TY - GEN A1 - Franzone, Piero Colli A1 - Deuflhard, Peter A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Pavarino, Luca Franco T1 - Adaptivity in Space and Time for Reaction-Diffusion Systems in Electrocardiology N2 - 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 model or the more complex phase-I Luo-Rudy ionic model. The simulations are performed with the {\sc kardos} library, that employs adaptive finite elements in space and adaptive linearly implicit methods in time. The numerical results show that this adaptive method successfully solves these complex cardiac reaction-diffusion models on three-dimensional domains of moderate sizes. By automatically adapting the spatial meshes and time steps to the proper scales in each phase of the heartbeat, the method accurately resolves the evolution of the intra- and extra-cellular potentials, gating variables and ion concentrations during the excitation, plateau and recovery phases. T3 - ZIB-Report - 05-30 KW - reaction-diffusion equations KW - cardiac Bidomain and Monodomain models KW - adaptive finite elements KW - adaptive time integration Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8649 ER - TY - CHAP A1 - Erdmann, Bodo A1 - Kober, C. A1 - Lang, Jens A1 - Deuflhard, Peter A1 - Zeilhofer, J. A1 - Sader, Robert T1 - Efficient and Reliable Finite Element Methods for Simulation of the Human Mandible T2 - proceedings of 9th Workshop on The Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields Y1 - 2002 CY - Ulm, Germany ER - TY - CHAP A1 - Lang, Jens A1 - Erdmann, Bodo A1 - Kober, Cornelia A1 - Deuflhard, Peter A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian ED - Alt, Walter ED - Hermann, Martin T1 - Effiziente und zuverlässige Finite-Elemente-Methoden zur Simulation des menschlichen Unterkiefers T2 - Berichte des IZWR - Interdisziplinäres Zentrum für Wissenschaftliches Rechnen Y1 - 2003 VL - 1 SP - 49 EP - 57 PB - Universität Jena CY - Germany ER - TY - GEN A1 - Deuflhard, Peter A1 - Lang, Jens A1 - Nowak, Ulrich T1 - Adaptive Algorithms in Dynamical Process Simulation N2 - Dynamical simulation of industrially relevant processes strongly advises the use of algorithms, which are {\em adaptive} both in time and in space discretization. The paper presents two alternatives: (a) a fully adaptive method of lines approach, which is based on finite difference methods and essentially applicable to 1D problems; (b) a fully adaptive Rothe method, which is based on a fast multilevel finite element method and applicable to 1D up to 3D. T3 - ZIB-Report - SC-95-16 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1823 ER - TY - JOUR A1 - Colli Franzone, Piero A1 - Deuflhard, Peter A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Pavarino, Luca Franco T1 - Adaptivity in Space and Time for Reaction-Diffusion Systems in Electrocardiology JF - SIAM J. Sc. Comp. Y1 - 2006 VL - 28 SP - 942 EP - 962 ER - TY - CHAP A1 - Deuflhard, Peter A1 - Lang, Jens A1 - Nowak, Ulrich ED - Neunzert, H. T1 - Recent Progress in Dynamical Process Simulation T2 - Progress in Industrial Mathematics, Proc. 8th Conference of the European Consortium for Mathematics in Industry (ECMI 94) Y1 - 1996 SP - 122 EP - 137 PB - Wiley & Teubner ER - TY - GEN A1 - Erdmann, Bodo A1 - Kober, Cornelia A1 - Lang, Jens A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian A1 - Deuflhard, Peter T1 - Efficient and Reliable Finite Element Methods for Simulation of the Human Mandible N2 - By computed tomography data (CT), the individual geometry of the mandible is quite well reproduced, also the separation between cortical and trabecular bone. Using anatomical knowledge about the architecture and the functional potential of the masticatory muscles, realistic situations were approximated. The solution of the underlying partial differential equations describing linear elastic material behaviour is provided by an adaptive finite element method. Estimations of the discretization error, local grid refinement, and multilevel techniques guarantee the reliability and efficiency of the method. T3 - ZIB-Report - 01-14 KW - mandible KW - sensitivity analysis KW - finite element method KW - adaptive grid refinement Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6403 ER -