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 - CHAP A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Roitzsch, Rainer A1 - Lourenco, Maria José A1 - Rosa, S. A1 - de Castro, C.A. A1 - Albuquerque, C. ED - Kim, M. ED - Ro, S. T1 - Simulation of the Transient Heating in an Unsymmetrical Coated Hot-Strip Sensor With a Self-Adaptive Finite Element Method T2 - Proc. 5th Asian Thermophysical Properties Conference Y1 - 1998 VL - 1 SP - 91 EP - 94 CY - Seoul, South Corea ER - TY - CHAP A1 - Lang, Jens A1 - Erdmann, Bodo A1 - Roitzsch, Rainer ED - Sydow, Achim T1 - Adaptive Time-Space Discretization for Combustion Problems T2 - 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics, Vol. 2, Numerical Mathematics Y1 - 1997 SP - 49 EP - 155 PB - Wissenschaft und Technik Verlag, Berlin ER - TY - CHAP A1 - Lang, Jens A1 - Erdmann, Bodo A1 - Roitzsch, Rainer ED - Lewis, R. T1 - Three-Dimensional Fully Adaptive Solution of Thermo-Diffusive Flame Propagation Problems T2 - Numerical Methods in Thermal Problems Y1 - 1997 SP - 857 EP - 862 PB - Pineridge Press, Swansea, UK ER - TY - JOUR A1 - Deuflhard, Peter A1 - Erdmann, Bodo A1 - Roitzsch, Rainer A1 - Lines, Glenn Terje T1 - Adaptive Finite Element Simulation of Ventricular Dynamics JF - J. Computing and Visualization in Science Y1 - 2009 VL - 12 SP - 201 EP - 205 ER - TY - CHAP A1 - Roitzsch, Rainer A1 - Lang, Jens A1 - Erdmann, Bodo T1 - The Benefits of Modularization T2 - Proc. 14th GAMM-Seminar Kiel on ’Concepts of Numerical Software Y1 - 1998 PB - did not appear ER - TY - GEN A1 - Lang, Jens A1 - Erdmann, Bodo A1 - Roitzsch, Rainer T1 - Three-Dimensional Fully Adaptive Solution of Thermo-Diffusive Flame Propagation Problems N2 - In this paper we present a self--adaptive finite element method to solve flame propagation problems in 3D. An implicit time integrator of Rosenbrock type is coupled with a multilevel approach in space. The proposed method is applied to an unsteady thermo--diffusive combustion model to demonstrate its potential for the solution of complicated problems. T3 - ZIB-Report - SC-97-18 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2879 ER - TY - GEN A1 - Ackermann, Jörg A1 - Erdmann, Bodo A1 - Roitzsch, Rainer T1 - A self-adaptive multilevel finite element method for the stationary Schrödinger equation in three space dimensions. N2 - An error controlled finite elemente method (FEM) for solving stationary Schrödinger equations in three space dimensions is proposed. The method is based on an adaptive space discretization into tetrahedra and local polynomial basis functions of order $p=1$--$5$ defined on these tetrahedra. According to a local error estimator the triangulation is automatically adapted to the solution. Numerical results for standard problems appearing in vibrational motion and molecular structure calculations are presented and discussed. Relative precisions better than 1e-8 are obtained. For equilateral H$_3^{++}$ the adaptive FEM turns out to be superior to global basis set expansions in the literature. Our precise FEM results exclude in a definite manner the stability or metastability of equilateral H$_3^{++}$ in its groundstate. T3 - ZIB-Report - SC-94-10 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1403 ER - TY - GEN A1 - Lourenco, Maria José A1 - Rosa, Samuel Costa S. A1 - Castro, Carlos Alberto Nieto de A1 - Albuquerque, C. A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Roitzsch, Rainer T1 - Simulation of the Transient Heating in an Unsymmetrical Coated Hot--Strip Sensor with a Self--Adaptive Finite Element Method N2 - The transient heating in an unsymmetrical coated hot--strip sensor was simulated with a self--adaptive finite element method. The first tests of this model show that it can determine with a small error the thermal conductivity of liquids, from the transient temperature rise in the hot--strip, deposited in a substrate and coated by an alumina spray. T3 - ZIB-Report - SC-98-22 Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3656 ER - TY - GEN A1 - Lang, Jens A1 - Erdmann, Bodo A1 - Roitzsch, Rainer T1 - Adaptive Time-Space Discretization for Combustion Problems N2 - We present a self--adaptive finite element method to solve combustion problems in 1D, 2D, and 3D. An implicit time integrator of Rosenbrock type is coupled with a multilevel approach in space. A posteriori error estimates are obtained by constructing locally higher order solutions involving all variables of the problem. Adaptive strategies such as step size control, spatial refinement and coarsening allow us to get economically an accurate solution. Various examples are presented to demonstrate practical applications of the proposed method. T3 - ZIB-Report - SC-97-40 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3094 ER - TY - GEN A1 - Roitzsch, Rainer A1 - Erdmann, Bodo A1 - Lang, Jens T1 - The Benefits of Modularization: from KASKADE to KARDOS N2 - KARDOS solves nonlinear evolution problems in 1, 2, and 3D. An adaptive multilevel finite element algorithm is used to solve the spatial problems arising from linearly implicit discretization methods in time. Local refinement and derefinement techniques are used to handle the development of the mesh over time. The software engineering techniques used to implement the modules of the KASKADE toolbox are reviewed and their application to the extended problem class is described. A notification system and dynamic construction of records are discussed and their values for the implementation of a mesh transfer operation are shown. The need for low-level and high--level interface elements of a module is discussed for the assembling procedure of KARDOS. At the end we will summarize our experiences. T3 - ZIB-Report - SC-98-15 Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3586 ER -