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 - CHAP A1 - Beck, Rudolf A1 - Deuflhard, Peter A1 - Wust, Peter A1 - Felix, Roland T1 - Electromagnetic Field Calculations by Finite Elements T2 - Proc. 16th Ann. Meeting Europ. Soc. Hyperthermic Oncology (ESHO-97), Berlin, Germany, April 1997 Y1 - 1997 SP - 77 ER - TY - CHAP A1 - Beck, Rudolf A1 - Hege, Hans-Christian A1 - Seebass, Martin A1 - Wust, Peter A1 - Deuflhard, Peter A1 - Felix, Roland ED - Franconi, Cafiero T1 - Adaptive finite element codes for numerical calculations in hyperthermia treatment planning T2 - Proc. of the 7th Int. Congress on Hyperthermic Oncology, Rome, Italy, April 1996 Y1 - 1996 VL - 2 SP - 515 EP - 517 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 -