TY - GEN A1 - Deuflhard, Peter A1 - (Chairs), Hyung Yong Ra T1 - Korean-German Bilateral Symposium on Scientific Computing N2 - Collection of abstracts of the Korean-German Bilateral Symposium on Scientific Computing, Berlin January 15/16, 2004 T3 - ZIB-Report - 04-02 KW - Abstracts Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7778 ER - TY - GEN A1 - Deuflhard, Peter A1 - Erdmann, Bodo A1 - Roitzsch, Rainer A1 - Lines, Glenn Terje T1 - Adaptive Finite Element Simulation of Ventricular Fibrillation Dynamics N2 - The dynamics of ventricular fibrillation caused by irregular excitation is simulated in the frame of the monodomain model with an action potential model due to Aliev-Panfilov for a human 3D geometry. The numerical solution of this multiscale reaction-diffusion problem is attacked by algorithms which are fully adaptive in both space and time (code library {\sc Kardos}). The obtained results clearly demonstrate an accurate resolution of the cardiac potential during the excitation and the plateau phases (in the regular cycle) as well as after a reentrant excitation (in the irregular cycle). T3 - ZIB-Report - 06-49 KW - reaction-diffusion equations KW - Aliev-Panfilov model KW - electrocardiology KW - adaptive finite elements KW - adaptive time integration KW - adaptive Rothe method Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9431 ER - TY - GEN A1 - Deuflhard, Peter A1 - Huisinga, Wilhelm A1 - Jahnke, Tobias A1 - Wulkow, Michael T1 - Adaptive Discrete Galerkin Methods Applied to the Chemical Master Equation N2 - \begin{abstract} In systems biology, the stochastic description of biochemical reaction kinetics is increasingly being employed to model gene regulatory networks and signalling pathways. Mathematically speaking, such models require the numerical solution of the underlying evolution equat ion, also known as the chemical master equation (CME). Up to now, the CME has almost exclusively been treated by Monte-Carlo techniques, the most prominent of which is the simulation algorithm suggest ed by Gillespie in 1976. Since this algorithm requires an update for each single reaction event, realizations can be computationally very costly. As an alternative, we here propose a novel approach, which focuses on the discrete partial differential equation (PDE) structure of the CME and thus allows to adopt ideas from adaptive discrete Galerkin methods (as designed by two of the present authors in 1989), which have proven to be highly efficient in the mathematical modelling of polyreaction kinetics. Among the two different options of discretizing the CME as a discrete PDE, the method of lines approach (first space, then time) and the Rothe method (first time, then space), we select the latter one for clear theoretical and algorithmic reasons. First numeric al experiments at a challenging model problem illustrate the promising features of the proposed method and, at the same time, indicate lines of necessary further research. \end{abstract} T3 - ZIB-Report - 07-04 KW - adaptive discrete Galerkin methods KW - adaptive Rothe method KW - discrete Chebyshev polynomials KW - stochastic reactions kinetics KW - chemical master equation Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9471 ER - TY - GEN A1 - Reinecke, Isabel A1 - Deuflhard, Peter T1 - A Complex Mathematical Model of the Human Menstrual Cycle N2 - This paper aims at presenting the complex coupled network of the human menstrual cycle to the interested community. Beyond the presently popular smaller models, where important network components arise only as extremely simplified source terms, we add: the GnRH pulse generator in the hypothalamus, receptor binding, and the biosynthesis in the ovaries. Simulation and parameter identification are left to a forthcoming paper. T3 - ZIB-Report - 06-18 Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9112 ER - TY - CHAP A1 - Gladilin, Evgeny A1 - Zachow, Stefan A1 - Deuflhard, Peter A1 - Hege, Hans-Christian ED - Mun, Seong T1 - Validation of a Linear Elastic Model for Soft Tissue Simulation in Craniofacial Surgery T2 - Proc. SPIE Medical Imaging 2001 Y1 - 2001 U6 - https://doi.org/10.1117/12.428061 VL - 4319 SP - 27 EP - 35 CY - San Diego, USA ER - TY - CHAP A1 - Gladilin, Evgeny A1 - Zachow, Stefan A1 - Hege, Hans-Christian A1 - Deuflhard, Peter T1 - FE-based heuristic approach for the estimation of person-specific facial mimics T2 - Proceedings of Euro-Par 2001: 5-th International Symposium on Computer Methods Y1 - 2001 CY - Rome, Italy ER - TY - JOUR A1 - Deuflhard, Peter A1 - Weiser, Martin A1 - Seebaß, Martin T1 - A New Nonlinear Elliptic Multilevel FEM Applied to Regional Hyperthermia JF - Comput. Visual. Sci. Y1 - 2000 U6 - https://doi.org/10.1007/PL00013546 VL - 3 SP - 1 EP - 6 ER - TY - JOUR A1 - Gellermann, Johanna A1 - Wust, Peter A1 - Stalling, Detlev A1 - Seebaß, Martin A1 - Nadobny, Jacek A1 - Hege, Hans-Christian A1 - Deuflhard, Peter A1 - Felix, Roland T1 - Clinical evaluation and verification of the hyperthermia treatment planning system HyperPlan JF - Int. J. Radiat. Oncol. Biol. Phys. Y1 - 2000 U6 - https://doi.org/10.1016/S0360-3016(00)00425-9 VL - 47(4) SP - 1145 EP - 1156 ER - TY - CHAP A1 - Gladilin, Evgeny A1 - Zachow, Stefan A1 - Hege, Hans-Christian A1 - Deuflhard, Peter T1 - Towards a Realistic Simulation of Individual Facial Mimics T2 - Vision Modeling and Visualization 2001 (VMV) Y1 - 2001 SP - 129 EP - 134 CY - Stuttgart, Germany ER - TY - CHAP A1 - Gladilin, Evgeny A1 - Zachow, Stefan A1 - Deuflhard, Peter A1 - Hege, Hans-Christian T1 - A Biomechanical Model for Soft Tissue Simulation in Craniofacial Surgery T2 - Medical Imaging and Augmented Reality (MIAR) Y1 - 2001 U6 - https://doi.org/10.1109/MIAR.2001.930276 SP - 137 EP - 141 CY - Hong Kong, China ER - TY - CHAP A1 - Gladilin, Evgeny A1 - Zachow, Stefan A1 - Deuflhard, Peter A1 - Hege, Hans-Christian T1 - Virtual Fibers: A Robust Approach for Muscle Simulation T2 - IX Mediterranean Conference on Medical and Biological Engineering and Computing (MEDICON) Y1 - 2001 SP - 961 EP - 964 CY - Pula, Croatia ER - TY - CHAP A1 - Gladilin, Evgeny A1 - Zachow, Stefan A1 - Deuflhard, Peter A1 - Hege, Hans-Christian T1 - Validierung eines linear elastischen Modells für die Weichgewebesimulation in der Mund-Kiefer-Gesichtschirurgie T2 - Bildverarbeitung für die Medizin (BVM) Y1 - 2001 SP - 57 EP - 61 CY - Lübeck, Germany ER - TY - CHAP A1 - Gladilin, Evgeny A1 - Zachow, Stefan A1 - Deuflhard, Peter A1 - Hege, Hans-Christian ED - Galloway, Robert T1 - Realistic prediction of individual facial emotion expressions for craniofacial surgery simulations T2 - Proc. SPIE medical Imaging 2003 Y1 - 2003 U6 - https://doi.org/10.1117/12.479584 VL - 5029 SP - 520 EP - 527 CY - San Diego, CA, USA ER -