TY - GEN A1 - Wulkow, Michael A1 - Deuflhard, Peter T1 - Towards an Efficient Computational Treatment of Heterogeneous Polymer Reactions. N2 - 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. T3 - ZIB-Report - SC-90-01 Y1 - 1990 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-292 ER - TY - GEN A1 - Deuflhard, Peter T1 - Global Inexact Newton Methods for Very Large Scale Nonlinear Problems. N2 - 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). T3 - ZIB-Report - SC-90-02 Y1 - 1990 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-303 ER - TY - GEN A1 - Deuflhard, Peter A1 - Freund, R. A1 - Walter, Artur T1 - Fast Secant Methods for the Iterative Solution of Large Nonsymmetric Linear Systems. N2 - 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. T3 - ZIB-Report - SC-90-05 KW - nonsymmetric linear systems KW - secant method KW - rank-1 update KW - Broyden's method KW - line search KW - GMRES Y1 - 1990 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-330 ER - TY - GEN A1 - Deuflhard, Peter A1 - Nowak, Ulrich A1 - Wulkow, Michael T1 - Recent Developments in Chemical Computing. N2 - 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. T3 - ZIB-Report - SC-90-07 Y1 - 1990 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-359 ER - TY - GEN A1 - Deuflhard, Peter A1 - Potra, Florian T1 - Asymptotic Mesh Independence of Newton-Galerkin Methods via a Refined Mysovskii Theorem. N2 - 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. T3 - ZIB-Report - SC-90-09 Y1 - 1990 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-379 ER - TY - GEN A1 - Deuflhard, Peter A1 - Nowak, Ulrich T1 - Efficient Numerical Simulation and Identification of Large Chemical Reaction Systems. N2 - 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. T3 - ZIB-Report - SC-86-01 Y1 - 1986 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14 ER - TY - GEN A1 - Deuflhard, Peter T1 - Uniqueness Theorems for Stiff ODE Initial Value Problems. N2 - 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. T3 - ZIB-Report - SC-87-03 Y1 - 1987 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-53 ER - TY - GEN A1 - Deuflhard, Peter T1 - A Note on Extrapolation Methods for Second Order ODE Systems. N2 - 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. T3 - ZIB-Report - SC-87-05 Y1 - 1987 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-79 ER - TY - GEN A1 - Schütte, Christof A1 - Fischer, Alexander A1 - Huisinga, Wilhelm A1 - Deuflhard, Peter T1 - A Direct Approach to Conformational Dynamics based on Hybrid Monte Carlo N2 - 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. T3 - ZIB-Report - SC-98-45 KW - conformation KW - conformational dynamics KW - hybrid Monte Carlo KW - reweighting KW - essential degrees of freedom KW - transition probabilities KW - Markov operator Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3889 ER - TY - GEN A1 - Ehrig, Rainald A1 - Nowak, Ulrich A1 - Deuflhard, Peter T1 - Massively Parallel Linearly-Implicit Extrapolation Algorithms as a Powerful Tool in Process Simulation. N2 - 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. T3 - ZIB-Report - SC-97-43 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3127 ER - TY - GEN A1 - Lipnikov, Konstantin A1 - Deuflhard, Peter T1 - Domain Decomposition with Subdomain CCG for Material Jump Elliptic Problems. N2 - 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. T3 - ZIB-Report - SC-97-36 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3057 ER - TY - GEN A1 - Ehrig, Rainald A1 - Deuflhard, Peter T1 - GMERR - an Error Minimizing Variant of GMRES N2 - 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. T3 - ZIB-Report - SC-97-63 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3323 ER - TY - GEN A1 - Beck, Rudolf A1 - Deuflhard, Peter A1 - Hiptmair, Ralf A1 - Hoppe, Ronald H. W. A1 - Wohlmuth, Barbara T1 - Adaptive Multilevel Methods for Edge Element Discretizations of Maxwell's Equations N2 - 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. T3 - ZIB-Report - SC-97-66 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3356 ER - TY - GEN A1 - Deuflhard, Peter A1 - Seebass, Martin T1 - Adaptive Multilevel FEM as Decisive Tools in the Clinical Cancer Therapy Hyperthermia N2 - 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). T3 - ZIB-Report - SC-98-30 KW - hyperthermia KW - Maxwell's equations KW - nonlinear heat transfer KW - finite elements Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3739 ER - TY - GEN A1 - Deuflhard, Peter A1 - Weiser, Martin A1 - Seebass, Martin T1 - A New Nonlinear Elliptic Multilevel FEM Applied to Regional Hyperthermia N2 - 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. T3 - ZIB-Report - SC-98-35 KW - hyperthermia KW - nonlinear elliptic KW - multilevel FEM Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3785 ER - TY - GEN A1 - Weiser, Martin A1 - Schiela, Anton A1 - Deuflhard, Peter T1 - Asymptotic Mesh Independence of Newton's Method Revisited N2 - 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. T3 - ZIB-Report - 03-13 KW - mesh independence KW - nonlinear partial differential equations KW - Newton method KW - finite element method KW - collocation method Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7352 ER - TY - GEN A1 - Deuflhard, Peter T1 - A Comparison of Related Concepts in Computational Chemistry and Mathematics N2 - 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. T3 - ZIB-Report - 02-46 KW - dimension reduction KW - model reduction KW - QSSA KW - ILDM KW - reaction kinetics KW - polyreaction kinetics KW - Hamilton systems KW - conformations KW - metastability KW - d Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7138 ER - TY - GEN A1 - Deuflhard, Peter T1 - Adaptive Pseudo-transient Continuation for Nonlinear Steady State Problems N2 - 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. T3 - ZIB-Report - 02-14 KW - pseudo--transient continuation KW - linearly implicit KW - Euler discretization KW - stiff integration KW - contractivity of ordinary differential equations KW - lar Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6814 ER - TY - GEN A1 - Deuflhard, Peter T1 - From Molecular Dynamics to Conformational Dynamics in Drug Design N2 - 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. Schütte. 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. T3 - ZIB-Report - 02-20 KW - molecular dynamics KW - conformational dynamics KW - drug design KW - Hamiltonian dynamics KW - almost invariant sets KW - transition operator KW - Markov chain KW - Perro Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6878 ER - TY - GEN A1 - Hochmuth, Reinhard A1 - Deuflhard, Peter T1 - Multiscale Analysis for the Bio-Heat Transfer Equation N2 - 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. T3 - ZIB-Report - 03-08 KW - bio-heat equation KW - hyperthermia KW - homogenization KW - correctors KW - heat transfer KW - Robin boundary conditions Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7302 ER - TY - GEN A1 - Deuflhard, Peter A1 - Hochmuth, Reinhard T1 - Multiscale Analysis of Thermoregulation in the Human Microvascular System N2 - 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. T3 - ZIB-Report - 02-31 KW - bio-heat equation KW - hyperthermia KW - homogenization Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6985 ER - TY - GEN A1 - Deuflhard, Peter A1 - Nowak, Ulrich A1 - Weiser, Martin T1 - Affine Invariant Adaptive Newton Codes for Discretized PDEs N2 - 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. T3 - ZIB-Report - 02-33 KW - Affine invariant Newton methods KW - global Newton methods KW - inexact Newton methods KW - adaptive trust region methods KW - nonlinear partial differential equa Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7005 ER - TY - GEN A1 - Deuflhard, Peter A1 - Weber, Marcus T1 - Robust Perron Cluster Analysis in Conformation Dynamics N2 - 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. T3 - ZIB-Report - 03-19 KW - Markov chains KW - cluster algorithms KW - Perron cluster analysis KW - conformation dynamics Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7415 ER - TY - GEN A1 - Deuflhard, Peter A1 - Schütte, Christof T1 - Molecular Conformation Dynamics and Computational Drug Design N2 - 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. T3 - ZIB-Report - 03-20 KW - conformation dynamics KW - Monte Carlo methods KW - transfer operations KW - Hamiltonian dynamics KW - Smoluchowski dynamics KW - metastable sets KW - Perron cluster an Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7427 ER - TY - GEN A1 - Gajewski(Ed.), Herbert A1 - Deuflhard, Peter A1 - Markowich(ed.), A. T1 - Tagung NUMSIM '91 5.-08. Mai 1991. Collected Abstracts and Papers. N2 - NUMSIM 91 fand vom 6.-08. Mai 1991 im Wissenschaftlichen Kommunikations- & Konferenz- Zentrum der Humboldt-Universität in Gosen bei Berlin statt. Im Mittelpunkt dieses Seminars standen Probleme der numerischen Simulation von Ladungstransport- und Technologieprozessen der Mikro- und Optoelektronik. Es führte 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. T3 - ZIB-Report - TR-91-08 Y1 - 1991 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4838 ER - TY - GEN A1 - Deuflhard, Peter A1 - Nowak, Ulrich A1 - Pöhle, Uwe A1 - Schmidt, B. Ch. A1 - Weyer, J. T1 - Die Ausbreitung von HIV/AIDS in Ballungsgebieten. N2 - 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. T3 - ZIB-Report - TR-91-09 Y1 - 1991 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4844 ER - TY - GEN A1 - Ehrig, Rainald A1 - Nowak, Ulrich A1 - Deuflhard, Peter T1 - Highly scalable parallel linearly-implicit extrapolation algorithms N2 - 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. T3 - ZIB-Report - TR-96-11 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5405 ER - TY - GEN A1 - Deuflhard, Peter A1 - Bölling, Reinhard A1 - Bott, Raoul H. T1 - Materialien zur Euler-Vorlesung in Sanssouci. N2 - Aus dem Inhalt: Vorwort; Leonhard Euler - aus der Zeit seines Wirkens in Berlin; Introductory Remarks. T3 - ZIB-Report - TR-93-10 Y1 - 1993 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5029 ER - TY - GEN A1 - Deuflhard, Peter A1 - Hege, Hans-Christian A1 - Sedlmayr(ed.), E. T1 - Scientific Computing in der Theoretischen Physik. Collected Abstracts. N2 - 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. März 1994 am Fachbereich Mathematik und Informatik der Freien Universität 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 für partielle Differentialgleichungen sowie Monte-Carlo-Methoden und molekulardynamische Verfahren für Probleme der Statistischen Physik und Quantenfeldtheorie. Der Workshop fand ein äusserst positives Echo und führte über 70 Teilnehmer der verschiedenen Teilgebiete der Theoretischen Physik und ca. 50 Teilnehmer aus dem Bereich der Numerischen Mathematik zusammen. \originalTeX T3 - ZIB-Report - TR-94-01 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5068 ER - TY - GEN A1 - Deuflhard, Peter A1 - Hege, Hans-Christian A1 - Seebass, Martin T1 - Progress Towards a Combined MRI/Hyperthermia System N2 - 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. T3 - ZIB-Report - 00-07 KW - hyperthermia KW - medical therapy planning KW - applicator design KW - interventional MRI Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5755 ER - TY - GEN A1 - Deuflhard, Peter A1 - Reich, Sebastian T1 - 2nd International Symposium Algorithms for Macromolecular Modelling N2 - The report contains the program and the collected abstracts of the 2nd International Symposium ``Algorithms for Macromolecular Modelling''. T3 - ZIB-Report - TR-97-03 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5455 ER - TY - GEN A1 - Deuflhard, Peter A1 - Louis, Alfred A1 - Schlegel, W. A1 - Seebass, Martin T1 - Workshop "Scientific Computing in der Medizin" SCMED '97 N2 - Die Arbeitstagung \glqq Scientific Computing in der Medizin\grqq , kurz SCMED \grq 97, findet vom 22. - 23. September 1997 im neu errichteten Gebäude des Konrad-Zuse-Zentrums auf dem Dahlemer naturwissenschaftlichen Campus der Freien Universtät Berlin statt. T3 - ZIB-Report - TR-97-05 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5474 ER - TY - GEN A1 - Deuflhard, Peter A1 - Gottschewski, Jürgen T1 - Das Konrad-Zuse-Zentrum für Informationstechnik Berlin. Struktur, wissenschaftliches Konzept und Einbettung in die Region N2 - Die Arbeit beschreibt Konzept, Struktur und Ausstattung des ZIB. Übergeordnetes Ziel des ZIB ist die Beschleunigung des {\it Know-how Transfers} aus der mathematischen Grundlagenforschung über die Entwicklung von Algorithmen und Software bis hin zur tatsächlichen Nutzung in der Industrie. In der Tat ist Computational Mathematics inzwischen zu einer der wichtigsten {\it Schlüsseltechnologien} geworden, die nicht zuletzt im Zusammenhang mit der Standort-Diskussion eine wichtige Rolle spielt und vermehrt spielen wird. Dazu müssen Methodenentwicklung und Rechenzentrum auf höchstem Niveau sowie interdisziplinäre Forschung möglichst vereint in einer Institution mit enger Anbindung an ein universitäres Umfeld realisiert sein. Das Konrad-Zuse-Zentrum hat die wesentlichen Voraussetzungen als SC Zentrum bereits geschaffen; ein Ausbau zum HPSC Zentrum wäre eine natürliche Entwicklung - falls die Politik diese Chance rechtzeitig begreift! T3 - ZIB-Report - TR-95-12 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5274 ER - TY - GEN A1 - Deuflhard, Peter A1 - Hohmann, Andreas T1 - Einführung in die Numerische Mathematik. N2 - Diese Vorlesung ist eine Einführung 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 für Probleme aus den Naturwissenschaften mit Hilfe mathematischer Methoden. T3 - ZIB-Report - TR-90-06 Y1 - 1990 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4704 ER - TY - GEN A1 - Deuflhard, Peter T1 - Numerik von Anfangswertmethoden für gewöhnliche Differentialgleichungen. N2 - Das voliegende Skriptum entstand aus einer Vorlesung, die ich im WS 87/88 an der Freien Universität Berlin im Fachbereich Mathematik gehalten habe. Mein ursprüngliches Vorlesungsmanuskript wurde von Herrn F. Bornemann in weiten Teilen überarbeitet, reorganisiert und substantiell ergänzt. Der Inhalt stammt größtenteils aus Originalarbeiten jüngeren Datums. Darüberhinaus finden sich zahlreiche Teile, die aus meiner jahrelangen Beschäftigung mit dem Thema entstanden aber unpubliziert geblieben sind. Das Skriptum erhebt nicht den Anspruch, ein Lehrbuch zu sein. Es war zunächst als Ausarbeitung für meinen studentischen Hörerkreis sowie als internes Arbeitspapier für das ZIB bestimmt. Die Kunde von der bloßen Existenz eines solchen Skriptums hat jedoch zu einer derart regen Nachfrage geführt, daß es hiermit als Technischer Report des ZIB einer breiteren ffentlichkeit zugänglich gemacht werden soll. In der vorliegenden Form richtet es sich in erster Linie an Mathematiker; es soll sich jedoch auch für Naturwissenschaftler und Ingenieure eignen, die sich einen Einblick in den theoretischen und algorithmischen Hintergrund der von ihnen verwendeten wissenschaftlichen Software verschaffen wollen. T3 - ZIB-Report - TR-89-02 Y1 - 1989 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4580 ER - TY - GEN A1 - Braess, Dietrich A1 - Deuflhard, Peter A1 - Lipnikov, Konstantin T1 - A Subspace Cascadic Multigrid Method for Mortar Elements N2 - 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. T3 - ZIB-Report - SC-99-07 KW - Finite Elements KW - Rayleigh-Ritz and Galerkin Methods KW - Multigrid Methods KW - Domain Decomposition Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3954 ER - TY - GEN A1 - Deuflhard, Peter T1 - Differential Equations in Technology and Medicine. Computational Concepts, Adaptive Algorithms, and Virtual Labs N2 - 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 Schrödinger--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. T3 - ZIB-Report - SC-99-34 KW - differential equations: KW - ordinary KW - partial KW - countable KW - hamiltonian KW - finite element methods: KW - adaptive KW - multilevel KW - grid generation KW - medical t Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4223 ER - TY - GEN A1 - Schütte, Christof A1 - Huisinga, Wilhelm A1 - Deuflhard, Peter T1 - Transfer Operator Approach to Conformational Dynamics in Biomolecular Systems N2 - 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. T3 - ZIB-Report - SC-99-36 KW - Transfer operator KW - Markov process KW - Markov chain KW - molecular dynamics KW - biomolecular conformations KW - canonical ensemble KW - transition prohability KW - Ha Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4247 ER - TY - GEN A1 - Galliat, Tobias A1 - Huisinga, Wilhelm A1 - Deuflhard, Peter T1 - Self-Organizing Maps Combined with Eigenmode Analysis for Automated Cluster Identification N2 - 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. T3 - ZIB-Report - SC-99-38 KW - Self-Organizing Maps KW - cluster analysis Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4279 ER - TY - GEN A1 - Deuflhard, Peter T1 - Zuses Werk weiterdenken. (Vortrag) T3 - ZIB-Report - TR-90-07 Y1 - 1990 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4717 ER - TY - GEN A1 - Deuflhard, Peter A1 - Huisinga, Wilhelm A1 - Fischer, Alexander A1 - Schütte, Christof T1 - Identification of Almost Invariant Aggregates in Reversible Nearly Uncoupled Markov Chains N2 - 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. T3 - ZIB-Report - SC-98-03 KW - essential molecular dynamics KW - nearly reducible KW - nearly completely decomposable KW - nearly uncoupled Markov chain KW - almost invariant aggregates KW - trans Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3469 ER - TY - GEN A1 - Schütte, Christof A1 - Fischer, Alexander A1 - Huisinga, Wilhelm A1 - Deuflhard, Peter T1 - A Hybrid Monte Carlo Method for Essential Molecular Dynamics N2 - 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. T3 - ZIB-Report - SC-98-04 Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3474 ER - TY - GEN A1 - Deuflhard, Peter A1 - Friese, Tilmann A1 - Schmidt, Frank T1 - A Nonlinear Multigrid Eigenproblem Solver for the Complex Helmholtz Equation N2 - 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. T3 - ZIB-Report - SC-97-55 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3240 ER - TY - BOOK A1 - Deuflhard, Peter A1 - Bornemann, Folkmar A. T1 - Numerische Mathematik. II Y1 - 1994 PB - De Gruyter Lehrbuch. Berlin: de Gruyter ER - TY - BOOK A1 - Deuflhard, Peter A1 - Hohmann, Andreas T1 - Numerische Mathematik I. Eine algorithmisch orientierte Einführung.(Numerical mathematics I. An algorithmically oriented introduction) Y1 - 1993 PB - de Gruyter Lehrbuch. Berlin: Walter de Gruyter, ET - 2 ER - TY - JOUR A1 - Weiser, Martin A1 - Deuflhard, Peter T1 - Inexact central path following algorithms for optimal control problems JF - SIAM J. Control Opt. Y1 - 2007 VL - 46 IS - 3 SP - 792 EP - 815 ER - TY - CHAP A1 - Bader, G. A1 - Nowak, Ulrich A1 - Deuflhard, Peter ED - Aiken, R. T1 - An Advanced Simulation Package for Large Chemical Reaction Systems T2 - Stiff Computation. Proc. Intern. Conf. Park City, Utah/USA Y1 - 1985 PB - Oxford University Press ER - TY - CHAP A1 - Beck, Rudolf A1 - Deuflhard, Peter A1 - Hege, Hans-Christian A1 - Seebass, Martin A1 - Stalling, Detlev ED - Hege, Hans-Christian ED - Polthier, Konrad T1 - Numerical Algorithms and Visualization in Medical Treament Planning T2 - Visualization and Mathematics Y1 - 1997 SP - 303 EP - 328 PB - Springer-Verlag ER - TY - JOUR A1 - Beck, Rudolf A1 - Deuflhard, Peter A1 - Hiptmair, Ralf A1 - Hoppe, Ronald H. W. A1 - Wohlmuth, Barbara T1 - Adaptive multilevel methods for edge element discretizations of Maxwell’s equations JF - Surv. Math. Ind. Y1 - 1999 VL - 8 IS - 3-4 SP - 271 EP - 312 ER - TY - JOUR A1 - Bornemann, Folkmar A. A1 - Deuflhard, Peter T1 - The cascadic multigrid method for elliptic problems JF - Numer. Math. Y1 - 1996 VL - 75 SP - 135 EP - 152 ER - TY - CHAP A1 - Bornemann, Folkmar A. A1 - Deuflhard, Peter ED - Glowinski, J. R. ED - Widlund, Olof T1 - Cascadic Multigrid Methods T2 - Domain Decomposition Methods in Sciences and Engineering Y1 - 1996 SP - 205 EP - 212 PB - John Wiley & Sons Ltd ER - TY - JOUR A1 - Böck, J. A1 - Deuflhard, Peter A1 - Hoeft, A. A1 - Korb, H. A1 - Wolpers, H. A1 - Steinmann, J. A1 - Hellige, G. T1 - Thermal recovery after passage of the pulmonary circulation assessed by deconvolution JF - J. Appl. Physiol. Y1 - 1988 VL - 64 IS - 3 SP - 1210 EP - 1216 ER - TY - JOUR A1 - Böck, J. A1 - Deuflhard, Peter A1 - Hoeft, A. A1 - Korb, H. A1 - Steinmann, J. A1 - Wolpers, H. A1 - Hellige, G. T1 - Evaluation of monoexponential extrapolation of transpulmonary thermal-dye kinetics by use of a new model-free deconvolution algorithm JF - Med Instrum Y1 - 1988 VL - 22 IS - 1 SP - 20 EP - 28 ER - TY - JOUR A1 - Boer, H. Marike T. A1 - Stötzel, Claudia A1 - Röblitz, Susanna A1 - Deuflhard, Peter A1 - Veerkamp, Roel F. A1 - Woelders, Henri T1 - A simple mathematical model of the bovine estrous cycle JF - Journal of Theoretical Biology Y1 - 2011 U6 - https://doi.org/10.1016/j.jtbi.2011.02.021 VL - 278 IS - 1 SP - 20 EP - 31 ER - TY - JOUR A1 - Asam, P. A1 - Deuflhard, Peter A1 - Kaiser, Wolfgang T1 - Intensity Limiting and Stimulated Brillouin Scattering in Germanium JF - Physics Letters Y1 - 1968 VL - 27 A SP - 78 EP - 79 ER - TY - JOUR A1 - Braess, Dietrich A1 - Deuflhard, Peter A1 - Lipnikov, Konstantin T1 - A Subspace Cascadic Multigrid Method for Mortar Elements JF - Computing Y1 - 2002 VL - 69 SP - 205 EP - 225 ER - TY - JOUR A1 - Colli Franzone, Piero A1 - Deuflhard, Peter A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Pavarino, Luca Franco T1 - Adaptivity in Space and Time for Reaction-Diffusion Systems in Electrocardiology JF - SIAM J. Sc. Comp. Y1 - 2006 VL - 28 SP - 942 EP - 962 ER - TY - CHAP A1 - Deuflhard, Peter A1 - Schütte, Christof ED - Hill, James ED - Moore, Ross T1 - Molecular Conformation Dynamics and Computational Drug Design T2 - Applied Mathematics Entering the 21st Century Y1 - 2004 UR - ftp://ftp.zib.de/pub/zib-publications/reports/ZR-03-20.pdf IS - 116 SP - 91 EP - 119 PB - SIAM ER - TY - GEN A1 - Deuflhard, Peter A1 - Schütte, Christof A1 - Cordes, Frank A1 - Müller-Kurth, L. T1 - Konformationsdynamik. Mathematischer Entwurf hochspezifischer Biomoleküle Y1 - 1999 PB - In: D. Hömberg (ed.), 8. Veranstaltungsreihe Forschungspolitische Dialoge in Berlin: Angewandte Mathematik - die verborgene Schlüsseltechnologie, 30. April 1999, Konrad-Zuse-Zentrum Berlin, pp. 30-34 ER - TY - CHAP A1 - Deuflhard, Peter A1 - Seebass, Martin ED - Lai, Choi-Hong ED - Bjørstad, Petter E. ED - Cross, Mark ED - Widlund, Olof T1 - Adaptive Multilevel FEM as Decisive Tools in the Clinical Cancer Therapy Hyperthermia T2 - Procs. Eleventh International Conference on Domain Decomposition Methods Y1 - 1999 SP - 403 EP - 414 PB - DDM-org Press,Bergen ER - TY - CHAP A1 - Deuflhard, Peter A1 - Seebass, Martin A1 - Stalling, Detlev A1 - Beck, Rudolf A1 - Hege, Hans-Christian ED - Sydow, Achim T1 - Hyperthermia Treatment Planning in Clinical Cancer Therapy:Modelling, Simulation, and Visualization T2 - Computational Physics, Chemistry and Biology Y1 - 1997 VL - 3 PB - Wissenschaft und Technik Verlag CY - Plenary keynote talk, 15th IMACS World Congress 1997 on Scientific Computation, Modelling and Applied Mathematics ER - TY - CHAP A1 - Deuflhard, Peter A1 - Weiser, Martin ED - et al. Bristeau, M.-O. T1 - Local inexact Newton multilevel FEM for nonlinear elliptic problems T2 - Computational science for the 21st century Y1 - 1997 SP - 129 EP - 138 PB - Chichester: John Wiley & Sons. ER - TY - CHAP A1 - Deuflhard, Peter A1 - Weiser, Martin ED - et al. Hackbusch, Wolfgang T1 - Global inexact Newton multilevel FEM for nonlinear elliptic problems T2 - Multigrid methods V. proceedings of the 5th European multigrid conference, held in Stuttgart, Germany, October 1–4, 1996. Y1 - 1998 VL - 3 SP - 71 EP - 89 PB - Berlin: Springer ER - TY - JOUR A1 - Deuflhard, Peter A1 - Weiser, Martin A1 - Seebass, Martin T1 - A new nonlinear elliptic multilevel FEM in clinical cancer therapy planning JF - Comput. Vis. Sci. Y1 - 2000 VL - 3 SP - 115 EP - 120 ER - TY - BOOK A1 - Deuflhard, Peter A1 - Weiser, Martin T1 - Numerische Mathematik 3 Y1 - 2011 PB - de Gruyter, Berlin ER - TY - BOOK A1 - Deuflhard, Peter A1 - Weiser, Martin T1 - Adaptive numerical solution of PDEs Y1 - 2012 PB - de Gruyter CY - Berlin ER - TY - JOUR A1 - Deuflhard, Peter A1 - Weiser, Martin A1 - Zachow, Stefan T1 - Mathematics in Facial Surgery JF - AMS Notices Y1 - 2006 VL - 53 IS - 9 SP - 1012 EP - 1016 ER - TY - BOOK A1 - Deuflhard, Peter A1 - Bornemann, Folkmar A. T1 - Numerische Mathematik. II Y1 - 2002 PB - de Gruyter Lehrbuch. Berlin: de Gruyter ET - 2 ER - TY - CHAP A1 - Deuflhard, Peter A1 - Dellnitz, M. A1 - Junge, Oliver A1 - Schütte, Christof ED - Deuflhard, Peter T1 - Computation of essential molecular dynamics by subdivision techniques T2 - Computational molecular dynamics Y1 - 1998 VL - 4 SP - 98 EP - 115 PB - Berlin: Springer. ER - TY - JOUR A1 - Deuflhard, Peter A1 - Engl, H. A1 - Scherzer, O. T1 - A convergence analysis of iterative methods for the solution of nonlinear ill-posed problems under affinely invariant conditions JF - Inverse Probl. Y1 - 1998 VL - 14 SP - 1081 EP - 1106 ER - TY - JOUR A1 - Deuflhard, Peter A1 - Fiedler, P. A1 - Kunkel, P. T1 - Efficient numerical pathfollowing beyond critical points JF - SIAM J. Numer. Anal. Y1 - 1987 VL - 24 SP - 912 EP - 927 ER - TY - CHAP A1 - Deuflhard, Peter A1 - Fiedler, B. A1 - Kunkel, P. T1 - Numerical Pathfollowing Beyond Critical Points in ODE Models T2 - Large Scale Scientific Computing Y1 - 1987 SP - 97 EP - 113 PB - Birkhäuser/Boston ER - TY - JOUR A1 - Deuflhard, Peter A1 - Freund, R. A1 - Walter, Artur T1 - Fast secant methods for the iterative solution of large nonsymmetric linear systems JF - IMPACT Comput. Sci. Eng. Y1 - 1990 VL - 2 SP - 244 EP - 276 ER - TY - JOUR A1 - Deuflhard, Peter A1 - Hairer, E. A1 - Zugck, J. T1 - One-step and extrapolation methods for differential-algebraic systems JF - Numer. Math. Y1 - 1987 VL - 51 SP - 501 EP - 516 ER - TY - CHAP A1 - Deuflhard, Peter ED - Sydow, Achim T1 - Computational Mathematics as Key Technology T2 - Systems Analysis Modelling Simulation (SAMS),Proc. IMACS Symposium on Systems Analysis and Simulation, Berlin, 26-30 June 1995 Y1 - 1995 VL - 18-19 SP - 19 EP - 26 PB - Gordon and Breach Science Publishers SA ER - TY - GEN A1 - Deuflhard, Peter ED - et al. Begehr, H. T1 - Fast algorithms, fast computers: The Konrad-Zuse-Zentrum Berlin (ZIB) T2 - Mathematics in Berlin Y1 - 1998 SP - 183 EP - 184 PB - Basel: Birkhäuser ER - TY - CHAP A1 - Deuflhard, Peter ED - Davis, W. ED - Chu, M. ED - Dolan, P. ED - McConnell, J. ED - Noris, L. ED - Ortiz, E. ED - Plemmons, R. ED - Ridgeway, D. ED - Stewart, W. ED - York, Jr., J. ED - Doggett, W. ED - Gellai, B. ED - Gsponer, A. ED - Prioli, C. T1 - Commentary on Cornelius Lanczos’s Extended Boundary Value Problems T2 - Cornelius Lanczos Collected Published Papers with Commentaries Y1 - 1999 VL - VI SP - 3 EP - 650–3–653 PB - North Carolina State University, Raleigh ER - TY - CHAP A1 - Deuflhard, Peter ED - Davis, W. ED - Chu, M. ED - Dolan, P. ED - McConnell, J. ED - Noris, L. ED - Ortiz, E. ED - Plemmons, R. ED - Ridgeway, D. ED - Stewart, W. ED - York, Jr., J. ED - Doggett, W. ED - Gellai, B. ED - Gsponer, A. ED - Prioli, C. T1 - Commentary on Cornelius Lanczos’s Solution of Ordinary Differential Equations by Trigonometric Interpolation T2 - Cornelius Lanczos Collected Published Papers with Commentaries Y1 - 1999 VL - VI SP - 3 EP - 667–3–669 PB - North Carolina State University, Raleigh ER - TY - CHAP A1 - Deuflhard, Peter A1 - Ackermann, Jörg ED - Dikshit, H. ED - Michelli, C. T1 - Adaptive Discrete Galerkin-Methods for Macromolecular Processes T2 - Advances in Computational Mathematics Y1 - 1994 SP - 59 EP - 72 PB - World Scientific Publishing Co. Inc. ER - TY - CHAP A1 - Deuflhard, Peter A1 - Ackermann, Jörg ED - et al. Dikshit, H. T1 - Adaptive discrete Galerkin methods for macromolecular processes T2 - proceedings of the conference on advances in computational mathematics, held at New Delhi, India, January 5-9, 1993. Singapore Y1 - 1994 SP - 59 EP - 72 ER - TY - CHAP A1 - Deuflhard, Peter A1 - Apostolescu, Victor T1 - A Study of the Gauss-Newton Method for the Solution of Nonlinear Least Squares Problems T2 - Special Topics of Applied Mathematics Y1 - 1980 SP - 129 EP - 150 PB - Amsterdam: North-Holland Publ. ER - TY - CHAP A1 - Deuflhard, Peter A1 - Bader, G. T1 - Multiple Shooting Techniques Revisited T2 - Numerical Treatment of Inverse Problems in Differential and Integral Equations Y1 - 1983 VL - 2 SP - 74 EP - 94 PB - Boston: Birkhäuser ER - TY - CHAP A1 - Deuflhard, Peter A1 - Bader, G. A1 - Nowak, Ulrich T1 - LARKIN - a Software Package for the Numerical Simulation of LARge Systems Arising in Chemical Reaction KINetics T2 - Modelling of Chemical Reaction Systems Y1 - 1981 VL - 18 SP - 38 EP - 55 PB - Springer Verlag ER - TY - BOOK A1 - Deuflhard, Peter A1 - Bornemann, Folkmar A. T1 - Scientific computing with ordinary differential equations. Transl. from the German by Werner C. Rheinboldt T3 - Texts in Applied Mathematics Y1 - 2002 VL - 42 PB - New York, NY: Springer ER - TY - JOUR A1 - Deuflhard, Peter A1 - Krause, Rolf A1 - Ertel, Susanne T1 - A Contact-Stabilized Newmark Method for Dynamical Contact Problems JF - International Journal for Numerical Methods in Engineering Y1 - 2007 VL - 73 IS - 9 SP - 1274 EP - 1290 ER - TY - CHAP A1 - Deuflhard, Peter A1 - Lang, Jens A1 - Nowak, Ulrich ED - Neunzert, H. T1 - Recent Progress in Dynamical Process Simulation T2 - Progress in Industrial Mathematics, Proc. 8th Conference of the European Consortium for Mathematics in Industry (ECMI 94) Y1 - 1996 SP - 122 EP - 137 PB - Wiley & Teubner ER - TY - JOUR A1 - Deuflhard, Peter A1 - Leinen, P. A1 - Yserentant, H. T1 - Concepts of an adaptive hierarchical finite element code JF - IMPACT Comput. Sci. Eng. Y1 - 1989 VL - 1 IS - 1 SP - 3 EP - 35 ER - TY - JOUR A1 - Deuflhard, Peter A1 - Lipnikov, Konstantin T1 - Domain decomposition with subdomain CCG for material jump elliptic problems JF - East-West J. Numer. Math. Y1 - 1998 VL - 6 IS - 2 SP - 81 EP - 100 ER - TY - GEN A1 - Deuflhard, Peter A1 - Mehrmann, Volker T1 - Numerical analysis and scientific computing in key technologies Y1 - 2002 SP - 9 EP - 19 ER - TY - CHAP A1 - Deuflhard, Peter A1 - Nowak, Ulrich ED - Deuflhard, Peter ED - Engquist, B. T1 - Extrapolation integrators for quasilinear implicit ODEs. T2 - Large scale scientific computing, Proc. Meet., Oberwolfach/FRG 1985, Y1 - 1987 VL - 7 SP - 37 EP - 50 PB - Boston-Basel-Stuttgart: Birkhäuser ER - TY - JOUR A1 - Deuflhard, Peter A1 - Nowak, Ulrich A1 - Wulkow, Michael T1 - Recent Developments in Chemical Computing JF - Computers in Chemical Engineering Y1 - 1990 VL - 14 SP - 1249 EP - 1258 ER - TY - JOUR A1 - Deuflhard, Peter A1 - Pesch, H.-J. A1 - Rentrop, P. T1 - A Modified Continuation Method for the Numerical Solution of Nonlinear Two-Point Boundary Value Problems by Shooting Techniques JF - Numer. Math. Y1 - 1976 VL - 26 SP - 327 EP - 343 ER - TY - JOUR A1 - Deuflhard, Peter A1 - Potra, Florian T1 - Asymptotic Mesh Independence for Newton-Galerkin Methods via a Refined Mysovskii Theorem JF - SIAM J. Numer. Anal. Y1 - 1992 VL - 29 IS - 5 SP - 1395 EP - 1412 ER - TY - JOUR A1 - Deuflhard, Peter A1 - Sautter, W. T1 - On Rank-Deficient Pseudoinverses JF - Lin. Alg. Appl. Y1 - 1980 VL - 29 SP - 91 EP - 111 ER - TY - JOUR A1 - Deuflhard, Peter A1 - Heindl, G. T1 - Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods JF - SIAM J. Numer. Anal. Y1 - 1979 VL - 16 SP - 1 EP - 10 ER - TY - CHAP A1 - Deuflhard, Peter A1 - Heroth, Jörg ED - et al. Keil, Frerich T1 - Dynamic dimension reduction in ODE models T2 - Scientific computing in chemical engineering Y1 - 1996 SP - 29 EP - 43 PB - Berlin: Springer-Verlag ER - TY - CHAP A1 - Deuflhard, Peter A1 - Heroth, Jörg A1 - Maas, Ulrich T1 - Towards Dynamic Dimension Reduction in Reactive Flow Problems T2 - Proc. 3rd Workshop on Modelling of Chemical Reaction Systems Y1 - 1996 CY - Heidelberg ER - TY - CHAP A1 - Deuflhard, Peter A1 - Hege, Hans-Christian A1 - Seebass, Martin ED - Grönemeyer, W. T1 - Progress Towards a Combined MRI Hyperthermia System T2 - Proc. Second Int. Congress HIGH CARE 2000, Bochum Y1 - 2000 ER - TY - BOOK A1 - Deuflhard, Peter A1 - Hohmann, Andreas T1 - Numerische Mathematik. I Y1 - 2002 PB - de Gruyter Lehrbuch. Berlin: de Gruyter ET - 3 ER - TY - BOOK A1 - Deuflhard, Peter A1 - Hohmann, Andreas T1 - Numerical analysis in modern scientific computing. An introduction. 2nd revised ed. T3 - Texts in Applied Mathematics Y1 - 2003 VL - 43 PB - New York, NY: Springer ER - TY - JOUR A1 - Deuflhard, Peter A1 - Hochmuth, Reinhard T1 - Multiscale analysis of thermoregulation in the human microvascular system JF - Math. Methods Appl. Sci. Y1 - 2004 VL - 27 IS - 8 SP - 971 EP - 989 PB - Wiley Verlag ER -