-638}, number = {SC-91-13}, abstract = {The numerical solution of optimal control problems by indirect methods (such as multiple shooting or collocation) requires a considerable amount of analytic calculation to establish a numerically tractable system. These analytic calculations, though being rather tedious in realistic examples, are nowadays mostly still done by hand-and thus prone to calculation errors. The paper aims at automating this analytic processing to a reasonable extent by means of a modern symbolic manipulation language (here: REDUCE). In its present stage of development the package OCCAL (mnemotechnically for \underline{O}ptimal \underline{C}ontrol \underline{CAL}culator) permits an interactive use, covering tasks like automatic determination of control and, in case of a singular control, of its order. In simpler problems, the present version of OCCAL automatically produces the full subroutine input for a MULtiple shooting code (MULCON) with adaptive numerical CONtinuation. In more complicate problems where singular sub-arcs may occur or where the sequence of sub-arcs of the optimal trajectory is unclear OCCAL is a significant help in reducing analytic pre-processing. Numerical examples illustrate the performance of OCCAL/MULCON.}, language = {en} } @misc{DeuflhardLeinenYserentant, author = {Deuflhard, Peter and Leinen, P. and Yserentant, Harry}, title = {Concepts of an Adaptive Hierarchical Finite Element Code.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-131}, number = {SC-88-05}, abstract = {The paper presents the mathematical concepts underlying the new adaptive finite element code KASKADE, which, in its present form, applies to linear scalar second-order 2-D elliptic problems on general domains. Starting point for the new development is the recent work on hierarchical finite element bases due to Yserentant (1986). It is shown that this approach permits a flexible balance between iterative solver, local error estimator, and local mesh refinement device - which are the main components of an adaptive PDE code. Without use of standard multigrid techniques, the same kind of computational complexity is achieved - independent of any uniformity restrictions on the applied meshes. In addition, the method is extremely simple and all computations are purely local - making the method particularly attractive in view of parallel computing. The algorithmic approach is illustrated by a well-known critical test problem. {\bf Keywords:} finite elements, hierarchical basis, adaptive mesh refinement, preconditioned conjugate gradient methods.}, language = {en} } @misc{DeuflhardWulkow, author = {Deuflhard, Peter and Wulkow, Michael}, title = {Computational Treatment of Polyreaction Kinetics by Orthogonal Polynomials of a Discrete Variable.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-140}, number = {SC-88-06}, abstract = {The paper presents a new approach to the computational treatment of polyreaction kinetics. This approach is characterized by a Galerkin method based on orthogonal polynomials of a discrete variable, the polymer degree (or chain length). In comparison with the known competing approaches (statistical moment treatment, Galerkin methods for continuous polymer models), the suggested method is shown to avoid the disadvantages and preserve the adventages of either of them. The basic idea of the method is the construction of a discrete inner product associated with a reasonably chosen probability density function. For the so-called Schulz-Flory distribution one thus obtains the discrete Laguerre polynomials, whereas the Poisson distribution leads to the Charlier polynomials. Numerical experiments for selected polyreaction mechanisms illustrate the efficiency of the proposed method.}, language = {en} } @misc{DeuflhardPotra, author = {Deuflhard, Peter and Potra, Florian}, title = {A Refined Gauss-Newton- Mysovskii Theorem.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-541}, number = {SC-91-04}, abstract = {The present paper contains a generalization of a refinement of the Newton- Mysovskii theorem, recently obtained by the authors, to the case of Gauss-Newton procedures for solving nonlinear least-squares problems with full Jacobians. Invariant sufficient conditions are given that ensure the convergence of the Gauss-Newton iterates towards a solution of the problem, as well as the uniqueness of that solution in an explicitely defined neighborhood. It is shown by a counter- example that the results do not carry over to the rank deficient case.}, language = {en} } @misc{WulkowDeuflhard, author = {Wulkow, Michael and Deuflhard, Peter}, title = {Towards an Efficient Computational Treatment of Heterogeneous Polymer Reactions.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-292}, number = {SC-90-01}, abstract = {The discrete Galerkin method developed by the authors has turned out to be an efficient tool for the computational treatment of very large scale ODE systems arising in polyreaction kinetics. Up to now, this approach has been worked out in detail for homogeneous polymer reactions. The present paper deals with one line of possible extensions of the method to the case of so-called heterogeneous processes, which may appear e. g. in smog reactions. The associated mathematical models involve reaction coefficients depending on the chain length of the reacting polymer. The herein suggested extension is worked out in some detail on the basis of the earlier paper. In addition, a numerical example describing polymer degradation is included.}, language = {en} } @misc{Deuflhard, author = {Deuflhard, Peter}, title = {Global Inexact Newton Methods for Very Large Scale Nonlinear Problems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-303}, number = {SC-90-02}, abstract = {Newton methods for nonlinear problems are known to require the solution of a sequence of linear problems of the same type. For very large scale problems, as understood herein, the arising linear systems can only be solved by iterative methods. Then Newtons iteration appears as outer iteration. The question of interest will be to control the accuracy of the inner iteration such that the convergence speed of Newtons method is preserved. The purpose of the paper is to combine the concept of inexact Newton methods with the concept of the affine invariant exact Newton methods - which is important for problems with ill- conditioned Jacobian matrices (such as typical 2-D or 3-D discretized partial differential equations).}, language = {en} } @misc{DeuflhardFreundWalter, author = {Deuflhard, Peter and Freund, R. and Walter, Artur}, title = {Fast Secant Methods for the Iterative Solution of Large Nonsymmetric Linear Systems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-330}, number = {SC-90-05}, abstract = {A family of secant methods based on general rank-1 updates has been revisited in view of the construction of iterative solvers for large non- Hermitian linear systems. As it turns out, both Broydens "good" and "bad" update techniques play a special role - but should be associated with two different line search principles. For Broydens "bad" update technique, a minimum residual principle is natural - thus making it theorectically comparable with a series of well-known algorithms like GMRES. Broydens "good" update technique, however, is shown to be naturally linked with a minimum "next correction" principle - which asymptotically mimics a minimum error principle. The two minimization principles differ significantly for sufficiently large system dimension. Numerical experiments on discretized PDE's of convection diffusion type in 2-D with internal layers give a first impression of the possible power of the derived "good" Broyden variant. {\bf Key Words:} nonsymmetric linear system, secant method, rank-1 update, Broydens method, line search, GMRES. AMS(MOS) {\bf Subject Classifications:} 65F10, 65N20.}, language = {en} } @misc{DeuflhardNowakWulkow, author = {Deuflhard, Peter and Nowak, Ulrich and Wulkow, Michael}, title = {Recent Developments in Chemical Computing.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-359}, number = {SC-90-07}, abstract = {The paper surveys three aspects of chemical computing, which seem to play a role in recent developments. First, extrapolation methods for the numerical treatment of differential- algebraic equations are introduced. The associated extrapolation code LIMEX has reached a certain level of sophistication, which makes it a real competitor to the elsewhere widely used multi-step code DASSL of Petzold. Second, adaptive methods of lines for partial differential equations such as those arising in combustion problems are treated. Both static and dynamic regridding techniques are discussed in some detail. Finally, some new ideas about the treatment of the kinetic equations arising from polymer reactions are presented. The new feature of the suggested approach is the application of a Galerkin procedure using sets of orthogonal polynomials over a discrete variable (which, of course, in the case of polymer reactions is the polymer degree). The new approach may open the door to a new reliable low dimensional treatment of complex polymer reactions.}, language = {en} } @misc{DeuflhardPotra, author = {Deuflhard, Peter and Potra, Florian}, title = {Asymptotic Mesh Independence of Newton-Galerkin Methods via a Refined Mysovskii Theorem.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-379}, number = {SC-90-09}, abstract = {The paper presents a theoretical characterization of the often observed asymptotic mesh independence of Newton's method, which means that Newton's method applied to discretized operator equations behaves essentially the same for all sufficiently fine discretizations. The theory does not need any uniform Lipschitz assumptions that were necessary in comparable earlier treatments. The refined Newton-Mysovskii theorem, which will be of interest in a wider context, gives both existence and uniqueness of the solution and quadratic convergence for sufficiently good starting points. Attention is restricted to Galerkin approximations even though similar results should hold for finite difference methods - but corresponding proofs would certainly be more technical. As an illustrative example, adaptive 1-D collocation methods are discussed.}, language = {en} } @misc{DeuflhardNowak, author = {Deuflhard, Peter and Nowak, Ulrich}, title = {Efficient Numerical Simulation and Identification of Large Chemical Reaction Systems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14}, number = {SC-86-01}, abstract = {New, highly efficient techniques for the numerical simulation and parameter identification of large chemical reaction systems are surveyed. The survey particularly addresses to chemists, which are understood to be potential users of the distributed software packages. These packages are written in the form of interactive dialogue systems - thus enabling chemists to concentrate on the chemistry of their problem. Large scale examples from chemical research environments are included.}, language = {en} } @misc{Deuflhard, author = {Deuflhard, Peter}, title = {Uniqueness Theorems for Stiff ODE Initial Value Problems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53}, number = {SC-87-03}, abstract = {The paper presents a new uniqueness theory for ODE initial value problems, derived in view of numerical stiff integration. The theory supplies stepsize bounds for stiff integrators that can easily be estimated in extrapolation methods. The additional devices lead to a significant speed-up of computations - in particular in combustion PDE problems.}, language = {en} } @misc{Deuflhard, author = {Deuflhard, Peter}, title = {A Note on Extrapolation Methods for Second Order ODE Systems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-79}, number = {SC-87-05}, abstract = {A slight modification of the extended Stoermer discretization for non self-adjoint second order ODE systems is derived on the basis of a simple stability analysis. This discretization easily extends to implicit ODE systems, which are known to arise e.g. in mechanical engineering. In addition, a special variant of semi-implicit Euler discretization is proposed, which essentially treats the state variables explicitly, but their derivatives implicitly. Numerical tests over critical parameter values of the van der Pol oscillator illustrate the domain of efficiency of the suggested discretizations.}, language = {en} } @misc{Deuflhard, author = {Deuflhard, Peter}, title = {A Study of Lanczos-Type Iterations for Symmetric Indefinite Linear Systems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1029}, number = {SC-93-06}, abstract = {The Lanczos iteration for symmetric indefinite linear systems seems to be well--known for quite a while. However, in order to modify it with the aim of improved performance, the present paper studies certain aspects in terms of an adjoint scalar three--term recurrence. Thus, at least a different view is opened. Moreover, an alternative \$3n\$--implementation in terms of the Euclidean orthogonal basis has been found that easily permits generalizations. The study is understood as a start--off for further numerical investigations and experiments.}, language = {en} } @misc{FroehlichDeuflhard, author = {Fr{\"o}hlich, Jochen and Deuflhard, Peter}, title = {Moving Weight Galerkin Methods for Turbulent Reactive Flows}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1646}, number = {SC-94-36}, abstract = {Adopting a statistical approach for the computation of turbulent combustion flows an approximation for the probability density function (PDF) of the composition variables is often required to treat the highly non-linear reaction term in a satisfactory way. One class of methods currently being used are the moment methods which employ transport equations for low order statistical moments and use a parametrized shape of the PDF. A second class solves a transport equation for the joint PDF by a Monte Carlo method. In the present paper we develop an intermediate algorithm based on a Galerkin method for the PDF transport equation. The solution is developed in terms of an orthogonal or bi-orthogonal basis of a suitable Hilbert space. The unconventional use of the related weight function as a prefactor (moving weight approach) permits adaptivity and results in a generalization of the \$\beta-\$closure for bounded scalar quantities. We present the approximation procedure in detail and apply it to the evolution of the composition in a homogeneous well-stirred reactor. The extension to non-homogeneous flow simulations is straightforward.}, language = {en} } @misc{WulffHohmannDeuflhard, author = {Wulff, Claudia and Hohmann, Andreas and Deuflhard, Peter}, title = {Numerical Continuation of Periodic Orbits with Symmetry.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1421}, number = {SC-94-12}, abstract = {We consider periodic orbits of autonomous parameter dependent ODE's. Starting from a shooting algorithm for the numerical computation of periodic orbits via an adaptive Poincar\'e-section we develop a pathfollowing algorithm for periodic solutions based on a tangential continuation method with implicit reparametrization. For ODE's equivariant w.r.t. a finite group we show that spatial as well as spatio-temporal symmetries of periodic orbits can be exploited within the (multiple) shooting context. We describe how turning points, period doubling bifurcations and Hopf points along the branch of periodic solutions can be handled. Furthermore equivariant Hopf points and generic secondary bifurcations of periodic orbits with \$ Z_m\$-symmetry are treated. We tested the code with standard examples, e.g., the period doubling cascade in the Lorenz equations. To show the efficiency of the described methods we also used the program for an application from electronics, a ring oscillator with \$n \$ inverters. In this example the exploitation of symmetry reduces the amount of work for the continuation of periodic orbits from \${\cal O}(n^2)\$ to \${\cal O}(n)\$}, language = {en} } @misc{DeuflhardWulkow, author = {Deuflhard, Peter and Wulkow, Michael}, title = {Simulationsverfahren f{\"u}r die Polymerchemie}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1502}, number = {SC-94-22}, abstract = {Die enorme algorithmische Beschleunigung durch diskrete Galerkin-Methoden f{{\"u}}r abz{{\"a}}hlbare Differentialgleichungssysteme hat der Simulation von Polymerisationsprozessen neue, industriell relevante Problembereiche er{{\"o}}ffnet, die mit den bis dahin verf{{\"u}}gbaren Methoden nicht zug{{\"a}}nglich waren.}, language = {de} } @misc{SeebassSullivanWustetal., author = {Seebass, Martin and Sullivan, Dennis and Wust, Peter and Deuflhard, Peter and Felix, Roland}, title = {The Berlin Extension of the Stanford Hyperthermia Treatment.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1304}, number = {SC-93-35}, abstract = {In the field of deep regional hyperthermia, one of the most widely used devices is the BSD--2000 Hyperthermia System which employs the Sigma 60 applicator. The Sigma 60 consists of four independent sources, giving it the potential to control the energy pattern within the patient. The independent amplitudes and phases, as well as frequency selection and applicator position, present a large number of parameters for the operator to determine. Computer simulation has long been recognized as an attractive approach to optimizing these parameters. A treatment planning program was used in clinical practice at Stanford University Medical Center for two years. It demonstrated the feasibility of computer simulation for deep regional hyperthermia in a clinical situation. However, several parts of this system were written in a language specific to one workstation, which severely restricted the wider distribution of the program to other users of the Sigma 60. A new treatment planning system for the BSD 2000 has been developed and put into clinical practice at the Rudolf Virchow Clinic of the Free University of Berlin. The new method, which we will refer to as the Berlin system, has a simpler model construction program and a considerably better graphics capability. However, the most important feature is that all programs are written in FORTRAN, C, or the X Window graphics system. Therefore, the entire treatment planning system is completely portable to other workstations.}, language = {en} } @misc{DeuflhardAckermann, author = {Deuflhard, Peter and Ackermann, J{\"o}rg}, title = {Adaptive Discrete Galerkin-Methods for Macromolecular Processes.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1180}, number = {SC-93-22}, abstract = {In this paper, a rather recent algorithmic approac to the numerical simulation of macromolecula processes is surveyed. It avoids the numerical stiff integration o thousands up to millions of ODE's by constructing a scale of discret Hilbert spaces, especially weighted sequence spaces, and establishing corresponding Galerkin method. Examples including polyreactions o industrial relevance and ecological waste management by biochemica recycling illustrate the importance and efficiency of the algorithm.}, language = {en} } @misc{Deuflhard, author = {Deuflhard, Peter}, title = {Cascadic Conjugate Gradient Methods for Elliptic Partial Differential Equations I. Algorithm and Numerical Results.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1197}, number = {SC-93-23}, abstract = {Cascadic conjugate gradient methods for the numerical solution of elliptic partial differential equations consists of Galerkin finite element methods as outer iteration and (possibly preconditioned) conjugate gradient methods as inner iteration. Both iterations are known to minimize the energy norm of the arising iterations errors. A simple but efficient strategy to control the discretization errors versus the PCG iteration errors in terms of energy error norms is derived and worked out in algorithmic detail. In a unified setting, the relative merits of different preconditioners versus the case of no preconditioning is compared. Surprisingly, it appears that the cascadic conjugate gradient method without any preconditioning is not only simplest but also fastest. The numerical results seem to indicate that the cascade principle in itself already realizes some kind of preconditioning. A theoretical explanation of these observations will be given in Part II of this paper.}, language = {en} } @misc{DeuflhardSchmidt, author = {Deuflhard, Peter and Schmidt, Frank}, title = {Discrete Transparent Boundary Conditions for the Numerical Solution of Fresnel's Equation.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1205}, number = {SC-93-24}, abstract = {The paper presents a construction scheme of deriving transparent , i. e. reflection-free, boundary conditions for the numerical solution of Fresnel's equation (being formally equivalent to Schr{\"o}dinger's equation). These boundary conditions appear to be of a nonlocal Cauchy type. As it turns out, each kind of linear implicit discretization induces its own discrete transparent boundary conditions.}, language = {en} } @misc{DeuflhardNowakWeyer, author = {Deuflhard, Peter and Nowak, Ulrich and Weyer, J.}, title = {Prognoserechnung zur AIDS-Ausbreitung in der Bundesrepublik Deutschland}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1511}, number = {SC-94-23}, abstract = {Die Autoren sind sich dar{{\"u}}ber im klaren, daß zahlreiche Imponderabilien die Ergebnisse der vorgelegten Modellrechnungen beeinflussen k{{\"o}}nnen. Immerhin repr{\"a}sentiert jedoch das vorgelegte mathematische Modell die Summe unserer derzeitigen Kenntnisse zur Fragestellung AIDS--Epidemie; neu hinzukommende Erkenntnisse lassen sich rasch einarbeiten und in ihren Konsequenzen {\"u}berschauen. Die Entwicklung neuer effizienter numerischer Methoden spielte eine Schl{\"u}sselrolle bei der tats{\"a}chlichen Simulation dieses umfangreichen realit{\"a}tsnahen mathematischen Modells.}, language = {de} } @misc{BeckDeuflhardHegeetal., author = {Beck, Rudolf and Deuflhard, Peter and Hege, Hans-Christian and Seebass, Martin and Stalling, Detlev}, title = {Numerical Algorithms and Visualization in Medical Treament Planning}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2643}, number = {SC-96-54}, abstract = {After a short summary on therapy planning and the underlying technologies we discuss quantitative medicine by giving a short overview on medical image data, summarizing some applications of computer based treatment planning, and outlining requirements on medical planning systems. Then we continue with a description of our medical planning system {\sf HyperPlan}. It supports typical working steps in therapy planning, like data aquisition, segmentation, grid generation, numerical simulation and optimization, accompanying these with powerful visualization and interaction techniques.}, language = {en} } @misc{DeuflhardSeebassStallingetal., author = {Deuflhard, Peter and Seebass, Martin and Stalling, Detlev and Beck, Rudolf and Hege, Hans-Christian}, title = {Hyperthermia Treatment Planning in Clinical Cancer Therapy: Modelling, Simulation and Visualization}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2958}, number = {SC-97-26}, abstract = {\noindent The speaker and his co-workers in Scientific Computing and Visualization have established a close cooperation with medical doctors at the Rudolf--Virchow--Klinikum of the Humboldt University in Berlin on the topic of regional hyperthermia. In order to permit a patient--specific treatment planning, a special software system ({\sf\small HyperPlan}) has been developed. \noindent A mathematical model of the clinical system ({\it radio frequency applicator with 8 antennas, water bolus, individual patient body}) involves Maxwell's equations in inhomogeneous media and a so--called bio--heat transfer PDE describing the temperature distribution in the human body. The electromagnetic field and the thermal phenomena need to be computed at a speed suitable for the clinical environment. An individual geometric patient model is generated as a quite complicated tetrahedral ``coarse'' grid (several thousands of nodes). Both Maxwell's equations and the bio--heat transfer equation are solved on that 3D--grid by means of {\em adaptive} multilevel finite element methods, which automatically refine the grid where necessary in view of the required accuracy. Finally optimal antenna parameters for the applicator are determined . \noindent All steps of the planning process are supported by powerful visualization methods. Medical images, contours, grids, simulated electromagnetic fields and temperature distributions can be displayed in combination. A number of new algorithms and techniques had to be developed and implemented. Special emphasis has been put on advanced 3D interaction methods and user interface issues.}, language = {en} } @misc{EhrigDeuflhard, author = {Ehrig, Rainald and Deuflhard, Peter}, title = {GMERR - an Error Minimizing Variant of GMRES}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3323}, number = {SC-97-63}, abstract = {The paper analyzes a recently proposed iterative error minimizing method for the solution of linear systems. Sufficient and necessary conditions for convergence are studied, which show that the method essentially requires normal matrices. An efficient implementation similar to GMRES has been worked out in detail. Numerical tests on general non--normal matrices, of course, indicate that this approach is not competitive with GMRES. Summarizing, if error minimizing is important, one should rather choose CGNE. A computational niche for GMERR might be problems, where normal but non--symmetric matrices occur, like dissipative quantum mechanics.}, language = {en} } @misc{BeckDeuflhardHiptmairetal., author = {Beck, Rudolf and Deuflhard, Peter and Hiptmair, Ralf and Hoppe, Ronald H. W. and Wohlmuth, Barbara}, title = {Adaptive Multilevel Methods for Edge Element Discretizations of Maxwell's Equations}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3356}, number = {SC-97-66}, abstract = {The focus of this paper is on the efficient solution of boundary value problems involving the double-- curl operator. Those arise in the computation of electromagnetic fields in various settings, for instance when solving the electric or magnetic wave equation with implicit timestepping, when tackling time--harmonic problems or in the context of eddy--current computations. Their discretization is based on on N\'ed\'elec's {\bf H(curl}; \$\Omega\$)--conforming edge elements on unstructured grids. In order to capture local effects and to guarantee a prescribed accuracy of the approximate solution adaptive refinement of the grid controlled by a posteriori error estimators is employed. The hierarchy of meshes created through adaptive refinement forms the foundation for the fast iterative solution of the resulting linear systems by a multigrid method. The guiding principle underlying the design of both the error estimators and the multigrid method is the separate treatment of the kernel of the curl--operator and its orthogonal complement. Only on the latter we have proper ellipticity of the problem. Yet, exploiting the existence of computationally available discrete potentials for edge element spaces, we can switch to an elliptic problem in potential space to deal with nullspace of curl. Thus both cases become amenable to strategies of error estimation and multigrid solution developed for second order elliptic problems. The efficacy of the approach is confirmed by numerical experiments which cover several model problems and an application to waveguide simulation.}, language = {en} } @misc{DeuflhardDellnitzJungeetal., author = {Deuflhard, Peter and Dellnitz, Michael and Junge, Oliver and Sch{\"u}tte, Christof}, title = {Computation of Essential Molecular Dynamics by Subdivision Techniques I: Basic Concept}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2553}, number = {SC-96-45}, abstract = {The paper presents the concept of a new type of algorithm for the numerical computation of what the authors call the {\em essential dynamics\/} of molecular systems. Mathematically speaking, such systems are described by Hamiltonian differential equations. In the bulk of applications, individual trajectories are of no specific interest. Rather, time averages of physical observables or relaxation times of conformational changes need to be actually computed. In the language of dynamical systems, such information is contained in the natural invariant measure (infinite relaxation time) or in almost invariant sets ("large" finite relaxation times). The paper suggests the direct computation of these objects via eigenmodes of the associated Frobenius-Perron operator by means of a multilevel subdivision algorithm. The advocated approach is different to both Monte-Carlo techniques on the one hand and long term trajectory simulation on the other hand: in our setup long term trajectories are replaced by short term sub-trajectories, Monte-Carlo techniques are just structurally connected via the underlying Frobenius-Perron theory. Numerical experiments with a first version of our suggested algorithm are included to illustrate certain distinguishing properties. A more advanced version of the algorithm will be presented in a second part of this paper.}, language = {en} } @misc{DeuflhardWeiser, author = {Deuflhard, Peter and Weiser, Martin}, title = {Global Inexact Multilevel FEM for Nonlinear Elliptic Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2430}, number = {SC-96-33}, abstract = {The paper deals with the multilevel solution of {\em elliptic} partial differential equations (PDEs) in a {\em finite element} setting: {\em uniform ellipticity} of the PDE then goes with {\em strict monotonicity} of the derivative of a nonlinear convex functional. A {\em Newton multigrid method} is advocated, wherein {\em linear residuals} are evaluated within the multigrid method for the computation of the Newton corrections. The globalization is performed by some {\em damping} of the ordinary Newton corrections. The convergence results and the algorithm may be regarded as an extension of those for local Newton methods presented recently by the authors. An {\em affine conjugate} global convergence theory is given, which covers both the {\em exact} Newton method (neglecting the occurrence of approximation errors) and {\em inexact} Newton--Galerkin methods addressing the crucial issue of accuracy matching between discretization and iteration errors. The obtained theoretical results are directly applied for the construction of adaptive algorithms. Finally, illustrative numerical experiments with a~{\sf NEWTON--KASKADE} code are documented.}, language = {en} } @misc{DeuflhardHuisingaFischeretal., author = {Deuflhard, Peter and Huisinga, Wilhelm and Fischer, Alexander and Sch{\"u}tte, Christof}, title = {Identification of Almost Invariant Aggregates in Reversible Nearly Uncoupled Markov Chains}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3469}, number = {SC-98-03}, abstract = {The topic of the present paper bas been motivated by a recent computational approach to identify chemical conformations and conformational changes within molecular systems. After proper discretization, the conformations show up as almost invariant aggregates in reversible nearly uncoupled Markov chains. Most of the former work on this subject treated the direct problem: given the aggregates, analyze the loose coupling in connection with the computation of the stationary distribution (aggregation/disaggregation techniques). In contrast to that the present paper focuses on the inverse problem: given the system as a whole, identify the almost invariant aggregates together with the associated transition probabilites. A rather simple and robust algorithm is suggested and illustrated by its application to the n-pentane molecule.}, language = {en} } @misc{SchuetteFischerHuisingaetal., author = {Sch{\"u}tte, Christof and Fischer, Alexander and Huisinga, Wilhelm and Deuflhard, Peter}, title = {A Hybrid Monte Carlo Method for Essential Molecular Dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3474}, number = {SC-98-04}, abstract = {Recently, a novel concept for the computation of essential features of Hamiltonian systems (such as those arising in molecular dynamics) has been proposed. The realization of that concept was based on subdivision techniques applied to the Frobenius--Perron operator for the dynamical system. The present paper suggests an alternative but related concept based on statistical mechanics, which allows to attack realistic molecular systems. In a first step, the frequency of conformational changes is characterized in statistical terms leading to the definition of some Markov operator \$T\$ that describes the corresponding transition probabilities within the canonical ensemble. In a second step, a discretization of \$T\$ via hybrid Monte Carlo techniques (based on short term subtrajectories only) is shown to lead to a stochastic matrix \$P\$. With these theoretical preparations, an identification algorithm for conformations is applicable (to be presented elsewhere). Numerical results for the n-pentane molecule are given and interpreted.}, language = {en} } @misc{DeuflhardFrieseSchmidt, author = {Deuflhard, Peter and Friese, Tilmann and Schmidt, Frank}, title = {A Nonlinear Multigrid Eigenproblem Solver for the Complex Helmholtz Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3240}, number = {SC-97-55}, abstract = {The paper is motivated by the need for a fast robust adaptive multigrid method to solve complex Helmholtz eigenvalue problems arising from the design of optical chips. A nonlinear multigrid method is developed, which can be regarded as an extension of a previous adaptive Rayleigh quotient minimization method for selfadjoint Helmholtz eigenproblems. Since the complex Helmholtz operator is just a compact nonselfadjoint perturbation of a selfadjoint operator, linear algebra techniques like Schur decomposition can be extended from the finite dimensional case. The efficiency of the derived adaptive nonlinear multigrid method is illustrated by computations for a technologically relevant integrated optics component containing Multi Quantum Well Layers.}, language = {en} } @misc{GalliatDeuflhard, author = {Galliat, Tobias and Deuflhard, Peter}, title = {Adaptive hierarchical cluster analysis by Self-Organizing Box Maps}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5815}, number = {00-13}, abstract = {The present paper aims at an extension of {\sc Kohonen's} Self-Organizing Map (SOM) algorithm to be called Self-Organizing Box Map (SOBM) algorithm; it generates box codebooks in lieu of point codebooks. Box codebooks just like point codebooks indirectly define a Voronoi tessellation of the input space, so that each codebook vector represents a unique set of points. Each box codebook vector comprises a multi-dimensional interval that approximates the related partition of the Voronoi tessellation. Upon using the automated cluster identification method that has recently been developed by the authors, the codebook vectors can be grouped in such a way that each group represents a point cluster in the input space. Since the clustering usually depends on the size of the SOM, one cannot be sure, whether the clustering comes out to be optimal. Refinement of part of the identified clusters would often improve the results. This paper presents the concept of an adaptive multilevel cluster algorithm that performs such refinements automatically. Moreover the paper introduces a concept of essential dimensions and suggests a method for their identification based on our herein suggested box codebooks. Applications of the algorithm to molecular dynamics will be described in a forthcoming paper.}, language = {en} } @misc{GajewskiEdDeuflhardMarkowiched, author = {Gajewski(Ed.), Herbert and Deuflhard, Peter and Markowich(ed.), A.}, title = {Tagung NUMSIM '91 5.-08. Mai 1991. Collected Abstracts and Papers.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4838}, number = {TR-91-08}, abstract = {NUMSIM 91 fand vom 6.-08. Mai 1991 im Wissenschaftlichen Kommunikations- \& Konferenz- Zentrum der Humboldt-Universit{\"a}t in Gosen bei Berlin statt. Im Mittelpunkt dieses Seminars standen Probleme der numerischen Simulation von Ladungstransport- und Technologieprozessen der Mikro- und Optoelektronik. Es f{\"u}hrte Spezialisten der physikalischen Modellierung, der numerischen Mathematik und mathematischen Analysis sowie Nutzer von Simulationsprogrammen aus dem deutschsprachigen Raum zusammen. Ziel war die Vermittlung und der Austausch von Erfahrungen, die Diskussion gemeinsamer Aufgabenstellungen und Projekte und - in Anbetracht der deutschen Vereinigung nicht zuletzt - das gegenseitige Kennen- und Verstehenlernen.}, language = {en} } @misc{DeuflhardNowakPoehleetal., author = {Deuflhard, Peter and Nowak, Ulrich and P{\"o}hle, Uwe and Schmidt, B. Ch. and Weyer, J.}, title = {Die Ausbreitung von HIV/AIDS in Ballungsgebieten.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4844}, number = {TR-91-09}, abstract = {The rapidly increasing number of AIDS cases requires a realistic estimation of the future development of the HIV/AIDS disease. For that purpose we develop a large system of coupled nonlinear differential equations describing simultaneously the dynamics of the development of the disease, the population size, the gender and age structure. A set of 1650 coupled equations are linked by balanced parameters. The balancing procedure is described by a set of (formally) 2,178,000 additional algebraic conditions. As the considered system is stiff, it requires new special extrapolation methods combined with techniquees of dynamical sparsing for the solution of sparsely filled systems. According to our simulations we expect 19,0,000 deaths caused by AIDS in the Federal Republic of Germany (former territories) in the year 2000. Such an epidemical spread would tie up about 4-7 percent of the actual health care workers.}, language = {de} } @misc{SchmidtFrieseZschiedrichetal., author = {Schmidt, Frank and Friese, Tilmann and Zschiedrich, Lin and Deuflhard, Peter}, title = {Adaptive Multigrid Methods for the Vectorial Maxwell Eigenvalue Problem for Optical Waveguide Design}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6228}, number = {00-54}, abstract = {This paper has been motivated by the need for a fast robust adaptive multigrid method to solve the vectorial Maxwell eigenvalue problem arising from the design of optical chips. Our nonlinear multigrid methods are based on a previous method for the scalar Helmholtz equation, which must be modified to cope with the null space of the Maxwell operator due to the divergence condition. We present two different approaches. First, we present a multigrid algorithm based on an edge element discretization of time-harmonic Maxwell's equations, including the divergence condition. Second, an explicit elimination of longitudinal magnetic components leads to a nodal discretization known to avoid discrete \emph{spurious modes} also and a vectorial eigenvalue problem, for which we present a multigrid solver. Numerical examples show that the edge element discretization clearly outperforms the nodal element approach.}, language = {en} } @misc{FischerSchuetteDeuflhardetal., author = {Fischer, Alexander and Sch{\"u}tte, Christof and Deuflhard, Peter and Cordes, Frank}, title = {Hierarchical Uncoupling-Coupling of Metastable Conformations}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6296}, number = {01-03}, abstract = {Uncoupling-coupling Monte Carlo (UCMC) combines uncoupling techniques for finite Markov chains with Markov chain Monte Carlo methodology. UCMC aims at avoiding the typical metastable or trapping behavior of Monte Carlo techniques. From the viewpoint of Monte Carlo, a slowly converging long-time Markov chain is replaced by a limited number of rapidly mixing short-time ones. Therefore, the state space of the chain has to be hierarchically decomposed into its metastable conformations. This is done by means of combining the technique of conformation analysis as recently introduced by the authors, and appropriate annealing strategies. We present a detailed examination of the uncoupling-coupling procedure which uncovers its theoretical background, and illustrates the hierarchical algorithmic approach. Furthermore, application of the UCMC algorithm to the \$n\$-pentane molecule allows us to discuss the effect of its crucial steps in a typical molecular scenario.}, language = {en} } @misc{BoerStoetzelRoeblitzetal., author = {Boer, H. Marike T. and St{\"o}tzel, Claudia and R{\"o}blitz, Susanna and Deuflhard, Peter and Veerkamp, Roel F. and Woelders, Henri}, title = {A simple mathematical model of the bovine estrous cycle: follicle development and endocrine interactions}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11682}, number = {10-06}, abstract = {Bovine fertility is the subject of extensive research in animal sciences, especially because fertility of dairy cows has declined during the last decades. The regulation of estrus is controlled by the complex interplay of various organs and hormones. Mathematical modeling of the bovine estrous cycle could help in understanding the dynamics of this complex biological system. In this paper we present a mathematical model of the bovine estrous cycle that includes the processes of follicle and corpus luteum development and the key hormones that interact to control these processes. Focus in this paper is on development of the model, but also some simulation results are presented, showing that a set of equations and parameters is obtained that describes the system consistent with empirical knowledge. Even though the majority of the mechanisms that are included are only known qualitatively as stimulatory or inhibitory effects, the model surprisingly well features quantitative observations made in reality. This model of the bovine estrous cycle could be used as a basis for more elaborate models with the ability to study effects of external manipulations and genetic differences.}, language = {en} } @misc{RoeblitzStoetzelDeuflhardetal., author = {R{\"o}blitz, Susanna and St{\"o}tzel, Claudia and Deuflhard, Peter and Jones, Hannah M. and Azulay, David-Olivier and van der Graaf, Piet and Martin, Steven}, title = {A mathematical model of the human menstrual cycle for the administration of GnRH analogues}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12732}, number = {11-16}, abstract = {This study presents a differential equation model for the feedback mechanisms between Gonadotropin-releasing Hormone (GnRH), Follicle-Stimulating Hormone (FSH), Luteinizing Hormone (LH), development of follicles and corpus luteum, and the production of estradiol (E2), progesterone (P4), inhibin A (IhA), and inhibin B (IhB) during the female menstrual cycle. In contrast to other models, this model does not involve delay differential equations and is based on deterministic modelling of the GnRH pulse pattern, which allows for faster simulation times and efficient parameter identification. These steps were essential to tackle the task of developing a mathematical model for the administration of GnRH analogues. The focus of this paper is on model development for GnRH receptor binding and the integration of a pharmacokinetic/pharmacodynamic model for the GnRH agonist Nafarelin and the GnRH antagonist Cetrorelix into the menstrual cycle model. The final mathematical model describes the hormone profiles (LH, FSH, P4, E2) throughout the menstrual cycle in 12 healthy women. Moreover, it correctly predicts the changes in the cycle following single and multiple dose administration of Nafarelin or Cetrorelix at different stages in the cycle.}, language = {en} } @misc{SanderKlapprothYouettetal., author = {Sander, Oliver and Klapproth, Corinna and Youett, Jonathan and Kornhuber, Ralf and Deuflhard, Peter}, title = {Towards an Efficient Numerical Simulation of Complex 3D Knee Joint Motion}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14512}, number = {12-06}, abstract = {We present a time-dependent finite element model of the human knee joint of full 3D geometric complexity. Its efficient numerical simulation requires advanced numerical algorithms that have been developed just recently. Up to now, the model comprises bones, cartilage, and the major ligaments (patella and menisci are still missing). Bones (femur, tibia, and fibula) are modelled by linear elastic materials, cartilage by viscoelastic materials, ligaments by one-dimensional so-called Cosserat rods. In order to capture the dynamical contact problems correctly, we solve the full PDEs of elasticity in the presence of strict contact inequalities. For the total spatio-temporal discretization we apply a method of layers approach (first time, then space discretization). For the time discretization of the elastic and viscoelastic parts, we apply a new contact-stabilized Newmark method, while for the Cosserat rods we choose an energy-momentum method. For the space discretization, we use linear finite elements for the elastic and viscoelastic parts and novel geodesic finite elements for the Cosserat rods. The coupled system is solved by a Dirichlet-Neumann method, and the arising large algebraic systems are solved by a recent fast multigrid solver, the truncated non-smooth Newton multigrid method.}, language = {en} } @misc{DeuflhardSchielaWeiser, author = {Deuflhard, Peter and Schiela, Anton and Weiser, Martin}, title = {Mathematical Cancer Therapy Planning in Deep Regional Hyperthermia}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14204}, number = {11-39}, abstract = {This paper surveys the required mathematics for a typical challenging problem from computational medicine, the cancer therapy planning in deep regional hyperthermia. In the course of many years of close cooperation with clinics, the medical problem gave rise to quite a number of subtle mathematical problems, part of which had been unsolved when the common project started. Efficiency of numerical algorithms, i.e. computational speed and monitored reliability, play a decisive role for the medical treatment. Off-the-shelf software had turned out to be not sufficient to meet the requirements of medicine. Rather, new mathematical theory as well as new numerical algorithms had to be developed. In order to make our algorithms useful in the clinical environment, new visualization software, a virtual lab, including 3D geometry processing of individual virtual patients had to be designed and implemented. Moreover, before the problems could be attacked by numerical algorithms, careful mathematical modelling had to be done. Finally, parameter identification and constrained optimization for the PDEs had to be newly analyzed and realized over the individual patient's geometry. Our new techniques had an impact on the specificity of the individual patients' treatment and on the construction of an improved hyperthermia applicator.}, language = {en} } @misc{KlapprothSchielaDeuflhard, author = {Klapproth, Corinna and Schiela, Anton and Deuflhard, Peter}, title = {Adaptive Timestep Control for the Contact-Stabilized Newmark Method}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11714}, number = {10-09}, abstract = {The aim of this paper is to devise an adaptive timestep control in the contact--stabilized Newmark method (CONTACX) for dynamical contact problems between two viscoelastic bodies in the framework of Signorini's condition. In order to construct a comparative scheme of higher order accuracy, we extend extrapolation techniques. This approach demands a subtle theoretical investigation of an asymptotic error expansion of the contact--stabilized Newmark scheme. On the basis of theoretical insight and numerical observations, we suggest an error estimator and a timestep selection which also cover the presence of contact. Finally, we give a numerical example.}, language = {en} } @book{DeuflhardBornemann1994, author = {Deuflhard, Peter and Bornemann, Folkmar A.}, title = {Numerische Mathematik. II}, publisher = {De Gruyter Lehrbuch. Berlin: de Gruyter}, year = {1994}, language = {en} } @book{DeuflhardHohmann1993, author = {Deuflhard, Peter and Hohmann, Andreas}, title = {Numerische Mathematik I. Eine algorithmisch orientierte Einf{\"u}hrung.(Numerical mathematics I. An algorithmically oriented introduction)}, edition = {2}, publisher = {de Gruyter Lehrbuch. Berlin: Walter de Gruyter,}, year = {1993}, language = {en} } @article{BoerStoetzelRoeblitzetal.2011, author = {Boer, H. Marike T. and St{\"o}tzel, Claudia and R{\"o}blitz, Susanna and Deuflhard, Peter and Veerkamp, Roel F. and Woelders, Henri}, title = {A simple mathematical model of the bovine estrous cycle}, series = {Journal of Theoretical Biology}, volume = {278}, journal = {Journal of Theoretical Biology}, number = {1}, doi = {10.1016/j.jtbi.2011.02.021}, pages = {20 -- 31}, year = {2011}, language = {en} } @article{BraessDeuflhardLipnikov2002, author = {Braess, Dietrich and Deuflhard, Peter and Lipnikov, Konstantin}, title = {A Subspace Cascadic Multigrid Method for Mortar Elements}, series = {Computing}, volume = {69}, journal = {Computing}, pages = {205 -- 225}, year = {2002}, language = {en} } @inproceedings{BaderNowakDeuflhard1985, author = {Bader, G. and Nowak, Ulrich and Deuflhard, Peter}, title = {An Advanced Simulation Package for Large Chemical Reaction Systems}, series = {Stiff Computation. Proc. Intern. Conf. Park City, Utah/USA}, booktitle = {Stiff Computation. Proc. Intern. Conf. Park City, Utah/USA}, editor = {Aiken, R.}, publisher = {Oxford University Press}, year = {1985}, language = {en} } @inproceedings{BeckDeuflhardHegeetal.1997, author = {Beck, Rudolf and Deuflhard, Peter and Hege, Hans-Christian and Seebass, Martin and Stalling, Detlev}, title = {Numerical Algorithms and Visualization in Medical Treament Planning}, series = {Visualization and Mathematics}, booktitle = {Visualization and Mathematics}, editor = {Hege, Hans-Christian and Polthier, Konrad}, publisher = {Springer-Verlag}, pages = {303 -- 328}, year = {1997}, language = {en} } @article{BeckDeuflhardHiptmairetal.1999, author = {Beck, Rudolf and Deuflhard, Peter and Hiptmair, Ralf and Hoppe, Ronald H. W. and Wohlmuth, Barbara}, title = {Adaptive multilevel methods for edge element discretizations of Maxwell's equations}, series = {Surv. Math. Ind.}, volume = {8}, journal = {Surv. Math. Ind.}, number = {3-4}, pages = {271 -- 312}, year = {1999}, language = {en} } @inproceedings{BeckDeuflhardWustetal.1997, author = {Beck, Rudolf and Deuflhard, Peter and Wust, Peter and Felix, Roland}, title = {Electromagnetic Field Calculations by Finite Elements}, series = {Proc. 16th Ann. Meeting Europ. Soc. Hyperthermic Oncology (ESHO-97), Berlin, Germany, April 1997}, booktitle = {Proc. 16th Ann. Meeting Europ. Soc. Hyperthermic Oncology (ESHO-97), Berlin, Germany, April 1997}, pages = {77}, year = {1997}, language = {en} } @inproceedings{BeckHegeSeebassetal.1996, author = {Beck, Rudolf and Hege, Hans-Christian and Seebass, Martin and Wust, Peter and Deuflhard, Peter and Felix, Roland}, title = {Adaptive finite element codes for numerical calculations in hyperthermia treatment planning}, series = {Proc. of the 7th Int. Congress on Hyperthermic Oncology, Rome, Italy, April 1996}, volume = {2}, booktitle = {Proc. of the 7th Int. Congress on Hyperthermic Oncology, Rome, Italy, April 1996}, editor = {Franconi, Cafiero}, pages = {515 -- 517}, year = {1996}, language = {en} } @article{WeiserDeuflhard2007, author = {Weiser, Martin and Deuflhard, Peter}, title = {Inexact central path following algorithms for optimal control problems}, series = {SIAM J. Control Opt.}, volume = {46}, journal = {SIAM J. Control Opt.}, number = {3}, pages = {792 -- 815}, year = {2007}, language = {en} } @article{AsamDeuflhardKaiser1968, author = {Asam, P. and Deuflhard, Peter and Kaiser, Wolfgang}, title = {Intensity Limiting and Stimulated Brillouin Scattering in Germanium}, series = {Physics Letters}, volume = {27 A}, journal = {Physics Letters}, pages = {78 -- 79}, year = {1968}, language = {en} } @article{BornemannDeuflhard1996, author = {Bornemann, Folkmar A. and Deuflhard, Peter}, title = {The cascadic multigrid method for elliptic problems}, series = {Numer. Math.}, volume = {75}, journal = {Numer. Math.}, pages = {135 -- 152}, year = {1996}, language = {en} } @inproceedings{BornemannDeuflhard1996, author = {Bornemann, Folkmar A. and Deuflhard, Peter}, title = {Cascadic Multigrid Methods}, series = {Domain Decomposition Methods in Sciences and Engineering}, booktitle = {Domain Decomposition Methods in Sciences and Engineering}, editor = {Glowinski, J. R. and Widlund, Olof}, publisher = {John Wiley \& Sons Ltd}, pages = {205 -- 212}, year = {1996}, language = {en} } @article{BoeckDeuflhardHoeftetal.1988, author = {B{\"o}ck, J. and Deuflhard, Peter and Hoeft, A. and Korb, H. and Wolpers, H. and Steinmann, J. and Hellige, G.}, title = {Thermal recovery after passage of the pulmonary circulation assessed by deconvolution}, series = {J. Appl. Physiol.}, volume = {64}, journal = {J. Appl. Physiol.}, number = {3}, pages = {1210 -- 1216}, year = {1988}, language = {en} } @article{BoeckDeuflhardHoeftetal.1988, author = {B{\"o}ck, J. and Deuflhard, Peter and Hoeft, A. and Korb, H. and Steinmann, J. and Wolpers, H. and Hellige, G.}, title = {Evaluation of monoexponential extrapolation of transpulmonary thermal-dye kinetics by use of a new model-free deconvolution algorithm}, series = {Med Instrum}, volume = {22}, journal = {Med Instrum}, number = {1}, pages = {20 -- 28}, year = {1988}, language = {en} } @incollection{SchmidtFrieseZschiedrichetal.2003, author = {Schmidt, Frank and Friese, T. and Zschiedrich, Lin and Deuflhard, Peter}, title = {Adaptive Multigrid Methods for the Vectorial Maxwell Eigenvalue Problem for Optical Waveguide Design}, series = {Mathematics - Key Technology for the Future}, booktitle = {Mathematics - Key Technology for the Future}, publisher = {Springer}, pages = {270 -- 292}, year = {2003}, language = {en} } @incollection{SchuetteHuisingaDeuflhard2001, author = {Sch{\"u}tte, Christof and Huisinga, Wilhelm and Deuflhard, Peter}, title = {Transfer operator approach to conformational dynamics in biomolecular systems}, series = {Ergodic theory, analysis, and efficient simulation of dynamical systems}, booktitle = {Ergodic theory, analysis, and efficient simulation of dynamical systems}, editor = {Fiedler, Bernold}, publisher = {Berlin: Springer}, pages = {191 -- 223}, year = {2001}, language = {en} } @article{SchaberKoerberOfenlochetal.2002, author = {Schaber, Karlheinz and Koerber, Jens and Ofenloch, O. and Ehrig, Rainald and Deuflhard, Peter}, title = {Aerosol Formation in Gas-Liquid Contact Devices- Nucleation, Growth and Particle Dynamics}, series = {Chem.Eng.Sci.}, volume = {57}, journal = {Chem.Eng.Sci.}, pages = {4345 -- 4356}, year = {2002}, language = {en} } @article{DeuflhardErdmannRoitzschetal.2009, author = {Deuflhard, Peter and Erdmann, Bodo and Roitzsch, Rainer and Lines, Glenn Terje}, title = {Adaptive Finite Element Simulation of Ventricular Dynamics}, series = {J. Computing and Visualization in Science}, volume = {12}, journal = {J. Computing and Visualization in Science}, pages = {201 -- 205}, year = {2009}, language = {en} } @article{NadobnyFaehlingHagmannetal.2002, author = {Nadobny, Johanna and F{\"a}hling, Horst and Hagmann, M. and Turner, P. and Wlodarczyk, Waldemar and Gellermann, Johanna and Deuflhard, Peter and Wust, Peter}, title = {Experimental and numerical investigation of feed-point parameters in a 3-D hyperthermia applicator using different FDTD models of feed networks}, series = {IEEE Trans Biomed Eng}, volume = {49}, journal = {IEEE Trans Biomed Eng}, number = {11}, pages = {1348 -- 1359}, year = {2002}, language = {en} } @article{NadobnyPontaltiSullivanetal.2003, author = {Nadobny, Johanna and Pontalti, R. and Sullivan, Dennis and Wlodarczyk, Waldemar and Vaccari, A. and Deuflhard, Peter and Wust, Peter}, title = {A Thin-Rod Approximation for the Improved Modeling of Bare and Insulated Cylindrical Antennas Using the FDTD Method}, series = {IEEE Transactions on Antennas and Propagation}, volume = {51}, journal = {IEEE Transactions on Antennas and Propagation}, number = {8}, pages = {1780 -- 1796}, year = {2003}, language = {en} } @article{NadobnySullivanWlodarczyketal.2003, author = {Nadobny, Johanna and Sullivan, Dennis and Wlodarczyk, Waldemar and Deuflhard, Peter and Wust, Peter}, title = {A 3-D Tensor FDTD-Formulation for Treatment of Sloped Interfaces in Electrically Inhomogeneous Media}, series = {IEEE Transactions on Antennas and Propagation}, volume = {51}, journal = {IEEE Transactions on Antennas and Propagation}, number = {8}, pages = {1760 -- 1770}, year = {2003}, language = {en} } @inproceedings{NadobnySullivanWustetal.1998, author = {Nadobny, Johanna and Sullivan, Dennis and Wust, Peter and Seebass, Martin and Deuflhard, Peter and Felix, Roland}, title = {A High Resolution Interpretation at Arbitrary Interfaces for the FDTD Method}, series = {IEEE Transactions on Microwave Theory and Techniques}, volume = {46}, booktitle = {IEEE Transactions on Microwave Theory and Techniques}, number = {11}, pages = {1759 -- 1766}, year = {1998}, language = {en} } @inproceedings{NadobnyWlodarczykDeuflhardetal.2001, author = {Nadobny, Johanna and Wlodarczyk, Waldemar and Deuflhard, Peter and M{\"o}nich, Gerhard and Wust, Peter}, title = {Numerical and Experimental Investigations of Different Antenna Types for Deep Body Hyperthermia}, series = {Proc. 2001 URSI International Symposium on electromagnetic Theory}, booktitle = {Proc. 2001 URSI International Symposium on electromagnetic Theory}, editor = {Stuchly, M. and Shannon, D.}, pages = {473 -- 475}, year = {2001}, language = {en} } @inproceedings{NadobnyWustSeebassetal.1995, author = {Nadobny, Johanna and Wust, Peter and Seebass, Martin and Deuflhard, Peter and Felix, Roland}, title = {The Use of the Volume-Surface Integral Equation Method (VSIE) for Antenna Problems}, series = {Proc. COST 244 meeting on Reference Models for Bioelectromagnetic Test of Mobile Communication Systems, Roma, November 1994}, booktitle = {Proc. COST 244 meeting on Reference Models for Bioelectromagnetic Test of Mobile Communication Systems, Roma, November 1994}, editor = {Simunic, D.}, pages = {67 -- 74}, year = {1995}, language = {en} } @inproceedings{SchoepfDeuflhard1994, author = {Sch{\"o}pf, R. and Deuflhard, Peter}, title = {OCCAL. A mixed symbolic-numeric optimal control calculator}, series = {Computational optimal control}, volume = {115}, booktitle = {Computational optimal control}, editor = {et al. Bulirsch, R.}, publisher = {Birkh{\"a}user Verlag Basel}, pages = {269 -- 278}, year = {1994}, language = {en} } @inproceedings{SchmidtDeuflhard1994, author = {Schmidt, Frank and Deuflhard, Peter}, title = {Discrete Transparent Boundary Conditions for Fresnel's Equation}, series = {Integrated Photonics Research}, booktitle = {Integrated Photonics Research}, address = {San Francisco, California, USA}, pages = {45 -- 47}, year = {1994}, language = {en} } @article{SchmidtDeuflhard1995, author = {Schmidt, Frank and Deuflhard, Peter}, title = {Discrete Transparent Boundary Conditions for the Numerical Solution of Fresnel's Equation.}, series = {Comput. Math. Appl.}, volume = {29}, journal = {Comput. Math. Appl.}, pages = {53 -- 76}, year = {1995}, language = {en} } @article{NadobnyWustSeebassetal.1996, author = {Nadobny, Johanna and Wust, Peter and Seebass, Martin and Deuflhard, Peter and Felix, Roland}, title = {A Volume-Surface Integral Method for Solving Maxwell's Equations in Electrically Inhomogeneous Media Using Tetrahedral Grids}, series = {IEEE Transactions on Microwave Theory and Techniques}, volume = {44}, journal = {IEEE Transactions on Microwave Theory and Techniques}, number = {4}, pages = {543 -- 554}, year = {1996}, language = {en} } @inproceedings{NadobnyWustSeebassetal.1997, author = {Nadobny, Johanna and Wust, Peter and Seebass, Martin and Stalling, Detlev and Hege, Hans-Christian and Deuflhard, Peter and Felix, Roland}, title = {A Quantitative Comparison between the VSIE and the FDTD method using Electrically Equivalent Patient and Antenna Models}, series = {Proc. 16th Ann. Meeting Europ. Soc. Hyperthermic Oncology (ESHO-97), Berlin, Germany, April 1997}, booktitle = {Proc. 16th Ann. Meeting Europ. Soc. Hyperthermic Oncology (ESHO-97), Berlin, Germany, April 1997}, pages = {145}, year = {1997}, language = {en} } @inproceedings{NadobnyWustWlodarczyketal.1996, author = {Nadobny, Johanna and Wust, Peter and Wlodarczyk, Waldemar and Seebass, Martin and Deuflhard, Peter and Felix, Roland}, title = {Simulation Studies for Combination of Hyperthermia and Magnetic Resonance Systems}, series = {Proc. of the 7th Int. Congress on Hyperthermic Oncology, Rome, Italy, April 1996}, volume = {2}, booktitle = {Proc. of the 7th Int. Congress on Hyperthermic Oncology, Rome, Italy, April 1996}, editor = {Franconi, Cafiero}, pages = {549 -- 551}, year = {1996}, language = {en} } @inproceedings{NowakDeuflhard1983, author = {Nowak, Ulrich and Deuflhard, Peter}, title = {Towards Parameter Identification for Large Chemical Reaction Systems}, series = {Numerical Treatment of Inverse Problems in Differential and Integral Equations}, volume = {2}, booktitle = {Numerical Treatment of Inverse Problems in Differential and Integral Equations}, publisher = {Boston: Birkh{\"a}user}, pages = {13 -- 26}, year = {1983}, language = {en} } @article{NowakDeuflhard1985, author = {Nowak, Ulrich and Deuflhard, Peter}, title = {Numerical Identification of Selected Rate Constants in Large Chemical Reaction Systems}, series = {Appl. Numer. Math.}, volume = {1}, journal = {Appl. Numer. Math.}, pages = {59 -- 75}, year = {1985}, language = {en} } @article{SchuetteFischerHuisingaetal.1999, author = {Sch{\"u}tte, Christof and Fischer, Alexander and Huisinga, Wilhelm and Deuflhard, Peter}, title = {A Direct Approach to Conformational Dynamics Based on Hybrid Monte Carlo}, series = {J. Comput. Phys.}, volume = {151}, journal = {J. Comput. Phys.}, pages = {146 -- 168}, year = {1999}, language = {en} } @inproceedings{ReineckeDeuflhard2008, author = {Reinecke, Isabel and Deuflhard, Peter}, title = {Model Development and Decomposition in Physiology}, series = {Handbook of Research on Systems Biology Applications in Medicine}, volume = {2}, booktitle = {Handbook of Research on Systems Biology Applications in Medicine}, editor = {Daskalaki, A.}, pages = {759 -- 797}, year = {2008}, language = {en} } @article{ReineckeDeuflhard2007, author = {Reinecke, Isabel and Deuflhard, Peter}, title = {A Complex Mathematical Model of the Human Menstrual Cycle}, series = {Journal of Theoretical Biology}, volume = {247}, journal = {Journal of Theoretical Biology}, number = {2}, pages = {303 -- 330}, year = {2007}, language = {en} } @inproceedings{DeuflhardDellnitzJungeetal.1999, author = {Deuflhard, Peter and Dellnitz, M. and Junge, Oliver and Sch{\"u}tte, Christof}, title = {Computation of Essential Molecular Dynamics by Subdivision Techniques}, series = {Computational Molecular Dynamics}, volume = {4}, booktitle = {Computational Molecular Dynamics}, editor = {Deuflhard, Peter and Hermans, J. and Leimkuhler, Benedict and Marks, A. and Reich, Sebastian and Skeel, R.}, publisher = {Springer}, pages = {98 -- 115}, year = {1999}, language = {en} } @article{ColliFranzoneDeuflhardErdmannetal.2006, author = {Colli Franzone, Piero and Deuflhard, Peter and Erdmann, Bodo and Lang, Jens and Pavarino, Luca Franco}, title = {Adaptivity in Space and Time for Reaction-Diffusion Systems in Electrocardiology}, series = {SIAM J. Sc. Comp.}, volume = {28}, journal = {SIAM J. Sc. Comp.}, pages = {942 -- 962}, year = {2006}, language = {en} } @inproceedings{DeuflhardFiedlerKunkel1987, author = {Deuflhard, Peter and Fiedler, B. and Kunkel, P.}, title = {Numerical Pathfollowing Beyond Critical Points in ODE Models}, series = {Large Scale Scientific Computing}, booktitle = {Large Scale Scientific Computing}, publisher = {Birkh{\"a}user/Boston}, pages = {97 -- 113}, year = {1987}, language = {en} } @inproceedings{DeuflhardFrieseSchmidtetal.1996, author = {Deuflhard, Peter and Friese, T. and Schmidt, Frank and M{\"a}rz, Reinhard and Nolting, Hans-Peter}, title = {Effiziente Eigenmodenberechnung f{\"u}r den Entwurf integriert-optischer Chips}, series = {Mathematik - Schl{\"u}sseltechnologie f{\"u}r die Zukunft}, booktitle = {Mathematik - Schl{\"u}sseltechnologie f{\"u}r die Zukunft}, editor = {et al. Hoffmann, K.-H.}, publisher = {Springer Verlag}, pages = {267 -- 279}, year = {1996}, language = {en} } @article{DeuflhardFreundWalter1990, author = {Deuflhard, Peter and Freund, R. and Walter, Artur}, title = {Fast secant methods for the iterative solution of large nonsymmetric linear systems}, series = {IMPACT Comput. Sci. Eng.}, volume = {2}, journal = {IMPACT Comput. Sci. Eng.}, pages = {244 -- 276}, year = {1990}, language = {en} } @article{DeuflhardHairerZugck1987, author = {Deuflhard, Peter and Hairer, E. and Zugck, J.}, title = {One-step and extrapolation methods for differential-algebraic systems}, series = {Numer. Math.}, volume = {51}, journal = {Numer. Math.}, pages = {501 -- 516}, year = {1987}, language = {en} } @article{DeuflhardHeindl1979, author = {Deuflhard, Peter and Heindl, G.}, title = {Affine Invariant Convergence Theorems for Newton's Method and Extensions to Related Methods}, series = {SIAM J. Numer. Anal.}, volume = {16}, journal = {SIAM J. Numer. Anal.}, pages = {1 -- 10}, year = {1979}, language = {en} } @incollection{DeuflhardHeroth1996, author = {Deuflhard, Peter and Heroth, J{\"o}rg}, title = {Dynamic dimension reduction in ODE models}, series = {Scientific computing in chemical engineering}, booktitle = {Scientific computing in chemical engineering}, editor = {et al. Keil, Frerich}, publisher = {Berlin: Springer-Verlag}, pages = {29 -- 43}, year = {1996}, language = {en} } @inproceedings{DeuflhardHerothMaas1996, author = {Deuflhard, Peter and Heroth, J{\"o}rg and Maas, Ulrich}, title = {Towards Dynamic Dimension Reduction in Reactive Flow Problems}, series = {Proc. 3rd Workshop on Modelling of Chemical Reaction Systems}, booktitle = {Proc. 3rd Workshop on Modelling of Chemical Reaction Systems}, address = {Heidelberg}, year = {1996}, language = {en} } @inproceedings{DeuflhardHegeSeebass2000, author = {Deuflhard, Peter and Hege, Hans-Christian and Seebass, Martin}, title = {Progress Towards a Combined MRI Hyperthermia System}, series = {Proc. Second Int. Congress HIGH CARE 2000, Bochum}, booktitle = {Proc. Second Int. Congress HIGH CARE 2000, Bochum}, editor = {Gr{\"o}nemeyer, W.}, year = {2000}, language = {en} } @book{DeuflhardHohmann2002, author = {Deuflhard, Peter and Hohmann, Andreas}, title = {Numerische Mathematik. I}, edition = {3}, publisher = {de Gruyter Lehrbuch. Berlin: de Gruyter}, year = {2002}, language = {en} } @inproceedings{DeuflhardAckermann1994, author = {Deuflhard, Peter and Ackermann, J{\"o}rg}, title = {Adaptive discrete Galerkin methods for macromolecular processes}, series = {proceedings of the conference on advances in computational mathematics, held at New Delhi, India, January 5-9, 1993. Singapore}, booktitle = {proceedings of the conference on advances in computational mathematics, held at New Delhi, India, January 5-9, 1993. Singapore}, editor = {et al. Dikshit, H.}, pages = {59 -- 72}, year = {1994}, language = {en} } @incollection{DeuflhardApostolescu1980, author = {Deuflhard, Peter and Apostolescu, Victor}, title = {A Study of the Gauss-Newton Method for the Solution of Nonlinear Least Squares Problems}, series = {Special Topics of Applied Mathematics}, booktitle = {Special Topics of Applied Mathematics}, publisher = {Amsterdam: North-Holland Publ.}, pages = {129 -- 150}, year = {1980}, language = {en} } @inproceedings{DeuflhardBader1983, author = {Deuflhard, Peter and Bader, G.}, title = {Multiple Shooting Techniques Revisited}, series = {Numerical Treatment of Inverse Problems in Differential and Integral Equations}, volume = {2}, booktitle = {Numerical Treatment of Inverse Problems in Differential and Integral Equations}, publisher = {Boston: Birkh{\"a}user}, pages = {74 -- 94}, year = {1983}, language = {en} } @incollection{DeuflhardBaderNowak1981, author = {Deuflhard, Peter and Bader, G. and Nowak, Ulrich}, title = {LARKIN - a Software Package for the Numerical Simulation of LARge Systems Arising in Chemical Reaction KINetics}, series = {Modelling of Chemical Reaction Systems}, volume = {18}, booktitle = {Modelling of Chemical Reaction Systems}, publisher = {Springer Verlag}, pages = {38 -- 55}, year = {1981}, language = {en} } @book{DeuflhardBornemann2002, author = {Deuflhard, Peter and Bornemann, Folkmar A.}, title = {Scientific computing with ordinary differential equations. Transl. from the German by Werner C. Rheinboldt}, series = {Texts in Applied Mathematics}, volume = {42}, journal = {Texts in Applied Mathematics}, publisher = {New York, NY: Springer}, year = {2002}, language = {en} } @book{DeuflhardBornemann2002, author = {Deuflhard, Peter and Bornemann, Folkmar A.}, title = {Numerische Mathematik. II}, edition = {2}, publisher = {de Gruyter Lehrbuch. Berlin: de Gruyter}, year = {2002}, language = {en} } @incollection{DeuflhardDellnitzJungeetal.1998, author = {Deuflhard, Peter and Dellnitz, M. and Junge, Oliver and Sch{\"u}tte, Christof}, title = {Computation of essential molecular dynamics by subdivision techniques}, series = {Computational molecular dynamics}, volume = {4}, booktitle = {Computational molecular dynamics}, editor = {Deuflhard, Peter}, publisher = {Berlin: Springer.}, pages = {98 -- 115}, year = {1998}, language = {en} } @article{DeuflhardEnglScherzer1998, author = {Deuflhard, Peter and Engl, H. and Scherzer, O.}, title = {A convergence analysis of iterative methods for the solution of nonlinear ill-posed problems under affinely invariant conditions}, series = {Inverse Probl.}, volume = {14}, journal = {Inverse Probl.}, pages = {1081 -- 1106}, year = {1998}, language = {en} } @article{DeuflhardFiedlerKunkel1987, author = {Deuflhard, Peter and Fiedler, P. and Kunkel, P.}, title = {Efficient numerical pathfollowing beyond critical points}, series = {SIAM J. Numer. Anal.}, volume = {24}, journal = {SIAM J. Numer. Anal.}, pages = {912 -- 927}, year = {1987}, language = {en} } @article{Deuflhard1989, author = {Deuflhard, Peter}, title = {Numerical Treatment of Implicit Differential Equations and Differential Algebraic Systems}, series = {ZAMM}, volume = {69}, journal = {ZAMM}, number = {4}, pages = {T32}, year = {1989}, language = {en} } @inproceedings{Deuflhard1990, author = {Deuflhard, Peter}, title = {Uniqueness Theorems for Stiff ODE Initial Value Problems}, series = {Numerical analysis 1989, proceedings 13th Biennial Conference on Numerical Analysis 1989,}, booktitle = {Numerical analysis 1989, proceedings 13th Biennial Conference on Numerical Analysis 1989,}, editor = {Griffiths, D. and Watson, G.}, publisher = {Dundee, Longman Scientific \& Technical, Harlow, Essex, UK,}, pages = {74 -- 205}, year = {1990}, language = {en} } @article{Deuflhard1991, author = {Deuflhard, Peter}, title = {Global inexact Newton methods for very large scale nonlinear problems}, series = {IMPACT Comput. Sci. Eng.}, volume = {3}, journal = {IMPACT Comput. Sci. Eng.}, pages = {366 -- 393}, year = {1991}, language = {en} } @inproceedings{Deuflhard1992, author = {Deuflhard, Peter}, title = {Stochastic Versus Deterministic Numerical ODE Integration}, series = {Proc. 1st Workshop on Stochastic Numerics, Berlin}, booktitle = {Proc. 1st Workshop on Stochastic Numerics, Berlin}, editor = {Platen, E.}, pages = {16 -- 20}, year = {1992}, language = {en} } @inproceedings{Deuflhard1994, author = {Deuflhard, Peter}, title = {Cascadic conjugate gradient methods for elliptic partial differential equations}, series = {Domain decomposition methods in scientific and engineering computing}, volume = {180}, booktitle = {Domain decomposition methods in scientific and engineering computing}, editor = {et al. Keyes, David}, publisher = {Providence, RI: American Mathematical Society}, pages = {29 -- 42}, year = {1994}, language = {en} } @inproceedings{Deuflhard1995, author = {Deuflhard, Peter}, title = {Computational Mathematics as Key Technology}, series = {Systems Analysis Modelling Simulation (SAMS),Proc. IMACS Symposium on Systems Analysis and Simulation, Berlin, 26-30 June 1995}, volume = {18-19}, booktitle = {Systems Analysis Modelling Simulation (SAMS),Proc. IMACS Symposium on Systems Analysis and Simulation, Berlin, 26-30 June 1995}, editor = {Sydow, Achim}, publisher = {Gordon and Breach Science Publishers SA}, pages = {19 -- 26}, year = {1995}, language = {en} } @misc{Deuflhard1998, author = {Deuflhard, Peter}, title = {Fast algorithms, fast computers: The Konrad-Zuse-Zentrum Berlin (ZIB)}, series = {Mathematics in Berlin}, journal = {Mathematics in Berlin}, editor = {et al. Begehr, H.}, publisher = {Basel: Birkh{\"a}user}, pages = {183 -- 184}, year = {1998}, language = {en} } @incollection{Deuflhard1999, author = {Deuflhard, Peter}, title = {Commentary on Cornelius Lanczos's Extended Boundary Value Problems}, series = {Cornelius Lanczos Collected Published Papers with Commentaries}, volume = {VI}, booktitle = {Cornelius Lanczos Collected Published Papers with Commentaries}, editor = {Davis, W. and Chu, M. and Dolan, P. and McConnell, J. and Noris, L. and Ortiz, E. and Plemmons, R. and Ridgeway, D. and Stewart, W. and York, Jr., J. and Doggett, W. and Gellai, B. and Gsponer, A. and Prioli, C.}, publisher = {North Carolina State University, Raleigh}, pages = {3 -- 650-3-653}, year = {1999}, language = {en} } @incollection{Deuflhard1999, author = {Deuflhard, Peter}, title = {Commentary on Cornelius Lanczos's Solution of Ordinary Differential Equations by Trigonometric Interpolation}, series = {Cornelius Lanczos Collected Published Papers with Commentaries}, volume = {VI}, booktitle = {Cornelius Lanczos Collected Published Papers with Commentaries}, editor = {Davis, W. and Chu, M. and Dolan, P. and McConnell, J. and Noris, L. and Ortiz, E. and Plemmons, R. and Ridgeway, D. and Stewart, W. and York, Jr., J. and Doggett, W. and Gellai, B. and Gsponer, A. and Prioli, C.}, publisher = {North Carolina State University, Raleigh}, pages = {3 -- 667-3-669}, year = {1999}, language = {en} } @inproceedings{DeuflhardAckermann1994, author = {Deuflhard, Peter and Ackermann, J{\"o}rg}, title = {Adaptive Discrete Galerkin-Methods for Macromolecular Processes}, series = {Advances in Computational Mathematics}, booktitle = {Advances in Computational Mathematics}, editor = {Dikshit, H. and Michelli, C.}, publisher = {World Scientific Publishing Co. Inc.}, pages = {59 -- 72}, year = {1994}, language = {en} } @phdthesis{Deuflhard1968, author = {Deuflhard, Peter}, title = {Stimulierte Brillouinstreuung in Germanium bei 10.6 μ}, address = {Physics Dept.}, year = {1968}, language = {en} } @phdthesis{Deuflhard1972, author = {Deuflhard, Peter}, title = {Ein Newton-Verfahren bei fastsingul{\"a}rer Funktionalmatrix zur L{\"o}sung von nichtlinearen Randwertaufgaben mit der Mehrzielmethode}, address = {Math. Institute University of Cologne}, year = {1972}, language = {en} } @phdthesis{Deuflhard1976, author = {Deuflhard, Peter}, title = {A Stepsize Control for Continuation Methods with Special Application to Multiple Shooting Techniques}, address = {Math. Institute, Munich University of Technology}, year = {1976}, language = {en} } @misc{Deuflhard2000, author = {Deuflhard, Peter}, title = {Therapieplanung an virtuellen Krebspatienten}, publisher = {M. Aigner, E. Behrends (eds.): Alles Mathematik. Von Pythagoras zum CD-Player. Vieweg Verlag, pp. 22-30}, year = {2000}, language = {en} } @misc{Deuflhard2003, author = {Deuflhard, Peter}, title = {Maler, M{\"o}rder, Mathematiker}, publisher = {Gegenworte: Der Mythos und die Wissenschaft. Berlin-Brandenburgische Akademie der Wissenschaften (BBAW), 12. Heft, pp. 25-30}, year = {2003}, language = {en} } @misc{Deuflhard2003, author = {Deuflhard, Peter}, title = {Maler, M{\"o}rder, Mathematiker}, publisher = {Mitteilungen der Deutschen MathematikerVereinigung (DMV), pp. 16-21, Heft 4}, year = {2003}, language = {en} } @misc{Deuflhard2005, author = {Deuflhard, Peter}, title = {Pittori, assassini, matematici}, publisher = {M. Manaresi (ed.), Matematica e Cultura in Europa. Springer-Verlag Italia, pp. 145-155}, year = {2005}, language = {en} } @misc{Deuflhard1980, author = {Deuflhard, Peter}, title = {Linear and nonlinear least squares computing in view of control applications}, publisher = {Sonderforschungsbereich 123, Stochastische Mathematische Modelle. Universit{\"a}t Heidelberg}, pages = {85 -- 92}, year = {1980}, language = {en} } @misc{Deuflhard1998, author = {Deuflhard, Peter}, title = {Mathematics in Berlin}, editor = {et al. Begehr, H.}, publisher = {Basel: Birkh{\"a}user}, pages = {183 -- 184}, year = {1998}, language = {en} } @misc{DeuflhardFelixWust1999, author = {Deuflhard, Peter and Felix, Roland and Wust, Peter}, title = {W{\"a}rme f{\"u}r das Leben. Mathematische Hyperthermieplanung am virtuellen Krebspatienten}, publisher = {In: D. H{\"o}mberg (ed.), 8. Veranstaltungsreihe Forschungspolitische Dialoge in Berlin: Angewandte Mathematik - die verborgene Schl{\"u}sseltechnologie, 30. April 1999, Konrad-Zuse-Zentrum Berlin, pp. 23-29}, year = {1999}, language = {en} } @incollection{DeuflhardWeber2005, author = {Deuflhard, Peter and Weber, Marcus}, title = {Robust Perron Cluster Analysis in Conformation Dynamics}, series = {Lin. Alg. Appl. - Special Issue on Matrices and Mathematical Biology}, volume = {398}, booktitle = {Lin. Alg. Appl. - Special Issue on Matrices and Mathematical Biology}, publisher = {Elsevier Journals}, address = {Germany}, pages = {161 -- 184}, year = {2005}, language = {en} } @inproceedings{DeuflhardApostolescu1978, author = {Deuflhard, Peter and Apostolescu, Victor}, title = {An Underrelaxed Gauss-Newton Method for Equality Constrained Nonlinear Least Squares Problems}, series = {Optimization Techniques, Proc. 8th IFIP Conf., W{\"u}rzburg 1977, part 2}, volume = {7}, booktitle = {Optimization Techniques, Proc. 8th IFIP Conf., W{\"u}rzburg 1977, part 2}, editor = {Stoer, J.}, publisher = {Springer}, pages = {22 -- 32}, year = {1978}, language = {en} } @inproceedings{Deuflhard1979, author = {Deuflhard, Peter}, title = {Nonlinear Equation Solvers in Boundary Value Problem Codes}, series = {Proc. Working Conf. on Codes for BVPs in ODEs, Houston/Texas 1978}, volume = {74}, booktitle = {Proc. Working Conf. on Codes for BVPs in ODEs, Houston/Texas 1978}, editor = {Childs, B.}, publisher = {Springer}, pages = {40 -- 66}, year = {1979}, language = {en} } @article{Deuflhard1979, author = {Deuflhard, Peter}, title = {A study of extrapolation methods based on multistep schemes without parasitic solutions}, series = {J.App.Math.Phys.(ZAMP)}, volume = {30}, journal = {J.App.Math.Phys.(ZAMP)}, pages = {177 -- 189}, year = {1979}, language = {en} } @article{Deuflhard1979, author = {Deuflhard, Peter}, title = {A Stepsize Control for Continuation Methods and its Special Application to Multiple Shooting Techniques}, series = {Numer. Math.}, volume = {33}, journal = {Numer. Math.}, pages = {115 -- 146}, year = {1979}, language = {en} } @incollection{Deuflhard1980, author = {Deuflhard, Peter}, title = {Recent Advances in Multiple Shooting Techniques}, series = {Computational Techniques for Ordinary Differential Equations}, booktitle = {Computational Techniques for Ordinary Differential Equations}, publisher = {London: Academic Press}, pages = {217 -- 272}, year = {1980}, language = {en} } @article{Deuflhard1980, author = {Deuflhard, Peter}, title = {Kepler discretization in regular celestial mechanics}, series = {Celestial Mech.}, volume = {21}, journal = {Celestial Mech.}, pages = {213 -- 223}, year = {1980}, language = {en} } @article{BaderDeuflhard1983, author = {Bader, G. and Deuflhard, Peter}, title = {A semi-implicit mid-point rule for stiff systems of ordinary differential equations}, series = {Numer. Math.}, volume = {41}, journal = {Numer. Math.}, pages = {373 -- 398}, year = {1983}, language = {en} } @article{Deuflhard1983, author = {Deuflhard, Peter}, title = {Order and Stepsize Control in Extrapolation Methods}, series = {Numer. Math.}, volume = {41}, journal = {Numer. Math.}, pages = {399 -- 422}, year = {1983}, language = {en} } @article{Deuflhard1984, author = {Deuflhard, Peter}, title = {Computation of Periodic Solutions of Nonlinear ODEs}, series = {BIT}, volume = {24}, journal = {BIT}, pages = {456 -- 466}, year = {1984}, language = {en} } @article{Deuflhard1985, author = {Deuflhard, Peter}, title = {Recent Progress in Extrapolation Methods for Ordinary Differential Equations}, series = {SIAM Rev.}, volume = {27}, journal = {SIAM Rev.}, pages = {505 -- 535}, year = {1985}, language = {en} } @incollection{Deuflhard2000, author = {Deuflhard, Peter}, title = {Differential Equations in Technology and Medicine. Computational Concepts, Adaptive Algorithms, and Virtual Labs}, series = {Computational Mathematics Driven by Industrial Applications}, volume = {1739}, booktitle = {Computational Mathematics Driven by Industrial Applications}, publisher = {Springer-Verlag}, pages = {69 -- 125}, year = {2000}, language = {en} } @incollection{Deuflhard2003, author = {Deuflhard, Peter}, title = {A Comparison of Related Concepts in Computational Chemistry and Mathematics}, series = {Chemisty and Mathematics}, volume = {88}, booktitle = {Chemisty and Mathematics}, number = {330}, pages = {51 -- 66}, year = {2003}, language = {en} } @incollection{Deuflhard2003, author = {Deuflhard, Peter}, title = {From Molecular Dynamics to Conformational Dynamics in Drug Design}, series = {Trends in Nonlinear Analysis}, booktitle = {Trends in Nonlinear Analysis}, editor = {et al. Kirkilionis, Markus}, publisher = {Springer Verlag Berlin}, pages = {269 -- 288}, year = {2003}, language = {en} } @article{Deuflhard2004, author = {Deuflhard, Peter}, title = {bookreview}, series = {Annual Report DMV}, volume = {106}, journal = {Annual Report DMV}, pages = {43}, year = {2004}, language = {en} } @book{Deuflhard2004, author = {Deuflhard, Peter}, title = {Newton Methods for Nonlinear Problems. Affine Invariance and Adaptive Algorithms}, series = {Springer Series in Computational Mathematics}, journal = {Springer Series in Computational Mathematics}, publisher = {Springer}, year = {2004}, language = {en} } @book{Deuflhard2006, author = {Deuflhard, Peter}, title = {Newton Methods for Nonlinear Problems. Affine Invariance and Adaptive Algorithms}, series = {Springer Series in Computational Mathematics}, journal = {Springer Series in Computational Mathematics}, publisher = {Springer}, year = {2006}, language = {en} } @article{Deuflhard1974, author = {Deuflhard, Peter}, title = {A Modified Newton Method for the Solution of Ill-Conditioned Systems of Nonlinear Equations with Application to Multiple Shooting}, series = {Numer. Math.}, volume = {22}, journal = {Numer. Math.}, pages = {289 -- 315}, year = {1974}, language = {en} } @incollection{Deuflhard1975, author = {Deuflhard, Peter}, title = {A Relaxation Strategy for the Modified Newton Method}, series = {Optimization and Optimal Control}, volume = {477}, booktitle = {Optimization and Optimal Control}, publisher = {Springer}, pages = {59 -- 73}, year = {1975}, language = {en} } @article{Deuflhard1976, author = {Deuflhard, Peter}, title = {On Algorithms for the Summation of Certain Special Functions}, series = {Computing}, volume = {17}, journal = {Computing}, pages = {37 -- 48}, year = {1976}, language = {en} } @article{Deuflhard1977, author = {Deuflhard, Peter}, title = {A Summation Technique for Minimal Solutions of Linear Homogeneous Difference Equations}, series = {Computing}, volume = {18}, journal = {Computing}, pages = {1 -- 13}, year = {1977}, language = {en} } @inproceedings{FischerSchuetteDeuflhardetal.2002, author = {Fischer, Alexander and Sch{\"u}tte, Christof and Deuflhard, Peter and Cordes, Frank}, title = {Hierarchical Uncoupling-Coupling of Metastable Conformations}, series = {Computational Methods for Macromolecules}, booktitle = {Computational Methods for Macromolecules}, number = {24}, editor = {Schlick, T. and Gan, H.}, publisher = {Springer}, pages = {235 -- 259}, year = {2002}, language = {en} } @inproceedings{FroehlichDeuflhard1996, author = {Fr{\"o}hlich, Jochen and Deuflhard, Peter}, title = {An adaptive Galerkin method for the PDF transport equation of turbulent reactive flows}, series = {Progress in Industrial Mathematics, Proc. 8th Conference of the European Consortium for Mathematics in Industry (ECMI 94)}, booktitle = {Progress in Industrial Mathematics, Proc. 8th Conference of the European Consortium for Mathematics in Industry (ECMI 94)}, editor = {Neunzert, H.}, publisher = {Wiley \& Teubner}, pages = {176 -- 184}, year = {1996}, language = {en} } @inproceedings{FrieseDeuflhardSchmidt1999, author = {Friese, T. and Deuflhard, Peter and Schmidt, Frank}, title = {A Multigrid Method for the Complex Helmholtz Eigenvalue Problem}, series = {Procs. Eleventh International Conference on Domain Decomposition Methods in Sciences and Engineering (DD11), UK}, booktitle = {Procs. Eleventh International Conference on Domain Decomposition Methods in Sciences and Engineering (DD11), UK}, editor = {Lai, Choi-Hong and Bj{\o}rstad, Petter E. and Cross, Mark and Widlund, Olof}, publisher = {DDM.org}, pages = {19 -- 26}, year = {1999}, language = {en} } @inproceedings{GalliatDeuflhardRoitzschetal.2002, author = {Galliat, Tobias and Deuflhard, Peter and Roitzsch, Rainer and Cordes, Frank}, title = {Automatic identification of metastable conformations via self-organized neural networks}, series = {Proceedings of the 3rd International Workshop on Algorithms for Macromolecular Modelling}, booktitle = {Proceedings of the 3rd International Workshop on Algorithms for Macromolecular Modelling}, year = {2002}, language = {en} } @inproceedings{GalliatDeuflhardRoitzschetal.2002, author = {Galliat, Tobias and Deuflhard, Peter and Roitzsch, Rainer and Cordes, Frank}, title = {Automatic Identification of Metastable Conformations via Self-Organized Neural Networks}, series = {Computational Methods for Macromolecules}, booktitle = {Computational Methods for Macromolecules}, number = {24}, editor = {Schlick, T. and Gan, H.}, publisher = {Springer}, year = {2002}, language = {en} } @inproceedings{GalliatHuisingaDeuflhard2000, author = {Galliat, Tobias and Huisinga, Wilhelm and Deuflhard, Peter}, title = {Self-Organizing Maps Combined with Eigenmode Analysis for Automated Cluster Identification}, series = {Neural Computation, ICSC Academic Press}, booktitle = {Neural Computation, ICSC Academic Press}, editor = {H. Bothe, R.}, pages = {227 -- 232}, year = {2000}, language = {en} } @article{GellermannWustStallingetal.2000, author = {Gellermann, Johanna and Wust, Peter and Stalling, Detlev and Seebass, Martin and Nadobny, Johanna and Beck, Rudolf and Hege, Hans-Christian and Deuflhard, Peter and Felix, Roland}, title = {Clinical evaluation and verification of the hyperthermia treatment planning system hyperplan}, series = {Int J Radiat Oncol Biol Phys}, volume = {47}, journal = {Int J Radiat Oncol Biol Phys}, number = {4}, pages = {1145 -- 1156}, year = {2000}, language = {en} } @inproceedings{DeuflhardNowak1987, author = {Deuflhard, Peter and Nowak, Ulrich}, title = {Extrapolation integrators for quasilinear implicit ODEs.}, series = {Large scale scientific computing, Proc. Meet., Oberwolfach/FRG 1985,}, volume = {7}, booktitle = {Large scale scientific computing, Proc. Meet., Oberwolfach/FRG 1985,}, editor = {Deuflhard, Peter and Engquist, B.}, publisher = {Boston-Basel-Stuttgart: Birkh{\"a}user}, pages = {37 -- 50}, year = {1987}, language = {en} } @article{DeuflhardNowakWulkow1990, author = {Deuflhard, Peter and Nowak, Ulrich and Wulkow, Michael}, title = {Recent Developments in Chemical Computing}, series = {Computers in Chemical Engineering}, volume = {14}, journal = {Computers in Chemical Engineering}, pages = {1249 -- 1258}, year = {1990}, language = {en} } @article{DeuflhardPeschRentrop1976, author = {Deuflhard, Peter and Pesch, H.-J. and Rentrop, P.}, title = {A Modified Continuation Method for the Numerical Solution of Nonlinear Two-Point Boundary Value Problems by Shooting Techniques}, series = {Numer. Math.}, volume = {26}, journal = {Numer. Math.}, pages = {327 -- 343}, year = {1976}, language = {en} } @article{DeuflhardPotra1992, author = {Deuflhard, Peter and Potra, Florian}, title = {Asymptotic Mesh Independence for Newton-Galerkin Methods via a Refined Mysovskii Theorem}, series = {SIAM J. Numer. Anal.}, volume = {29}, journal = {SIAM J. Numer. Anal.}, number = {5}, pages = {1395 -- 1412}, year = {1992}, language = {en} } @article{DeuflhardSautter1980, author = {Deuflhard, Peter and Sautter, W.}, title = {On Rank-Deficient Pseudoinverses}, series = {Lin. Alg. Appl.}, volume = {29}, journal = {Lin. Alg. Appl.}, pages = {91 -- 111}, year = {1980}, language = {en} } @inproceedings{DeuflhardSchuette2004, author = {Deuflhard, Peter and Sch{\"u}tte, Christof}, title = {Molecular Conformation Dynamics and Computational Drug Design}, series = {Applied Mathematics Entering the 21st Century}, booktitle = {Applied Mathematics Entering the 21st Century}, number = {116}, editor = {Hill, James and Moore, Ross}, publisher = {SIAM}, pages = {91 -- 119}, year = {2004}, language = {en} } @misc{DeuflhardSchuetteCordesetal.1999, author = {Deuflhard, Peter and Sch{\"u}tte, Christof and Cordes, Frank and M{\"u}ller-Kurth, L.}, title = {Konformationsdynamik. Mathematischer Entwurf hochspezifischer Biomolek{\"u}le}, publisher = {In: D. H{\"o}mberg (ed.), 8. Veranstaltungsreihe Forschungspolitische Dialoge in Berlin: Angewandte Mathematik - die verborgene Schl{\"u}sseltechnologie, 30. April 1999, Konrad-Zuse-Zentrum Berlin, pp. 30-34}, year = {1999}, language = {en} } @inproceedings{DeuflhardSeebass1999, author = {Deuflhard, Peter and Seebass, Martin}, title = {Adaptive Multilevel FEM as Decisive Tools in the Clinical Cancer Therapy Hyperthermia}, series = {Procs. Eleventh International Conference on Domain Decomposition Methods}, booktitle = {Procs. Eleventh International Conference on Domain Decomposition Methods}, editor = {Lai, Choi-Hong and Bj{\o}rstad, Petter E. and Cross, Mark and Widlund, Olof}, publisher = {DDM-org Press,Bergen}, pages = {403 -- 414}, year = {1999}, language = {en} } @inproceedings{DeuflhardSeebassStallingetal.1997, author = {Deuflhard, Peter and Seebass, Martin and Stalling, Detlev and Beck, Rudolf and Hege, Hans-Christian}, title = {Hyperthermia Treatment Planning in Clinical Cancer Therapy:Modelling, Simulation, and Visualization}, series = {Computational Physics, Chemistry and Biology}, volume = {3}, booktitle = {Computational Physics, Chemistry and Biology}, editor = {Sydow, Achim}, publisher = {Wissenschaft und Technik Verlag}, address = {Plenary keynote talk, 15th IMACS World Congress 1997 on Scientific Computation, Modelling and Applied Mathematics}, year = {1997}, language = {en} } @inproceedings{EhrigNowakDeuflhard1998, author = {Ehrig, Rainald and Nowak, Ulrich and Deuflhard, Peter}, title = {Massively Parallel Simulation in Chemical Engineering by Extrapolation Algorithms}, series = {Procs. 16th International Workshop on Distributed Data Processing, Novosibirsk, Russia}, booktitle = {Procs. 16th International Workshop on Distributed Data Processing, Novosibirsk, Russia}, editor = {Khoroshevsky, V.}, pages = {1 -- 6}, year = {1998}, language = {en} } @incollection{EhrigNowakOeverdiecketal.1999, author = {Ehrig, Rainald and Nowak, Ulrich and Oeverdieck, Lars and Deuflhard, Peter}, title = {Advanced Extrapolation Methods for Large Scale Differential Algebraic Problems}, series = {High Performance Scientific and Engineering Computing}, volume = {8}, booktitle = {High Performance Scientific and Engineering Computing}, editor = {H.-J. Bungartz, F.}, publisher = {Springer Verlag}, pages = {233 -- 244}, year = {1999}, language = {en} } @article{EhrigOfenlochSchaberetal.2002, author = {Ehrig, Rainald and Ofenloch, O. and Schaber, Karlheinz and Deuflhard, Peter}, title = {Modelling and Simulation of Aerosol Formation by Heterogeneous Nucleation in Gas-Liquid Contact Devices}, series = {Chem.Eng.Sci.}, volume = {57}, journal = {Chem.Eng.Sci.}, number = {7}, pages = {1151 -- 1163}, year = {2002}, language = {en} } @inproceedings{ErdmannKoberLangetal.2002, author = {Erdmann, Bodo and Kober, C. and Lang, Jens and Deuflhard, Peter and Zeilhofer, J. and Sader, Robert}, title = {Efficient and Reliable Finite Element Methods for Simulation of the Human Mandible}, series = {proceedings of 9th Workshop on The Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields}, booktitle = {proceedings of 9th Workshop on The Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields}, address = {Ulm, Germany}, year = {2002}, language = {en} } @inproceedings{GellermannWustStallingetal.1997, author = {Gellermann, Johanna and Wust, Peter and Stalling, Detlev and Tilly, Wolfgang and Nadobny, Johanna and Seebass, Martin and Deuflhard, Peter and Felix, Roland and Budach, Volker}, title = {First Clinical Experiences with the Hyperthermia Planning System HyperPlan}, series = {Proc. 16th Ann. Meeting Europ. Soc. Hyperthermic Oncology (ESHO-97), Berlin, Germany, April 1997}, booktitle = {Proc. 16th Ann. Meeting Europ. Soc. Hyperthermic Oncology (ESHO-97), Berlin, Germany, April 1997}, pages = {79}, year = {1997}, language = {en} } @article{GladilinZachowDeuflhardetal.2002, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {A nonlinear elastic soft tissue model for craniofacial surgery simulations}, series = {ESAIM, Proc.}, volume = {12}, journal = {ESAIM, Proc.}, doi = {10.1051/proc:2002011}, pages = {61 -- 66}, year = {2002}, language = {en} } @inproceedings{GladilinZachowDeuflhardetal.2002, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {A nonlinear soft tissue model for craniofacial surgery simulations}, series = {Proc. of Modeling and Simulation for Computer-aided Medicine and Surgery (MS4CMS}, booktitle = {Proc. of Modeling and Simulation for Computer-aided Medicine and Surgery (MS4CMS}, publisher = {INRIA}, address = {Paris, France}, year = {2002}, language = {en} } @inproceedings{GladilinZachowDeuflhardetal.2002, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {Biomechanical modeling of individual facial emotion expressions}, series = {Proc. of Visualization, Imaging, and Image Processing (VIIP)}, booktitle = {Proc. of Visualization, Imaging, and Image Processing (VIIP)}, address = {Malaga, Spain}, pages = {7 -- 11}, year = {2002}, language = {en} } @inproceedings{DeuflhardWeiser1998, author = {Deuflhard, Peter and Weiser, Martin}, title = {Global inexact Newton multilevel FEM for nonlinear elliptic problems}, series = {Multigrid methods V. proceedings of the 5th European multigrid conference, held in Stuttgart, Germany, October 1-4, 1996.}, volume = {3}, booktitle = {Multigrid methods V. proceedings of the 5th European multigrid conference, held in Stuttgart, Germany, October 1-4, 1996.}, editor = {et al. Hackbusch, Wolfgang}, publisher = {Berlin: Springer}, pages = {71 -- 89}, year = {1998}, language = {en} } @article{DeuflhardWeiserSeebass2000, author = {Deuflhard, Peter and Weiser, Martin and Seebass, Martin}, title = {A new nonlinear elliptic multilevel FEM in clinical cancer therapy planning}, series = {Comput. Vis. Sci.}, volume = {3}, journal = {Comput. Vis. Sci.}, pages = {115 -- 120}, year = {2000}, language = {en} } @book{DeuflhardWeiser2011, author = {Deuflhard, Peter and Weiser, Martin}, title = {Numerische Mathematik 3}, publisher = {de Gruyter, Berlin}, year = {2011}, language = {de} } @book{DeuflhardWeiser2012, author = {Deuflhard, Peter and Weiser, Martin}, title = {Adaptive numerical solution of PDEs}, publisher = {de Gruyter}, address = {Berlin}, year = {2012}, language = {en} } @article{DeuflhardWeiserZachow2006, author = {Deuflhard, Peter and Weiser, Martin and Zachow, Stefan}, title = {Mathematics in Facial Surgery}, series = {AMS Notices}, volume = {53}, journal = {AMS Notices}, number = {9}, pages = {1012 -- 1016}, year = {2006}, language = {en} } @article{DeuflhardWulkow1989, author = {Deuflhard, Peter and Wulkow, Michael}, title = {Computational treatment of polyreaction kinetics by orthogonal polynomials of a discrete variable}, series = {IMPACT Comput. Sci. Eng.}, volume = {1}, journal = {IMPACT Comput. Sci. Eng.}, number = {3}, pages = {269 -- 301}, year = {1989}, language = {en} } @incollection{DeuflhardWulkow1995, author = {Deuflhard, Peter and Wulkow, Michael}, title = {Simulationsverfahren f{\"u}r die Polymerchemie}, series = {Mathematik in der Praxis. Fallstudien aus Industrie, Wirtschaft, Naturwissenschaften und Medizin}, booktitle = {Mathematik in der Praxis. Fallstudien aus Industrie, Wirtschaft, Naturwissenschaften und Medizin}, editor = {et al. Bachem, Achim}, publisher = {Berlin: Springer-Verlag}, pages = {117 -- 136}, year = {1995}, language = {en} } @incollection{Deuflhard2007, author = {Deuflhard, Peter}, title = {Painters, Murderers, Mathematicians}, series = {Mathematics and Culture in Europe. Mathematics in Art, Technology, Cinema, and Theatre}, booktitle = {Mathematics and Culture in Europe. Mathematics in Art, Technology, Cinema, and Theatre}, publisher = {Springer-Verlag}, pages = {141 -- 152}, year = {2007}, language = {en} } @book{DeuflhardHohmann2003, author = {Deuflhard, Peter and Hohmann, Andreas}, title = {Numerical analysis in modern scientific computing. An introduction. 2nd revised ed.}, series = {Texts in Applied Mathematics}, volume = {43}, journal = {Texts in Applied Mathematics}, publisher = {New York, NY: Springer}, year = {2003}, language = {en} } @article{DeuflhardHochmuth2004, author = {Deuflhard, Peter and Hochmuth, Reinhard}, title = {Multiscale analysis of thermoregulation in the human microvascular system}, series = {Math. Methods Appl. Sci.}, volume = {27}, journal = {Math. Methods Appl. Sci.}, number = {8}, publisher = {Wiley Verlag}, pages = {971 -- 989}, year = {2004}, language = {en} } @book{DeuflhardHohmann1991, author = {Deuflhard, Peter and Hohmann, Andreas}, title = {Numerische Mathematik I. Eine algorithmisch orientierte Einf{\"u}hrung}, publisher = {de Gruyter Lehrbuch,Berlin}, year = {1991}, language = {en} } @book{DeuflhardHohmann1995, author = {Deuflhard, Peter and Hohmann, Andreas}, title = {Numerical analysis. A 1st course in scientific computation. Transl. from the German by F. A. Potra and F. Schulz}, publisher = {de Gruyter Textbook. Berlin: De Gruyter}, year = {1995}, language = {en} } @article{DeuflhardHuisingaFischeretal.2000, author = {Deuflhard, Peter and Huisinga, Wilhelm and Fischer, Alexander and Sch{\"u}tte, Christof}, title = {Identification of Almost Invariant Aggregates in Reversible Nearly Uncoupled Markov Chains}, series = {Lin. Alg. Appl.}, volume = {315}, journal = {Lin. Alg. Appl.}, pages = {39 -- 59}, year = {2000}, language = {en} } @article{DeuflhardKrauseErtel2007, author = {Deuflhard, Peter and Krause, Rolf and Ertel, Susanne}, title = {A Contact-Stabilized Newmark Method for Dynamical Contact Problems}, series = {International Journal for Numerical Methods in Engineering}, volume = {73}, journal = {International Journal for Numerical Methods in Engineering}, number = {9}, pages = {1274 -- 1290}, year = {2007}, language = {en} } @inproceedings{DeuflhardLangNowak1996, author = {Deuflhard, Peter and Lang, Jens and Nowak, Ulrich}, title = {Recent Progress in Dynamical Process Simulation}, series = {Progress in Industrial Mathematics, Proc. 8th Conference of the European Consortium for Mathematics in Industry (ECMI 94)}, booktitle = {Progress in Industrial Mathematics, Proc. 8th Conference of the European Consortium for Mathematics in Industry (ECMI 94)}, editor = {Neunzert, H.}, publisher = {Wiley \& Teubner}, pages = {122 -- 137}, year = {1996}, language = {en} } @article{DeuflhardLeinenYserentant1989, author = {Deuflhard, Peter and Leinen, P. and Yserentant, H.}, title = {Concepts of an adaptive hierarchical finite element code}, series = {IMPACT Comput. Sci. Eng.}, volume = {1}, journal = {IMPACT Comput. Sci. Eng.}, number = {1}, pages = {3 -- 35}, year = {1989}, language = {en} } @article{DeuflhardLipnikov1998, author = {Deuflhard, Peter and Lipnikov, Konstantin}, title = {Domain decomposition with subdomain CCG for material jump elliptic problems}, series = {East-West J. Numer. Math.}, volume = {6}, journal = {East-West J. Numer. Math.}, number = {2}, pages = {81 -- 100}, year = {1998}, language = {en} } @misc{DeuflhardMehrmann2002, author = {Deuflhard, Peter and Mehrmann, Volker}, title = {Numerical analysis and scientific computing in key technologies}, pages = {9 -- 19}, year = {2002}, language = {en} } @article{HochmuthDeuflhard2003, author = {Hochmuth, Reinhard and Deuflhard, Peter}, title = {On the thermoregulation in the human microvascular system}, series = {PAMM}, volume = {3}, journal = {PAMM}, pages = {378 -- 379}, year = {2003}, language = {en} } @inproceedings{LameckerSeebassHegeetal.2004, author = {Lamecker, Hans and Seebaß, Martin and Hege, Hans-Christian and Deuflhard, Peter}, title = {A 3d statistical shape model of the pelvic bone for segmentation}, series = {Proc. SPIE Medical Imaging 2004}, volume = {5370}, booktitle = {Proc. SPIE Medical Imaging 2004}, editor = {Fitzpatrick, J. and Sonka, Milan}, pages = {1341 -- 1351}, year = {2004}, language = {en} } @inproceedings{LameckerSeebassLangeetal.2004, author = {Lamecker, Hans and Seebass, Martin and Lange, Thomas and Hege, Hans-Christian and Deuflhard, Peter}, title = {Visualization of the variability of 3D statistical shape models by animation}, series = {Proc. Medicine Meets Virtual Reality}, volume = {98}, booktitle = {Proc. Medicine Meets Virtual Reality}, editor = {Westwood, J.}, publisher = {IOS Press}, pages = {190 -- 196}, year = {2004}, language = {en} } @inproceedings{KoberSaderZeilhoferetal.2003, author = {Kober, C. and Sader, Robert and Zeilhofer, Hans-Florian and Deuflhard, Peter}, title = {An Individual Anisotropic and Inhomogeneous Material Description of the Human Mandible}, series = {Mathematical Modelling and Computing in Biology and Medicine}, booktitle = {Mathematical Modelling and Computing in Biology and Medicine}, editor = {Capasso, Vincenzo}, publisher = {ESTMB}, pages = {103 -- 109}, year = {2003}, language = {en} } @article{KoerberSchaberEhrigetal.1998, author = {Koerber, Jens and Schaber, Karlheinz and Ehrig, Rainald and Deuflhard, Peter}, title = {Modelling and simulation of aerosol formation in absorption processes}, series = {J. Aerosol Sci}, volume = {29}, journal = {J. Aerosol Sci}, pages = {579 -- 580}, year = {1998}, language = {en} } @incollection{LangErdmannKoberetal.2003, author = {Lang, Jens and Erdmann, Bodo and Kober, Cornelia and Deuflhard, Peter and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Effiziente und zuverl{\"a}ssige Finite-Elemente-Methoden zur Simulation des menschlichen Unterkiefers}, series = {Berichte des IZWR - Interdisziplin{\"a}res Zentrum f{\"u}r Wissenschaftliches Rechnen}, volume = {1}, booktitle = {Berichte des IZWR - Interdisziplin{\"a}res Zentrum f{\"u}r Wissenschaftliches Rechnen}, editor = {Alt, Walter and Hermann, Martin}, publisher = {Universit{\"a}t Jena}, address = {Germany}, pages = {49 -- 57}, year = {2003}, language = {en} } @inproceedings{GladilinZachowDeuflhardetal.2002, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {Biomechanisches Modell zur Absch{\"a}tzung der individuellen Gesichtsmimik}, series = {Proc.of Workshop Bildverarbeitung f{\"u}r die Medizin (BVM)}, booktitle = {Proc.of Workshop Bildverarbeitung f{\"u}r die Medizin (BVM)}, editor = {Meiler, M. and Saupe, D. and Krugel, F. and Handels, H. and Lehmann, T.}, address = {Leipzig, Germany}, pages = {25 -- 28}, year = {2002}, language = {en} } @article{HochmuthDeuflhard2004, author = {Hochmuth, Reinhard and Deuflhard, Peter}, title = {Multiscale Analysis for the Bio-Heat-Transfer Equation - The Nonisolated Case}, series = {Mathematical Models and Methods in Applied Sciences (M\$^3\$AS)}, volume = {14}, journal = {Mathematical Models and Methods in Applied Sciences (M\$^3\$AS)}, number = {11}, pages = {1621 -- 1634}, year = {2004}, language = {en} } @article{KlapprothDeuflhardSchiela2009, author = {Klapproth, Corinna and Deuflhard, Peter and Schiela, Anton}, title = {A Perturbation Result for Dynamical Contact Problems}, series = {Numer. Math}, volume = {2}, journal = {Numer. Math}, pages = {237 -- 257}, year = {2009}, language = {en} } @incollection{ZachowWeiserHegeetal.2005, author = {Zachow, Stefan and Weiser, Martin and Hege, Hans-Christian and Deuflhard, Peter}, title = {Soft Tissue Prediction in Computer Assisted Maxillofacial Surgery Planning}, series = {Biomechanics Applied to Computer Assisted Surgery}, booktitle = {Biomechanics Applied to Computer Assisted Surgery}, editor = {Payan, Y.}, publisher = {Research Signpost}, pages = {277 -- 298}, year = {2005}, language = {en} } @incollection{ZachowWeiserDeuflhard2008, author = {Zachow, Stefan and Weiser, Martin and Deuflhard, Peter}, title = {Modellgest{\"u}tzte Operationsplanung in der Kopfchirurgie}, series = {Modellgest{\"u}tzte Therapie}, booktitle = {Modellgest{\"u}tzte Therapie}, editor = {Niederlag, Wolfgang and Lemke, Heinz and Meixensberger, J{\"u}rgen and Baumann, Michael}, publisher = {Health Academy}, pages = {140 -- 156}, year = {2008}, language = {en} } @article{ZeilhoferZachowFairleyetal.2000, author = {Zeilhofer, Hans-Florian and Zachow, Stefan and Fairley, Jeffrey and Sader, Robert and Deuflhard, Peter}, title = {Treatment Planning and Simulation in Craniofacial Surgery with Virtual Reality Techiques}, series = {Journal of Cranio-Maxillofacial Surgery}, volume = {28 (Suppl. 1)}, journal = {Journal of Cranio-Maxillofacial Surgery}, pages = {82}, year = {2000}, language = {en} } @article{DeuflhardHuisingaJahnkeetal.2008, author = {Deuflhard, Peter and Huisinga, Wilhelm and Jahnke, Tobias and Wulkow, Michael}, title = {Adaptive Discrete Galerkin Methods Applied to the Chemical Master Equation}, series = {SIAM J. Sci. Comput}, volume = {30}, journal = {SIAM J. Sci. Comput}, number = {6}, pages = {2990 -- 3011}, year = {2008}, language = {en} } @misc{DeuflhardKornhuberSanderetal., author = {Deuflhard, Peter and Kornhuber, Ralf and Sander, Oliver and Schiela, Anton and Weiser, Martin}, title = {Mathematics cures virtual patients}, series = {MATHEON-Mathematics for Key Technologies}, volume = {1}, journal = {MATHEON-Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Horst, Ulrich and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Sch{\"u}tte, Christof and Skutella, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, pages = {7 -- 25}, language = {en} } @article{MoualeuNgangueWeiserEhrigetal., author = {Moualeu-Ngangue, Dany Pascal and Weiser, Martin and Ehrig, Rainald and Deuflhard, Peter}, title = {Optimal control for a tuberculosis model with undetected cases in Cameroon}, series = {Communications in Nonlinear Science and Numerical Simulation}, volume = {20}, journal = {Communications in Nonlinear Science and Numerical Simulation}, number = {3}, doi = {10.1016/j.cnsns.2014.06.037}, pages = {986 -- 1003}, abstract = {This paper considers the optimal control of tuberculosis through education, diagnosis campaign and chemoprophylaxis of latently infected. A mathematical model which includes important components such as undiagnosed infectious, diagnosed infectious, latently infected and lost-sight infectious is formulated. The model combines a frequency dependent and a density dependent force of infection for TB transmission. Through optimal control theory and numerical simulations, a cost-effective balance of two different intervention methods is obtained. Seeking to minimize the amount of money the government spends when tuberculosis remain endemic in the Cameroonian population, Pontryagin's maximum principle is used to characterize the optimal control. The optimality system is derived and solved numerically using the forward-backward sweep method (FBSM). Results provide a framework for designing cost-effective strategies for diseases with multiple intervention methods. It comes out that combining chemoprophylaxis and education, the burden of TB can be reduced by 80 \% in 10 years.}, language = {en} } @misc{SteinWeberScharkoietal., author = {Stein, Christoph and Weber, Marcus and Scharkoi, Olga and Deuflhard, Peter}, title = {Method and system for identifying compounds that bind and preferably activate a target opioid receptor in a pH-dependent manner}, series = {European Patent Application, Bulletin 2013/28}, journal = {European Patent Application, Bulletin 2013/28}, language = {en} } @misc{DeuflhardZachow2012, author = {Deuflhard, Peter and Zachow, Stefan}, title = {Mathematische Therapie- und Operationsplanung}, publisher = {Berliner Wirtschaftsgespr{\"a}che e.V.}, address = {Berlin}, pages = {89 -- 90}, year = {2012}, language = {en} } @article{ZachowHegeDeuflhard2005, author = {Zachow, Stefan and Hege, Hans-Christian and Deuflhard, Peter}, title = {Maxillofacial surgery planning with 3D soft tissue prediction - modeling, planning, simulation}, series = {2. Int. Conf. on Advanced Digital Technology in Head and Neck Reconstruction, Abstract 33}, journal = {2. Int. Conf. on Advanced Digital Technology in Head and Neck Reconstruction, Abstract 33}, address = {Banff, Alberta, CA}, pages = {64}, year = {2005}, language = {en} } @inproceedings{GladilinZachowDeuflhardetal.2003, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {Realistic prediction of individual facial emotion expressions for craniofacial surgery simulations}, series = {Proc. SPIE medical Imaging 2003}, volume = {5029}, booktitle = {Proc. SPIE medical Imaging 2003}, editor = {Galloway, Robert}, address = {San Diego, CA, USA}, doi = {10.1117/12.479584}, pages = {520 -- 527}, year = {2003}, language = {en} } @inproceedings{GladilinZachowDeuflhardetal.2003, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {On constitutive modeling of soft tissue for the long-term prediction of cranio-maxillofacial surgery outcome}, series = {International Congress Series, CARS2003, Computer Assisted Radiology and Surgery, Proceedings of the 17th International Congress and Exhibition}, volume = {1256}, booktitle = {International Congress Series, CARS2003, Computer Assisted Radiology and Surgery, Proceedings of the 17th International Congress and Exhibition}, doi = {10.1016/S0531-5131(03)00500-4}, pages = {343 -- 348}, year = {2003}, language = {en} } @inproceedings{ZachowHegeDeuflhard2004, author = {Zachow, Stefan and Hege, Hans-Christian and Deuflhard, Peter}, title = {Computergest{\"u}tzte Operationsplanung in der Gesichtschirurgie}, series = {Proc. VDE Kongress 2004 - Innovationen f{\"u}r Menschen, Band 2, Fachtagungsberichte DGBMT - GMM - GMA}, booktitle = {Proc. VDE Kongress 2004 - Innovationen f{\"u}r Menschen, Band 2, Fachtagungsberichte DGBMT - GMM - GMA}, pages = {53 -- 58}, year = {2004}, language = {en} } @article{HaberlHellZoeckleretal.2004, author = {Haberl, Hannes and Hell, Bertold and Z{\"o}ckler, Maja and Zachow, Stefan and Lamecker, Hans and Sarrafzadeh, Asita and Riecke, B. and Langsch, Wolfgang and Deuflhard, Peter and Bier, J{\"u}rgen and Brock, Mario}, title = {Technical aspects and results of surgery for craniosynostosis}, series = {Zentralblatt f{\"u}r Neurochirurgie}, volume = {65}, journal = {Zentralblatt f{\"u}r Neurochirurgie}, number = {2}, pages = {65 -- 74}, year = {2004}, language = {en} } @inproceedings{LameckerSeebassHegeetal.2004, author = {Lamecker, Hans and Seebaß, Martin and Hege, Hans-Christian and Deuflhard, Peter}, title = {A 3D statistical shape model of the pelvic bone for segmentation}, series = {Proceedings of SPIE - Volume 5370 Medical Imaging 2004}, booktitle = {Proceedings of SPIE - Volume 5370 Medical Imaging 2004}, editor = {Fitzpatrick, J. and Sonka, Milan}, doi = {10.1117/12.534145}, pages = {1341 -- 1351}, year = {2004}, language = {en} } @inproceedings{GladilinZachowDeuflhardetal.2002, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {Adaptive Nonlinear Elastic FEM for Realistic Prediction of Soft Tissue in Craniofacial Surgery Simulations}, series = {Proc. SPIE Medical Imaging 2002}, volume = {4681}, booktitle = {Proc. SPIE Medical Imaging 2002}, editor = {K. Mun, Seong}, address = {San Diego, USA}, doi = {10.1117/12.466906}, pages = {1 -- 8}, year = {2002}, language = {en} } @inproceedings{GladilinZachowDeuflhardetal.2002, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {Shape-based Modeling Approach for the Estimation of Individual Facial Mimics in Craniofacial Surgery Planning}, series = {Proc. SPIE Medical Imaging 2002: Visualization, Image-Guided Procedures, and Display}, volume = {4681}, booktitle = {Proc. SPIE Medical Imaging 2002: Visualization, Image-Guided Procedures, and Display}, editor = {Mun, Seong}, address = {San Diego, USA target}, pages = {242 -- 248}, year = {2002}, language = {en} } @inproceedings{ZachowGladilinHegeetal.2002, author = {Zachow, Stefan and Gladilin, Evgeny and Hege, Hans-Christian and Deuflhard, Peter}, title = {Towards Patient Specific, Anatomy Based Simulation of Facial Mimics for Surgical Nerve Rehabilitation}, series = {Computer Assisted Radiology and Surgery (CARS)}, booktitle = {Computer Assisted Radiology and Surgery (CARS)}, publisher = {Springer Verlag}, pages = {3 -- 6}, year = {2002}, language = {en} } @article{GladilinZachowDeuflhardetal.2004, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {Anatomy- and physics-based facial animation for craniofacial surgery simulations}, series = {Med Biol Eng Comput.}, volume = {42(2)}, journal = {Med Biol Eng Comput.}, doi = {10.1007/BF02344627}, pages = {167 -- 170}, year = {2004}, language = {en} } @inproceedings{ZachowErdmannHegeetal.2004, author = {Zachow, Stefan and Erdmann, Bodo and Hege, Hans-Christian and Deuflhard, Peter}, title = {Advances in 3D osteotomy planning with 3D soft tissue prediction}, series = {Proc. 2nd International Symposium on Computer Aided Surgery around the Head, Abstract}, booktitle = {Proc. 2nd International Symposium on Computer Aided Surgery around the Head, Abstract}, address = {Bern}, pages = {31}, year = {2004}, language = {en} } @article{DeuflhardWeiserSeebass2000, author = {Deuflhard, Peter and Weiser, Martin and Seebaß, Martin}, title = {A New Nonlinear Elliptic Multilevel FEM Applied to Regional Hyperthermia}, series = {Comput. Visual. Sci.}, volume = {3}, journal = {Comput. Visual. Sci.}, doi = {10.1007/PL00013546}, pages = {1 -- 6}, year = {2000}, language = {en} } @article{GellermannWustStallingetal.2000, author = {Gellermann, Johanna and Wust, Peter and Stalling, Detlev and Seebaß, Martin and Nadobny, Jacek and Hege, Hans-Christian and Deuflhard, Peter and Felix, Roland}, title = {Clinical evaluation and verification of the hyperthermia treatment planning system HyperPlan}, series = {Int. J. Radiat. Oncol. Biol. Phys.}, volume = {47(4)}, journal = {Int. J. Radiat. Oncol. Biol. Phys.}, doi = {10.1016/S0360-3016(00)00425-9}, pages = {1145 -- 1156}, year = {2000}, language = {en} } @inproceedings{ZachowGladilinHegeetal.2000, author = {Zachow, Stefan and Gladilin, Evgeny and Hege, Hans-Christian and Deuflhard, Peter}, title = {Finite-Element Simulation of Soft Tissue Deformation}, series = {Computer Assisted Radiology and Surgey (CARS)}, booktitle = {Computer Assisted Radiology and Surgey (CARS)}, publisher = {Elsevier Science B.V.}, pages = {23 -- 28}, year = {2000}, language = {en} } @inproceedings{GladilinZachowHegeetal.2001, author = {Gladilin, Evgeny and Zachow, Stefan and Hege, Hans-Christian and Deuflhard, Peter}, title = {Towards a Realistic Simulation of Individual Facial Mimics}, series = {Vision Modeling and Visualization 2001 (VMV)}, booktitle = {Vision Modeling and Visualization 2001 (VMV)}, address = {Stuttgart, Germany}, pages = {129 -- 134}, year = {2001}, language = {en} } @incollection{BeckDeuflhardHegeetal.1996, author = {Beck, Rudolf and Deuflhard, Peter and Hege, Hans-Christian and Seebaß, Martin and Stalling, Detlev}, title = {Numerical Algorithms and Visualization in Medical Treatment Planning}, series = {Visualization and Mathematics 1997}, booktitle = {Visualization and Mathematics 1997}, editor = {Hege, Hans-Christian and Polthier, Konrad}, publisher = {Springer, Heidelberg}, pages = {303 -- 328}, year = {1996}, language = {en} } @inproceedings{BeckHegeSeebassetal.1996, author = {Beck, Rudolf and Hege, Hans-Christian and Seebaß, Martin and Wust, Peter and Deuflhard, Peter and Felix, Roland}, title = {Adaptive Finite Element Codes for Numerical Calculations in Hyperthermia Treatment Planning}, series = {Proceedings of the 17th Congress on Hyperthermic Oncology}, volume = {2}, booktitle = {Proceedings of the 17th Congress on Hyperthermic Oncology}, address = {Rome, Italy}, pages = {515 -- 517}, year = {1996}, language = {en} } @article{NadobnyWustSeebassetal.1996, author = {Nadobny, Jacek and Wust, Peter and Seebaß, Martin and Deuflhard, Peter and Felix, Roland}, title = {A Volume Surface Integral Equation Method for Solving Maxwell's Equations in Electrically Inhomogeneous Media Using Tetrahedral Grids}, series = {IEEE Transactions Microwave Theory Techn.}, volume = {44}, journal = {IEEE Transactions Microwave Theory Techn.}, number = {4}, doi = {10.1109/22.491022}, pages = {543 -- 554}, year = {1996}, language = {en} } @inproceedings{DeuflhardHegeSeebass2000, author = {Deuflhard, Peter and Hege, Hans-Christian and Seebaß, Martin}, title = {Progress Towards a Combined MRI/Hyperthermia System}, series = {Proceedings Second International Congress HIGH CARE 2000}, booktitle = {Proceedings Second International Congress HIGH CARE 2000}, address = {Bochum}, year = {2000}, language = {en} } @inproceedings{NadobnyWlodarczykWustetal.1999, author = {Nadobny, Jacek and Wlodarczyk, Waldemar and Wust, Peter and M{\"o}nich, Gerhard and Deuflhard, Peter and Felix, Roland}, title = {3D Phased Array Applicator for Hyperthermia Treatment in Pelvis}, series = {Proc. XXVIth General Assembly of International Union of Radio Science (URSI)}, booktitle = {Proc. XXVIth General Assembly of International Union of Radio Science (URSI)}, address = {Toronto Ontario Canada}, pages = {648}, year = {1999}, language = {en} } @inproceedings{WlodarczykNadobnyWustetal.1999, author = {Wlodarczyk, Waldemar and Nadobny, Jacek and Wust, Peter and M{\"o}nich, Gerhard and Deuflhard, Peter and Felix, Roland}, title = {Systematic Design of Antennas for a Cylindrical 3D Phased Array Hyperthermia Applicator}, series = {Proc. 1999 IEEE Antennas and Propagation Society International Symposium}, booktitle = {Proc. 1999 IEEE Antennas and Propagation Society International Symposium}, address = {Orlando, FL}, doi = {10.1109/APS.1999.789482}, pages = {1004 -- 1007}, year = {1999}, language = {en} } @article{WustNadobnySeebassetal.1999, author = {Wust, Peter and Nadobny, Jacek and Seebaß, Martin and Stalling, Detlev and Gellermann, Johanna and Hege, Hans-Christian and Deuflhard, Peter}, title = {Influence of Patient Models and Numerical Methods on Predicted Power Deposition Patterns}, series = {Int. Journal Hyperthermia}, volume = {15}, journal = {Int. Journal Hyperthermia}, number = {6}, pages = {519 -- 540}, year = {1999}, language = {en} } @inproceedings{SeebassStallingHegeetal.1998, author = {Seebaß, Martin and Stalling, Detlev and Hege, Hans-Christian and Wust, Peter and Felix, Roland and Deuflhard, Peter}, title = {New Features of HyperPlan, a Hyperthermia Planning System}, series = {Proc. Hyperthermia in Clincal Oncology}, booktitle = {Proc. Hyperthermia in Clincal Oncology}, address = {Venice}, pages = {16}, year = {1998}, language = {en} } @inproceedings{SeebassStallingZoeckleretal.1997, author = {Seebaß, Martin and Stalling, Detlev and Z{\"o}ckler, Malte and Hege, Hans-Christian and Wust, Peter and Felix, Roland and Deuflhard, Peter}, title = {Surface Mesh Generation for Numerical Simulations of Hyperthermia Treatments}, series = {Proceedings of the 16th Annual Meeting of the European Society for Hyperthermic Oncology (ESHO-97)}, booktitle = {Proceedings of the 16th Annual Meeting of the European Society for Hyperthermic Oncology (ESHO-97)}, pages = {146}, year = {1997}, language = {en} } @inproceedings{DeuflhardSeebassStallingetal.1997, author = {Deuflhard, Peter and Seebaß, Martin and Stalling, Detlev and Beck, Rudolf and Hege, Hans-Christian}, title = {Hyperthermia Treatment Planning in Clinical Therapy}, series = {Computational Physics, Chemistry and Biology (Proceedings of the 15th IMACS World Congress 1997 on Scientific Computation 3, Modelling and Applied Mathematics)}, booktitle = {Computational Physics, Chemistry and Biology (Proceedings of the 15th IMACS World Congress 1997 on Scientific Computation 3, Modelling and Applied Mathematics)}, editor = {Sydow, Achim}, publisher = {Wissenschaft und Technik Verlag}, pages = {9 -- 17}, year = {1997}, language = {en} } @inproceedings{NadobnyWustStallingetal.1997, author = {Nadobny, Jacek and Wust, Peter and Stalling, Detlev and Hege, Hans-Christian and Deuflhard, Peter and Felix, Roland}, title = {A Quantitative Comparison Between VSIE and the FDTD Method Using Electrically Equivalent Patient and Antenna Models}, series = {Proceedings of 16th Annual Meeting of the European Society for Hyperthermic Oncology ESHO-97}, booktitle = {Proceedings of 16th Annual Meeting of the European Society for Hyperthermic Oncology ESHO-97}, address = {Berlin, Germany}, pages = {145}, year = {1997}, language = {en} } @inproceedings{WustNadobnyGellermannetal.1997, author = {Wust, Peter and Nadobny, Jacek and Gellermann, Johanna and Seebaß, Martin and Stalling, Detlev and Hege, Hans-Christian and Deuflhard, Peter and Felix, Roland}, title = {Patient Models and Algorithms for Hyperthermia Planning}, series = {Proceedings of the 16th Annual Meeting of the European Society for Hyperthermic Oncology ESHO-97}, booktitle = {Proceedings of the 16th Annual Meeting of the European Society for Hyperthermic Oncology ESHO-97}, year = {1997}, language = {en} } @inproceedings{GladilinZachowDeuflhardetal.2001, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {A Biomechanical Model for Soft Tissue Simulation in Craniofacial Surgery}, series = {Medical Imaging and Augmented Reality (MIAR)}, booktitle = {Medical Imaging and Augmented Reality (MIAR)}, address = {Hong Kong, China}, doi = {10.1109/MIAR.2001.930276}, pages = {137 -- 141}, year = {2001}, language = {en} } @inproceedings{GladilinZachowDeuflhardetal.2001, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {Virtual Fibers: A Robust Approach for Muscle Simulation}, series = {IX Mediterranean Conference on Medical and Biological Engineering and Computing (MEDICON)}, booktitle = {IX Mediterranean Conference on Medical and Biological Engineering and Computing (MEDICON)}, address = {Pula, Croatia}, pages = {961 -- 964}, year = {2001}, language = {en} } @inproceedings{GladilinZachowDeuflhardetal.2001, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {Validierung eines linear elastischen Modells f{\"u}r die Weichgewebesimulation in der Mund-Kiefer-Gesichtschirurgie}, series = {Bildverarbeitung f{\"u}r die Medizin (BVM)}, booktitle = {Bildverarbeitung f{\"u}r die Medizin (BVM)}, address = {L{\"u}beck, Germany}, pages = {57 -- 61}, year = {2001}, language = {en} } @inproceedings{GladilinZachowDeuflhardetal.2001, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {Validation of a Linear Elastic Model for Soft Tissue Simulation in Craniofacial Surgery}, series = {Proc. SPIE Medical Imaging 2001}, volume = {4319}, booktitle = {Proc. SPIE Medical Imaging 2001}, editor = {Mun, Seong}, address = {San Diego, USA}, doi = {10.1117/12.428061}, pages = {27 -- 35}, year = {2001}, language = {en} } @inproceedings{GladilinZachowHegeetal.2001, author = {Gladilin, Evgeny and Zachow, Stefan and Hege, Hans-Christian and Deuflhard, Peter}, title = {FE-based heuristic approach for the estimation of person-specific facial mimics}, series = {Proceedings of Euro-Par 2001: 5-th International Symposium on Computer Methods}, booktitle = {Proceedings of Euro-Par 2001: 5-th International Symposium on Computer Methods}, address = {Rome, Italy}, year = {2001}, language = {en} } @inproceedings{NadobnyWlodarczykWustetal.1998, author = {Nadobny, Jacek and Wlodarczyk, Waldemar and Wust, Peter and F{\"a}hling, Horst and M{\"o}nich, Gerhard and Deuflhard, Peter and Felix, Roland}, title = {Design and Optimization of Short Antennas for Phased-Array Hyperthermia Applicator}, series = {Proc. PIERS Progress in Electromagnetic Research Symposium}, booktitle = {Proc. PIERS Progress in Electromagnetic Research Symposium}, address = {Nantes}, pages = {839}, year = {1998}, language = {en} } @article{NadobnySullivanWustetal.1998, author = {Nadobny, Jacek and Sullivan, Dennis and Wust, Peter and Seebaß, Martin and Deuflhard, Peter and Felix, Roland}, title = {A High-Resolution Interpolation at Arbitary Interfaces for the FDTD Method}, series = {IEEE Trans. Microwave Theory Tech.}, volume = {46}, journal = {IEEE Trans. Microwave Theory Tech.}, number = {11}, doi = {10.1109/22.734576}, pages = {1759 -- 1766}, year = {1998}, language = {en} } @inproceedings{NadobnyWustFaehlingetal.1998, author = {Nadobny, Jacek and Wust, Peter and F{\"a}hling, Horst and Stalling, Detlev and Seebaß, Martin and Deuflhard, Peter and Felix, Roland}, title = {Numerical and Experimental Evaluation of E-Field and Absorbed Power in the Pelvic Region Using a Bone-Equivalent Phantom}, series = {Proc. PIERS Progress in Electromagnetic Research Symposium}, booktitle = {Proc. PIERS Progress in Electromagnetic Research Symposium}, address = {Nantes}, pages = {264}, year = {1998}, language = {en} } @article{WustGellermannBeieretal.1998, author = {Wust, Peter and Gellermann, Johanna and Beier, J{\"u}rgen and Wegner, Susan and Tilly, Wolfgang and Tr{\"o}ger, Jens and Stalling, Detlev and Hege, Hans-Christian and Deuflhard, Peter and Felix, Roland}, title = {Evaluation of Segmentation Algorithms for Generation of Patient Models in Radiofrequency Hyperthermia}, series = {Phys. Med. Biol.}, volume = {43 (11)}, journal = {Phys. Med. Biol.}, doi = {10.1088/0031-9155/43/11/009}, pages = {3295 -- 3307}, year = {1998}, language = {en} } @inproceedings{DeuflhardHege1994, author = {Deuflhard, Peter and Hege, Hans-Christian}, title = {Scientific Computing in der Theoretischen Physik - Collected Abstracts}, series = {Tagung organisiert von der DMV-Fachgruppe Scientific Computing in Kooperation mit dem GAMM Fachausschuss Scientific Computing}, booktitle = {Tagung organisiert von der DMV-Fachgruppe Scientific Computing in Kooperation mit dem GAMM Fachausschuss Scientific Computing}, address = {Berlin}, year = {1994}, language = {en} } @inproceedings{NadobnyWustWlodarczyketal.1996, author = {Nadobny, Jacek and Wust, Peter and Wlodarczyk, Waldemar and Seebaß, Martin and Deuflhard, Peter and M{\"o}nich, Gerhard and Felix, Roland}, title = {Simulation Studies for Combination of Hyperthermia and Magnetic Resonance Systems}, series = {Proceedings of the 17th Congress on Hyperthermic Oncology}, volume = {2}, booktitle = {Proceedings of the 17th Congress on Hyperthermic Oncology}, address = {Rome, Italy}, pages = {549 -- 551}, year = {1996}, language = {en} } @inproceedings{SeebassStallingNadobnyetal.1996, author = {Seebaß, Martin and Stalling, Detlev and Nadobny, Jacek and Wust, Peter and Felix, Roland and Deuflhard, Peter}, title = {Three-Dimensional Finite Elements Mesh Generation for Numerical Simulations of Hyperthermia Treatments}, series = {Proceedings of the 17th Congress on Hyperthermic Oncology}, volume = {2}, booktitle = {Proceedings of the 17th Congress on Hyperthermic Oncology}, address = {Rome, Italy}, pages = {547 -- 548}, year = {1996}, language = {en} } @inproceedings{StallingSeebassHegeetal.1996, author = {Stalling, Detlev and Seebaß, Martin and Hege, Hans-Christian and Wust, Peter and Deuflhard, Peter and Felix, Roland}, title = {HyperPlan - an Integrated System for Treatment Planning in Regional Hyperthermia}, series = {Proceedings of the 17th Congress on Hyperthermic Oncology}, volume = {2}, booktitle = {Proceedings of the 17th Congress on Hyperthermic Oncology}, address = {Rome, Italy}, pages = {552 -- 554}, year = {1996}, language = {en} } @article{WustSeebassNadobnyetal.1996, author = {Wust, Peter and Seebaß, Martin and Nadobny, Jacek and Deuflhard, Peter and M{\"o}nich, Gerhard and Felix, Roland}, title = {Simulation Studies Promote Technological Development of Radiofrequency Phased Array Hyperthermia}, series = {Int. Journal of Hyperthermia}, volume = {12}, journal = {Int. Journal of Hyperthermia}, pages = {477 -- 494}, year = {1996}, language = {en} } @misc{WeiserErdmannDeuflhard, author = {Weiser, Martin and Erdmann, Bodo and Deuflhard, Peter}, title = {On Efficiency and Accuracy in Cardioelectric Simulation}, series = {Progress in Industrial Mathematics at ECMI 2008}, journal = {Progress in Industrial Mathematics at ECMI 2008}, editor = {Wilson, E. and Fitt, A. and Ockendon, H. and Norbury, J.}, publisher = {Springer}, pages = {371 -- 376}, abstract = {Reasons for the failure of adaptive methods to deliver improved efficiency when integrating monodomain models for myocardiac excitation are discussed. Two closely related techniques for reducing the computational complexity of linearly implicit integrators, deliberate sparsing and splitting, are investigated with respect to their impact on computing time and accuracy.}, language = {en} } @article{DeuflhardSchielaWeiser, author = {Deuflhard, Peter and Schiela, Anton and Weiser, Martin}, title = {Mathematical Cancer Therapy Planning in Deep Regional Hyperthermia}, series = {Acta Numerica}, volume = {21}, journal = {Acta Numerica}, pages = {307 -- 378}, abstract = {This paper surveys the required mathematics for a typical challenging problem from computational medicine, the cancer therapy planning in deep regional hyperthermia. In the course of many years of close cooperation with clinics, the medical problem gave rise to quite a number of subtle mathematical problems, part of which had been unsolved when the common project started. Efficiency of numerical algorithms, i.e. computational speed and monitored reliability, play a decisive role for the medical treatment. Off-the-shelf software had turned out to be not sufficient to meet the requirements of medicine. Rather, new mathematical theory as well as new numerical algorithms had to be developed. In order to make our algorithms useful in the clinical environment, new visualization software, a virtual lab, including 3D geometry processing of individual virtual patients had to be designed and implemented. Moreover, before the problems could be attacked by numerical algorithms, careful mathematical modelling had to be done. Finally, parameter identification and constrained optimization for the PDEs had to be newly analyzed and realized over the individual patient's geometry. Our new techniques had an impact on the specificity of the individual patients' treatment and on the construction of an improved hyperthermia applicator.}, language = {en} } @misc{DeuflhardHege, author = {Deuflhard, Peter and Hege, Hans-Christian}, title = {Raumtiefe in Malerei und Computergrafik}, series = {R{\"a}ume - Bilder - Kulturen}, journal = {R{\"a}ume - Bilder - Kulturen}, editor = {Lepper, Verena and Deuflhard, Peter and Markschies, Christoph}, publisher = {Walter De Gruyter}, isbn = {978-3-11-035993-0}, pages = {33 -- 46}, abstract = {Einf{\"u}hrung: Die Tiefenwirkung dreidimensionaler R{\"a}ume in einem zweidimensionalen Bild einzufangen, ist ein Faszinosum nahezu aller Kulturen der Menschheitsgeschichte. Der vorliegende Aufsatz folgt den Spuren dieses Faszinosums, vergleichend in der Malerei und der mathematisierten Computergrafik. Die Entdeckung der Zentralperspektive in der italienischen Renaissance zeigt bereits den engen Zusammenhang von Malerei und Mathematik. Auf der Suche nach Maltechniken, mit denen Raumtiefe bildnerisch dargestellt werden kann, beginnen wir in Kap. 2 mit einem chronologischen Gang durch verschiedene Epochen der europ{\"a}ischen Malerei. Hieraus abgeleitete Prinzipien, soweit sie im Rechner realisierbar scheinen, stellen wir in Kap. 3 am Beispiel moderner Methoden der mathematischen Visualisierung vor.}, language = {de} } @misc{BockmayrSiebertRoeblitzetal., author = {Bockmayr, Alexander and Siebert, Heike and R{\"o}blitz, Susanna and Sch{\"u}tte, Christof and Deuflhard, Peter}, title = {Advanced mathematical modeling in systems biology}, series = {MATHEON-Mathematics for Key Technologies}, volume = {1}, journal = {MATHEON-Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Sch{\"u}tte, Christof and Skutela, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, pages = {29 -- 44}, language = {en} } @misc{SchuetteDeuflhardNoeetal., author = {Sch{\"u}tte, Christof and Deuflhard, Peter and No{\´e}, Frank and Weber, Marcus}, title = {Design of functional molecules}, series = {MATHEON-Mathematics for Key Technologies}, volume = {1}, journal = {MATHEON-Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Horst, Ulrich and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Sch{\"u}tte, Christof and Skutella, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, pages = {49 -- 65}, language = {en} } @misc{DeuflhardSchuette, author = {Deuflhard, Peter and Sch{\"u}tte, Christof}, title = {Life Sciences}, series = {MATHEON-Mathematics for Key Technologies}, volume = {1}, journal = {MATHEON-Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Horst, Ulrich and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Sch{\"u}tte, Christof and Skutella, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, pages = {1 -- 5}, language = {en} } @misc{Deuflhard, author = {Deuflhard, Peter}, title = {The Grand Four}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66038}, abstract = {This paper gives a concise synopsis and some new insights concerning four affine invariant globalizations of the local Newton method. The invariance classes include: affine covariance, affine contravariance, affine conjugacy, and affine similarity. In view of algorithmic robustness, each of these classes of algorithms is particularly suitable for some corresponding problem class.}, language = {en} } @article{WustNadobnySeebassetal.1999, author = {Wust, Peter and Nadobny, Johanna and Seebass, Martin and Stalling, Detlev and Gellermann, Johanna and Hege, Hans-Christian and Deuflhard, Peter and Felix, Roland}, title = {Influence of patient models and numerical methods on predicted power deposition patterns}, series = {Int. J. Hyperthermia}, volume = {15}, journal = {Int. J. Hyperthermia}, number = {6}, pages = {519 -- 540}, year = {1999}, language = {en} } @article{WustSeebassNadobnyetal.1996, author = {Wust, Peter and Seebass, Martin and Nadobny, Johanna and Deuflhard, Peter and M{\"o}nich, Gerhard and Felix, Roland}, title = {Simulation studies promote technological development of radiofrequency phased array hyperthermia}, series = {Int J Hyperthermia}, volume = {12}, journal = {Int J Hyperthermia}, number = {4}, pages = {477 -- 494}, year = {1996}, language = {en} } @techreport{DeuflhardFiedlerKunkel1984, author = {Deuflhard, Peter and Fiedler, B. and Kunkel, P.}, title = {Efficient numerical pathfollowing beyond critical points}, number = {278}, publisher = {Universit{\"a}t Heidelberg}, year = {1984}, language = {en} } @article{RoeblitzStoetzelDeuflhardetal.2013, author = {R{\"o}blitz, Susanna and St{\"o}tzel, Claudia and Deuflhard, Peter and Jones, Hannah M. and Azulay, David-Olivier and van der Graaf, Piet and Martin, Steven}, title = {A mathematical model of the human menstrual cycle for the administration of GnRH analogues}, series = {Journal of Theoretical Biology}, volume = {321}, journal = {Journal of Theoretical Biology}, doi = {10.1016/j.jtbi.2012.11.020}, pages = {8 -- 27}, year = {2013}, language = {en} } @inproceedings{SeebassStallingNadobnyetal.1996, author = {Seebass, Martin and Stalling, Detlev and Nadobny, Johanna and Wust, Peter and Felix, Roland and Deuflhard, Peter}, title = {Three-Dimensional Finite Element Mesh Generation for Numerical Simulations of Hyperthermia Treatments}, series = {Proc. of the 7th Int. Congress on Hyperthermic Oncology, Rome, Italy, April 1996}, volume = {2}, booktitle = {Proc. of the 7th Int. Congress on Hyperthermic Oncology, Rome, Italy, April 1996}, editor = {Franconi, Cafiero}, pages = {547 -- 548}, year = {1996}, language = {en} } @inproceedings{SeebassStallingZoeckleretal.1997, author = {Seebass, Martin and Stalling, Detlev and Z{\"o}ckler, M. and Hege, Hans-Christian and Wust, Peter and Felix, Roland and Deuflhard, Peter}, title = {Surface Mesh Generation for Numerical Simulations of Hyperthermia Treatments}, series = {Proc. 16th Ann. Meeting Europ. Soc. Hyperthermic Oncology (ESHO-97), Berlin, Germany, April 1997}, booktitle = {Proc. 16th Ann. Meeting Europ. Soc. Hyperthermic Oncology (ESHO-97), Berlin, Germany, April 1997}, pages = {146}, year = {1997}, language = {en} } @inproceedings{WlodarczykNadobnyWustetal.1999, author = {Wlodarczyk, Waldemar and Nadobny, Johanna and Wust, Peter and M{\"o}nich, Gerhard and Deuflhard, Peter and Felix, Roland}, title = {Systematic design of antennas for cylindrical 3D phased array hyperthermia applicator}, series = {Proc. IEEE Antennas Propagat. Soc. Intern. Symposium, July 11-16, 1999, Orlando, FL, USA,}, booktitle = {Proc. IEEE Antennas Propagat. Soc. Intern. Symposium, July 11-16, 1999, Orlando, FL, USA,}, pages = {1004 -- 1007}, year = {1999}, language = {en} } @incollection{WulkowDeuflhard1992, author = {Wulkow, Michael and Deuflhard, Peter}, title = {Towards an Efficient Computational Treatment of Heterogeneous Polymer Reactions}, series = {Computational Ordinary Differential Equations}, booktitle = {Computational Ordinary Differential Equations}, editor = {Fatunla, S.}, publisher = {University Press, Nigeria}, pages = {287 -- 306}, year = {1992}, language = {en} } @article{WustFahlingWlodarczyketal.2001, author = {Wust, Peter and Fahling, Horst and Wlodarczyk, Waldemar and Seebass, Martin and Gellermann, Johanna and Deuflhard, Peter and Nadobny, Johanna}, title = {Antenna arrays in the SIGMA-eye applicator}, series = {Med Phys}, volume = {28}, journal = {Med Phys}, number = {8}, pages = {1793 -- 1805}, year = {2001}, language = {en} } @misc{WustFelixDeuflhard1999, author = {Wust, Peter and Felix, Roland and Deuflhard, Peter}, title = {K{\"u}nstliches Fieber gegen Krebs}, publisher = {Spektrum der Wissenschaft, pp. 78-84 (December 1999).}, year = {1999}, language = {en} } @article{WustGellermannBeieretal.1998, author = {Wust, Peter and Gellermann, Johanna and Beier, J{\"u}rgen and Wegner, S. and Tilly, Wolfgang and Troger, J. and Stalling, Detlev and Oswald, H. and Hege, Hans-Christian and Deuflhard, Peter and Felix, Roland}, title = {Evaluation of segmentation algorithms for generation of patient models in radiofrequency hyperthermia}, series = {Phys Med Biol}, volume = {43}, journal = {Phys Med Biol}, pages = {3295 -- 3307}, year = {1998}, language = {en} } @article{WustNadobnyFelixetal.1989, author = {Wust, Peter and Nadobny, Johanna and Felix, Roland and Deuflhard, Peter and John, W. and Louis, Alfred}, title = {Numerical approaches to treatment planning in deep RF-hyperthermia}, series = {Strahlenther Onkol}, volume = {165}, journal = {Strahlenther Onkol}, number = {10}, pages = {751 -- 757}, year = {1989}, language = {en} } @article{WustNadobnyFelixetal.1991, author = {Wust, Peter and Nadobny, Johanna and Felix, Roland and Deuflhard, Peter and Louis, Alfred and John, W.}, title = {Strategies for optimized application of annular-phased-array systems in clinical hyperthermia}, series = {Int J Hyperthermia}, volume = {7}, journal = {Int J Hyperthermia}, pages = {157 -- 173}, year = {1991}, language = {en} } @inproceedings{WustNadobnyGellermannetal.1997, author = {Wust, Peter and Nadobny, Johanna and Gellermann, Johanna and Seebass, Martin and Stalling, Detlev and Hege, Hans-Christian and Deuflhard, Peter and Budach, Volker and Felix, Roland}, title = {Patient Models and Algorithms for Hyperthermia Planning}, series = {Proc. 16th Ann. Meeting Europ. Soc. Hyperthermic Oncology (ESHO-97), Berlin, Germany, April 1997}, booktitle = {Proc. 16th Ann. Meeting Europ. Soc. Hyperthermic Oncology (ESHO-97), Berlin, Germany, April 1997}, pages = {75}, year = {1997}, language = {en} } @article{SchaberOfenlochEhrigetal.2004, author = {Schaber, Karlheinz and Ofenloch, Oliver and Ehrig, Rainald and Deuflhard, Peter}, title = {Aerosolbildung in Gas/Fl{\"u}ssigkeits-Kontaktapparaten - Modellierungsstrategien und Simulation}, series = {Chemie Ingenieur Technik}, volume = {76}, journal = {Chemie Ingenieur Technik}, number = {9}, pages = {1358 -- 1359}, year = {2004}, language = {en} } @article{SreenivasaGellermannNadobnyetal.2003, author = {Sreenivasa, G. and Gellermann, Johanna and Nadobny, Johanna and Schlag, P. and Deuflhard, Peter and Felix, Roland and Wust, Peter}, title = {Clinical Use of the Hyperthermia Treatment Planning System Hyperplan to Predict Effectiveness and Toxicity}, series = {Int. J. Oncology Biol. Phys.}, volume = {55}, journal = {Int. J. Oncology Biol. Phys.}, number = {2}, pages = {407 -- 419}, year = {2003}, language = {en} } @inproceedings{StallingSeebassHegeetal.1996, author = {Stalling, Detlev and Seebass, Martin and Hege, Hans-Christian and Wust, Peter and Deuflhard, Peter and Felix, Roland}, title = {HyperPlan - an integrated system for treatment planning in regional hyperthermia}, series = {Proc. of the 7th Int. Congress on Hyperthermic Oncology, Rome, Italy, April 1996}, volume = {2}, booktitle = {Proc. of the 7th Int. Congress on Hyperthermic Oncology, Rome, Italy, April 1996}, editor = {Franconi, Cafiero}, pages = {552 -- 554}, year = {1996}, language = {en} } @article{WeberKubeWalteretal.2007, author = {Weber, Marcus and Kube, Susanna and Walter, Lionel and Deuflhard, Peter}, title = {Stable Computation of Probability Densities of Metastable Dynamical Systems}, series = {SIAM J. Multiscale Model. Simul.}, volume = {6}, journal = {SIAM J. Multiscale Model. Simul.}, number = {2}, pages = {396 -- 416}, year = {2007}, language = {en} } @article{WeiserSchielaDeuflhard2005, author = {Weiser, Martin and Schiela, Anton and Deuflhard, Peter}, title = {Asymptotic Mesh Independence of Newton's Method Revisited}, series = {SIAM J. Num. Anal.}, volume = {42}, journal = {SIAM J. Num. Anal.}, number = {5}, pages = {1830 -- 1845}, year = {2005}, language = {en} } @article{WeiserDeuflhardErdmann2007, author = {Weiser, Martin and Deuflhard, Peter and Erdmann, Bodo}, title = {Affine conjugate adaptive Newton methods for nonlinear elastomechanics}, series = {Opt. Meth. Softw.}, volume = {22}, journal = {Opt. Meth. Softw.}, number = {3}, pages = {413 -- 431}, year = {2007}, language = {en} } @article{WixSchaberOfenlochetal.2007, author = {Wix, A. and Schaber, Karlheinz and Ofenloch, O. and Ehrig, Rainald and Deuflhard, Peter}, title = {Simulation of Aerosol Formation in Gas-Liquid Contact Devices}, series = {Chem. Eng. Comm.}, volume = {194}, journal = {Chem. Eng. Comm.}, pages = {565 -- 577}, year = {2007}, language = {en} } @book{DeuflhardRoeblitz, author = {Deuflhard, Peter and R{\"o}blitz, Susanna}, title = {A guide to numerical modelling in systems biology}, volume = {12}, publisher = {Springer}, isbn = {978-3-319-20058-3}, doi = {10.1007/978-3-319-20059-0}, language = {en} } @incollection{DeuflhardDoesselLouisetal.2008, author = {Deuflhard, Peter and D{\"o}ssel, Olaf and Louis, Alfred and Zachow, Stefan}, title = {Mehr Mathematik wagen in der Medizin}, series = {acatech diskutiert, Produktionsfaktor Mathematik - Wie Mathematik Technik und Wirtschaft bewegt}, booktitle = {acatech diskutiert, Produktionsfaktor Mathematik - Wie Mathematik Technik und Wirtschaft bewegt}, publisher = {Springer}, doi = {10.1007/978-3-540-89435-3}, pages = {435 -- 459}, year = {2008}, language = {en} } @incollection{DeuflhardDoesselLouisetal.2010, author = {Deuflhard, Peter and D{\"o}ssel, Olaf and Louis, Alfred and Zachow, Stefan}, title = {More Mathematics into Medicine!}, series = {Production Factor Mathematics}, booktitle = {Production Factor Mathematics}, publisher = {Springer}, pages = {357 -- 378}, year = {2010}, language = {en} } @article{ZachowDeuflhard2008, author = {Zachow, Stefan and Deuflhard, Peter}, title = {Computergest{\"u}tzte Planung in der kraniofazialen Chirurgie}, series = {Face 01/08, Int. Mag. of Orofacial Esthetics}, journal = {Face 01/08, Int. Mag. of Orofacial Esthetics}, publisher = {Oemus Journale Leipzig}, pages = {43 -- 49}, year = {2008}, language = {en} } @article{WeiserZachowDeuflhard2010, author = {Weiser, Martin and Zachow, Stefan and Deuflhard, Peter}, title = {Craniofacial Surgery Planning Based on Virtual Patient Models}, series = {it - Information Technology}, volume = {52}, journal = {it - Information Technology}, number = {5}, publisher = {Oldenbourg Verlagsgruppe}, doi = {10.1524/itit.2010.0600}, pages = {258 -- 263}, year = {2010}, language = {en} } @article{ZachowHegeDeuflhard2006, author = {Zachow, Stefan and Hege, Hans-Christian and Deuflhard, Peter}, title = {Computer assisted planning in cranio-maxillofacial surgery}, series = {Journal of Computing and Information Technology}, volume = {14(1)}, journal = {Journal of Computing and Information Technology}, pages = {53 -- 64}, year = {2006}, language = {en} } @article{DeuflhardRoeblitzStoetzel, author = {Deuflhard, Peter and R{\"o}blitz, Susanna and St{\"o}tzel, Claudia}, title = {Mathematical Systems Biology at Zuse Institute Berlin (ZIB)}, series = {BioTOPics - Journal of Biotechnology in Berlin-Brandenburg}, volume = {39}, journal = {BioTOPics - Journal of Biotechnology in Berlin-Brandenburg}, language = {en} } @misc{DeuflhardWeber, author = {Deuflhard, Peter and Weber, Marcus}, title = {Mathematics without pain}, series = {MATHEON-Mathematics for Key Technologies}, volume = {1}, journal = {MATHEON-Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Horst, Ulrich and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Skutella, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, doi = {10.4171/137}, pages = {26 -- 28}, language = {en} } @misc{MoualeuNgangueRoeblitzEhrigetal., author = {Moualeu-Ngangue, Dany Pascal and R{\"o}blitz, Susanna and Ehrig, Rainald and Deuflhard, Peter}, title = {Parameter Identification for a Tuberculosis Model in Cameroon}, issn = {1438-0064}, doi = {10.1371/journal.pone.0120607}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-43087}, abstract = {A deterministic model of tuberculosis in sub-Saharan Africa in general and Cameroon in particular including lack of access to the treatment and weak diagnose capacity is designed and analyzed with respect to its transmission dynamics. The model includes both frequency- and density-dependent transmissions. It is shown that the model is mathematically well-posed and epidemiologically reasonable. Solutions are non-negative and bounded whenever the initial values are non-negative. A sensitivity analysis of model parameters is performed and most sensitive parameters of the model are identified using a state-of-the-art Gauss-Newton Method. In particular, parameters representing the proportion of individuals having access to medical facilities have a large impact on the dynamics of the disease. It has been shown that an increase of these parameter values over the time can significantly reduce the disease burden in the population within the next 15 years.}, language = {en} } @misc{MoualeuNgangueWeiserEhrigetal., author = {Moualeu-Ngangue, Dany Pascal and Weiser, Martin and Ehrig, Rainald and Deuflhard, Peter}, title = {Optimal control for a tuberculosis model with undetected cases in Cameroon}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-43142}, abstract = {This paper considers the optimal control of tuberculosis through education, diagnosis campaign and chemoprophylaxis of latently infected. A mathematical model which includes important components such as undiagnosed infectious, diagnosed infectious, latently infected and lost-sight infectious is formulated. The model combines a frequency dependent and a density dependent force of infection for TB transmission. Through optimal control theory and numerical simulations, a cost-effective balance of two different intervention methods is obtained. Seeking to minimize the amount of money the government spends when tuberculosis remain endemic in the Cameroonian population, Pontryagin's maximum principle is used to characterize the optimal control. The optimality system is derived and solved numerically using the forward-backward sweep method (FBSM). Results provide a framework for designing cost-effective strategies for diseases with multiple intervention methods. It comes out that combining chemoprophylaxis and education, the burden of TB can be reduced by 80 \% in 10 years}, language = {en} } @article{MoualeuNgangueRoeblitzEhrigetal., author = {Moualeu-Ngangue, Dany Pascal and R{\"o}blitz, Susanna and Ehrig, Rainald and Deuflhard, Peter}, title = {Parameter Identification in a Tuberculosis Model for Cameroon}, series = {PLOS ONE}, journal = {PLOS ONE}, doi = {10.1371/journal.pone.0120607}, abstract = {A deterministic model of tuberculosis in Cameroon is designed and analyzed with respect to its transmission dynamics. The model includes lack of access to treatment and weak diagnosis capacity as well as both frequency- and density-dependent transmissions. It is shown that the model is mathematically well-posed and epidemiologically reasonable. Solutions are non-negative and bounded whenever the initial values are non-negative. A sensitivity analysis of model parameters is performed and the most sensitive ones are identified by means of a state-of-the-art Gauss-Newton method. In particular, parameters representing the proportion of individuals having access to medical facilities are seen to have a large impact on the dynamics of the disease. The model predicts that a gradual increase of these parameters could significantly reduce the disease burden on the population within the next 15 years.}, language = {en} } @book{DeuflhardWeiser, author = {Deuflhard, Peter and Weiser, Martin}, title = {Numerische Mathematik 3. Adaptive L{\"o}sung partieller Differentialgleichungen}, edition = {2}, publisher = {de Gruyter}, isbn = {978-3-11-069168-9}, doi = {10.1515/9783110689655}, pages = {456}, language = {de} } @article{Deuflhard, author = {Deuflhard, Peter}, title = {The Grand Four. Affine Invariant Globalizations of Newton's Method}, series = {Vietnam Journal of Mathematics}, volume = {46}, journal = {Vietnam Journal of Mathematics}, number = {4}, doi = {10.1007/s10013-018-0301-3}, pages = {761 -- 777}, language = {en} } @misc{NaegelDeuflhardWittum, author = {N{\"a}gel, Arne and Deuflhard, Peter and Wittum, Gabriel}, title = {Efficient Stiff Integration of Density Driven Flow Problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-70891}, abstract = {The paper investigates the efficient use of a linearly implicit stiff integrator for the numerical solution of density driven flow problems. Upon choosing a one-step method of extrapolation type (code LIMEX), the use of full Jacobians and reduced approximations are discussed. Numerical experiments include nonlinear density flow problems such as diffusion from a salt dome (2D), a (modified) Elder problem (3D), the saltpool benchmark (3D) and a real life salt dome problem (2D). The arising linear equations are solved using either a multigrid preconditioner from the software package UG4 or the sparse matrix solver SuperLU.}, language = {en} } @misc{JeltschStrangDeuflhard, author = {Jeltsch, Rolf and Strang, Gilbert and Deuflhard, Peter}, title = {First SIAM-EMS Conference "Applied Mathematics in our Changing World" Berlin 2001 - Collection of Abstracts}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6452}, number = {01-19}, abstract = {Collection of abstracts of the first SIAM-EMS conference Applied Mathematics in our Changing World'' in Berlin, September 2-6, 2001.}, language = {en} } @misc{FranzoneDeuflhardErdmannetal., author = {Franzone, Piero Colli and Deuflhard, Peter and Erdmann, Bodo and Lang, Jens and Pavarino, Luca Franco}, title = {Adaptivity in Space and Time for Reaction-Diffusion Systems in Electrocardiology}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8649}, number = {05-30}, abstract = {Adaptive numerical methods in space and time are introduced and studied for multiscale cardiac reaction-diffusion models in three dimensions. The evolution of a complete heartbeat, from the excitation to the recovery phase, is simulated with both the anisotropic Bidomain and Monodomain models, coupled with either a variant of the simple FitzHugh-Nagumo model or the more complex phase-I Luo-Rudy ionic model. The simulations are performed with the {\sc kardos} library, that employs adaptive finite elements in space and adaptive linearly implicit methods in time. The numerical results show that this adaptive method successfully solves these complex cardiac reaction-diffusion models on three-dimensional domains of moderate sizes. By automatically adapting the spatial meshes and time steps to the proper scales in each phase of the heartbeat, the method accurately resolves the evolution of the intra- and extra-cellular potentials, gating variables and ion concentrations during the excitation, plateau and recovery phases.}, language = {en} } @article{DierkesRoeblitzWadeetal.2013, author = {Dierkes, Thomas and R{\"o}blitz, Susanna and Wade, Moritz and Deuflhard, Peter}, title = {Parameter identification in large kinetic networks with BioPARKIN}, series = {CoRR - Computing Research Repository - arXiv.org}, volume = {abs/1303.4928}, journal = {CoRR - Computing Research Repository - arXiv.org}, year = {2013}, language = {en} } @misc{DeuflhardErdmannRoitzschetal., author = {Deuflhard, Peter and Erdmann, Bodo and Roitzsch, Rainer and Lines, Glenn Terje}, title = {Adaptive Finite Element Simulation of Ventricular Fibrillation Dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9431}, number = {06-49}, abstract = {The dynamics of ventricular fibrillation caused by irregular excitation is simulated in the frame of the monodomain model with an action potential model due to Aliev-Panfilov for a human 3D geometry. The numerical solution of this multiscale reaction-diffusion problem is attacked by algorithms which are fully adaptive in both space and time (code library {\sc Kardos}). The obtained results clearly demonstrate an accurate resolution of the cardiac potential during the excitation and the plateau phases (in the regular cycle) as well as after a reentrant excitation (in the irregular cycle).}, language = {en} } @misc{DeuflhardHege, author = {Deuflhard, Peter and Hege, Hans-Christian}, title = {Die Vision einer individuellen quantitativen Medizin}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8805}, number = {05-47}, abstract = {Die Autoren schreiben dieses Papier aus der eingeschr{\"a}nkten Sicht der Mathematik und der Informationstechnik. Um den speziellen Beitrag dieser Disziplinen {\"u}berhaupt diskutieren zu k{\"o}nnen, sehen wir uns jedoch gezwungen, einen Rahmen abzustecken, den wir f{\"u}r das Jahr 2020 vorhersehen -- nach Wahrscheinlichkeit und aus unserem engeren fachlichen Blickwinkel. Vorab bitten wir schon einmal bei den medizinischen Fachleuten um Nachsicht, wenn wir uns in ihrem Revier allzu dillettantisch bewegen. Vielleicht f{\"o}rdert aber auch unser eingeschr{\"a}nkter Blickwinkel ansonsten unbedachte Aspekte zutage -- das hoffen wir zumindest.}, language = {de} } @misc{DeuflhardKleinReinefeldetal., author = {Deuflhard, Peter and Klein, Rupert and Reinefeld, Alexander and St{\"u}ben, Hinnerk}, title = {Power-User und Supercomputer}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4070}, number = {SC-99-19}, abstract = {Abstract-Sammlung zum gleichnamigen Workshop am ZIB vom 19.--20. Mai 1999}, language = {de} } @article{SchuetteFischerHuisingaetal.1999, author = {Sch{\"u}tte, Christof and Fischer, Alexander and Huisinga, Wilhelm and Deuflhard, Peter}, title = {A Direct Approach to Conformational Dynamics based on Hybrid Monte Carlo}, series = {J. Comp. Phys}, volume = {151}, journal = {J. Comp. Phys}, number = {1}, doi = {10.1006/jcph.1999.6231}, pages = {146 -- 168}, year = {1999}, language = {en} } @inproceedings{FischerSchuetteDeuflhardetal.2002, author = {Fischer, Alexander and Sch{\"u}tte, Christof and Deuflhard, Peter and Cordes, Frank}, title = {Hierarchical Uncoupling-Coupling of Metastable Conformations}, series = {Computational Methods for Macromolecules}, volume = {24}, booktitle = {Computational Methods for Macromolecules}, editor = {Schlick, T. and Gan, H.}, publisher = {Springer}, pages = {235 -- 259}, year = {2002}, language = {en} } @article{DeuflhardHuisingaFischeretal.2000, author = {Deuflhard, Peter and Huisinga, Wilhelm and Fischer, Alexander and Sch{\"u}tte, Christof}, title = {Identification of Almost Invariant Aggregates in Reversible Nearly Uncoupled Markov Chains}, series = {Lin. Alg. Appl.}, volume = {315}, journal = {Lin. Alg. Appl.}, number = {1-3}, doi = {10.1016/S0024-3795(00)00095-1}, pages = {39 -- 59}, year = {2000}, language = {en} } @inproceedings{SchuetteHuisingaDeuflhard2001, author = {Sch{\"u}tte, Christof and Huisinga, Wilhelm and Deuflhard, Peter}, title = {Transfer Operator Approach to Conformational Dynamics in Biomolecular Systems}, series = {Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems}, booktitle = {Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems}, editor = {Fiedler, B.}, publisher = {Springer}, pages = {191 -- 223}, year = {2001}, language = {en} } @inproceedings{DeuflhardSchuette2004, author = {Deuflhard, Peter and Sch{\"u}tte, Christof}, title = {Molecular Conformation Dynamics and Computational Drug Design}, series = {Applied Mathematics Entering the 21st Century}, volume = {116}, booktitle = {Applied Mathematics Entering the 21st Century}, editor = {Hill, James and Moore, Ross}, publisher = {SIAM}, pages = {91 -- 119}, year = {2004}, language = {en} } @inproceedings{DeuflhardSeebass1998, author = {Deuflhard, Peter and Seebaß, Martin}, title = {Adaptive Multilevel FEM as Decisive Tools in the Clinical Cancer Therapy Hyerthermia}, series = {Proc. Eleventh International Conference on Domain Decomposition Methods in Sciences and Engineering}, booktitle = {Proc. Eleventh International Conference on Domain Decomposition Methods in Sciences and Engineering}, editor = {Lai, Choi-Hong and Bjorstad, Petter and Cross, Mark and Widlund, Olof}, address = {Greenwich, UK}, pages = {410 -- 421}, year = {1998}, language = {en} } @incollection{DeuflhardWeiser1997, author = {Deuflhard, Peter and Weiser, Martin}, title = {Local inexact Newton multilevel FEM for nonlinear elliptic problems}, series = {Computational science for the 21st century}, booktitle = {Computational science for the 21st century}, editor = {et al. Bristeau, M.-O.}, publisher = {Chichester: John Wiley \& Sons.}, pages = {129 -- 138}, year = {1997}, language = {en} }