@article{DeuflhardHuisingaFischeretal.2000, author = {Deuflhard, Peter and Huisinga, Wilhelm and Fischer, Alexander and Sch{\"u}tte, Christof}, title = {Identification of Almost Invariant Aggregates in Reversible Nearly Uncoupled Markov Chains}, volume = {315}, journal = {Lin. Alg. Appl.}, number = {1-3}, doi = {10.1016/S0024-3795(00)00095-1}, pages = {39 -- 59}, year = {2000}, language = {en} } @inproceedings{DeuflhardDellnitzJungeetal.1999, author = {Deuflhard, Peter and Dellnitz, M. and Junge, Oliver and Sch{\"u}tte, Christof}, title = {Computation of Essential Molecular Dynamics by Subdivision Techniques}, volume = {4}, booktitle = {Computational Molecular Dynamics}, editor = {Deuflhard, Peter and Hermans, J. and Leimkuhler, Benedict and Marks, A. and Reich, Sebastian and Skeel, R.}, publisher = {Springer}, pages = {98 -- 115}, year = {1999}, language = {en} } @article{SchuetteFischerHuisingaetal.1999, author = {Sch{\"u}tte, Christof and Fischer, Alexander and Huisinga, Wilhelm and Deuflhard, Peter}, title = {A Direct Approach to Conformational Dynamics based on Hybrid Monte Carlo}, volume = {151}, journal = {J. Comp. Phys}, number = {1}, doi = {10.1006/jcph.1999.6231}, pages = {146 -- 168}, year = {1999}, language = {en} } @inproceedings{DeuflhardSchuette2004, author = {Deuflhard, Peter and Sch{\"u}tte, Christof}, title = {Molecular Conformation Dynamics and Computational Drug Design}, volume = {116}, booktitle = {Applied Mathematics Entering the 21st Century}, editor = {Hill, James and Moore, Ross}, publisher = {SIAM}, pages = {91 -- 119}, year = {2004}, language = {en} } @inproceedings{FischerSchuetteDeuflhardetal.2002, author = {Fischer, Alexander and Sch{\"u}tte, Christof and Deuflhard, Peter and Cordes, Frank}, title = {Hierarchical Uncoupling-Coupling of Metastable Conformations}, volume = {24}, booktitle = {Computational Methods for Macromolecules}, editor = {Schlick, T. and Gan, H.}, publisher = {Springer}, pages = {235 -- 259}, year = {2002}, language = {en} } @inproceedings{SchuetteHuisingaDeuflhard2001, author = {Sch{\"u}tte, Christof and Huisinga, Wilhelm and Deuflhard, Peter}, title = {Transfer Operator Approach to Conformational Dynamics in Biomolecular Systems}, booktitle = {Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems}, editor = {Fiedler, B.}, publisher = {Springer}, pages = {191 -- 223}, year = {2001}, language = {en} } @article{DeuflhardRoeblitzStoetzel2010, author = {Deuflhard, Peter and R{\"o}blitz, Susanna and St{\"o}tzel, Claudia}, title = {Mathematical Systems Biology at Zuse Institute Berlin (ZIB)}, volume = {39}, journal = {BioTOPics - Journal of Biotechnology in Berlin-Brandenburg}, year = {2010}, language = {en} } @misc{Deuflhard2017, author = {Deuflhard, Peter}, title = {The Grand Four}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66038}, year = {2017}, abstract = {This paper gives a concise synopsis and some new insights concerning four affine invariant globalizations of the local Newton method. The invariance classes include: affine covariance, affine contravariance, affine conjugacy, and affine similarity. In view of algorithmic robustness, each of these classes of algorithms is particularly suitable for some corresponding problem class.}, language = {en} } @misc{DeuflhardHerothMaas1996, author = {Deuflhard, Peter and Heroth, J{\"o}rg and Maas, Ulrich}, title = {Towards Dynamical Dimension Reduction in Reactive Flow Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2383}, number = {SC-96-27}, year = {1996}, abstract = {The paper addresses the possibilities of reducing the overall number of degrees of freedom in large scale reactive flow computations. Attention focusses on the dimension reduction technique ILDM due to {\sc Maas and Pope}, which treats certain automatically detected fast dynamic components as algebraic equations (so-called slow manifold). In earlier papers, the dimension of the reduction had been kept constant throughout each computation. Recently, a mathematically sound and nevertheless cheap dimension monitor for the chemistry part only has been suggested by {\sc Deuflhard and Heroth}. The present paper reports about first steps taken towards the implementation of that monitor into a flame code. Moreover, a sparse grid storage scheme is advocated and analyzed in view of the construction of efficient table look--ups for nested manifolds.}, language = {en} } @misc{DeuflhardWeiser1996, author = {Deuflhard, Peter and Weiser, Martin}, title = {Local Inexact Newton Multilevel FEM for Nonlinear Elliptic Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2401}, number = {SC-96-29}, year = {1996}, abstract = {The finite element setting for nonlinear elliptic PDEs directly leads to the minimization of convex functionals. Uniform ellipticity of the underlying PDE shows up as strict convexity of the arising nonlinear functional. The paper analyzes computational variants of Newton's method for convex optimization in an affine conjugate setting, which reflects the appropriate affine transformation behavior for this class of problems. First, an affine conjugate Newton--Mysovskikh type theorem on the local quadratic convergence of the exact Newton method in Hilbert spaces is given. It can be easily extended to inexact Newton methods, where the inner iteration is only approximately solved. For fixed finite dimension, a special implementation of a Newton--PCG algorithm is worked out. In this case, the suggested monitor for the inner iteration guarantees quadratic convergence of the outer iteration. In infinite dimensional problems, the PCG method may be just formally replaced by any Galerkin method such as FEM for linear elliptic problems. Instead of the algebraic inner iteration errors we now have to control the FE discretization errors, which is a standard task performed within any adaptive multilevel method. A careful study of the information gain per computational effort leads to the result that the quadratic convergence mode of the Newton--Galerkin algorithm is the best mode for the fixed dimensional case, whereas for an adaptive variable dimensional code a special linear convergence mode of the algorithm is definitely preferable. The theoretical results are then illustrated by numerical experiments with a {\sf NEWTON--KASKADE} algorithm.}, language = {en} } @misc{DeuflhardSeebassStallingetal.1997, author = {Deuflhard, Peter and Seebass, Martin and Stalling, Detlev and Beck, Rudolf and Hege, Hans-Christian}, title = {Hyperthermia Treatment Planning in Clinical Cancer Therapy: Modelling, Simulation and Visualization}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2958}, number = {SC-97-26}, year = {1997}, abstract = {\noindent The speaker and his co-workers in Scientific Computing and Visualization have established a close cooperation with medical doctors at the Rudolf--Virchow--Klinikum of the Humboldt University in Berlin on the topic of regional hyperthermia. In order to permit a patient--specific treatment planning, a special software system ({\sf\small HyperPlan}) has been developed. \noindent A mathematical model of the clinical system ({\it radio frequency applicator with 8 antennas, water bolus, individual patient body}) involves Maxwell's equations in inhomogeneous media and a so--called bio--heat transfer PDE describing the temperature distribution in the human body. The electromagnetic field and the thermal phenomena need to be computed at a speed suitable for the clinical environment. An individual geometric patient model is generated as a quite complicated tetrahedral ``coarse'' grid (several thousands of nodes). Both Maxwell's equations and the bio--heat transfer equation are solved on that 3D--grid by means of {\em adaptive} multilevel finite element methods, which automatically refine the grid where necessary in view of the required accuracy. Finally optimal antenna parameters for the applicator are determined . \noindent All steps of the planning process are supported by powerful visualization methods. Medical images, contours, grids, simulated electromagnetic fields and temperature distributions can be displayed in combination. A number of new algorithms and techniques had to be developed and implemented. Special emphasis has been put on advanced 3D interaction methods and user interface issues.}, language = {en} }