@misc{HochmuthDeuflhard2003, 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}, year = {2003}, 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{DeuflhardHochmuth2002, 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}, year = {2002}, 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{DeuflhardNowakWeiser2002, 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}, year = {2002}, 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{DeuflhardWeber2003, 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}, year = {2003}, 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{DeuflhardSchuette2003, 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}, year = {2003}, 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{GajewskiEdDeuflhardMarkowiched1991, 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}, year = {1991}, 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.1991, 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}, year = {1991}, 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{EhrigNowakDeuflhard1996, 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}, year = {1996}, 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{DeuflhardBoellingBott1993, 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}, year = {1993}, abstract = {Aus dem Inhalt: Vorwort; Leonhard Euler - aus der Zeit seines Wirkens in Berlin; Introductory Remarks.}, language = {de} } @misc{DeuflhardHegeSedlmayred1994, 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}, year = {1994}, 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{DeuflhardHegeSeebass2000, 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}, year = {2000}, 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{DeuflhardReich1997, 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}, year = {1997}, abstract = {The report contains the program and the collected abstracts of the 2nd International Symposium ``Algorithms for Macromolecular Modelling''.}, language = {en} } @misc{DeuflhardLouisSchlegeletal.1997, 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}, year = {1997}, 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{DeuflhardGottschewski1995, 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}, year = {1995}, 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{DeuflhardHohmann1990, 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}, year = {1990}, 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{Deuflhard1989, 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}, year = {1989}, 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{BraessDeuflhardLipnikov1999, 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}, year = {1999}, 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{Deuflhard1999, 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}, year = {1999}, 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{SchuetteHuisingaDeuflhard1999, 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}, year = {1999}, 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{GalliatHuisingaDeuflhard1999, 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}, year = {1999}, 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{Deuflhard1990, author = {Deuflhard, Peter}, title = {Zuses Werk weiterdenken. (Vortrag)}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4717}, number = {TR-90-07}, year = {1990}, language = {de} } @misc{DeuflhardHuisingaFischeretal.1998, 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}, year = {1998}, 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.1998, 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}, year = {1998}, 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{DeuflhardFrieseSchmidt1997, 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}, year = {1997}, 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} }