Peter Deuflhard

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The topic of the present paper has 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(More)
The paper presents the mathematical concepts underlying the new adaptive finite element code KASKADE, which, in its present form, applies to linear scalar second-order 2-D elliptic problems on general domains. Starting point for the new development is the recent work on hierarchical finite element bases due to Yserentant (1986). It is shown that this(More)
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 Broy-den's "good" and "bad" update techniques play a special role — but should be associated with two different line search principles. For Broyden's "bad" update(More)
In this paper the well-known modified (underrelaxed, damped) Newton method is extended in such a way as to apply to the solution of ill-conditioned systems of nonlinear equations, i.e. systems having a "nearly singular" Jacobian at some iterate. A special technique also derived herein may be useful, if only bad initial guesses of the solution point are(More)
Despite the fact that more than 100 million women worldwide use birth control pills and that half of the world's population is concerned, the menstrual cycle has so far received comparatively little attention in the field of mathematical modeling. The term menstrual cycle comprises the processes of the control system in the female body that, under healthy(More)
Adaptive numerical methods in space and time are introduced and studied for multiscale cardiac reaction-diffusion models in three dimensions. The evolution of a complete heartbeat, from the excitation to the recovery phase, is simulated with both the anisotropic Bidomain and Monodomain models, coupled with either a variant of the simple FitzHugh-Nagumo(More)
Statistical models of shape are a promising approach for robust and automatic segmentation of medical image data. This work describes the construction of a statistical shape model of the pelvic bone. An interactive approach is proposed for solving the correspondence problem which is able to handle shapes of arbitrary topology, suitable for the genus 3(More)
A modelling approach for the realistic simulation of facial expressions of emotion in craniofacial surgery planning is presented. The method is different from conventional, non-physical techniques for character animation in computer graphics. A consistent physiological mechanism for facial expressions was assumed, which was the effect of contracting muscles(More)
Acknowledgements The work described in this thesis has been carried out from 1995 to 1998 at the department of Scientific Visualization at the Konrad-Zuse-Zentrum Berlin (ZIB). First of all, I would like to thank my tutors Prof. Dr. Peter Deuflhard and Hans-Christian Hege for the opportunity to graduate. They introduced me into an interesting new field(More)