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 - 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 - Nowak, Ulrich A1 - Pöhle, Uwe A1 - Roitzsch, Rainer T1 - Eine graphische Oberfläche für numerische Programme N2 - Der Entwurf und die Implementierung des auf Tcl/Tk basierenden Werkzeugkastens ZGUI wird beschrieben und an einigen Beispielen erläutert. ZGUI unterstützt die Entwicklung einer graphischen Benutzeroberfläche (GUI) für die am ZIB erstellte numerische Software. Es sollen folgende Ziele erreicht werden: \begin{itemize} \item einfaches Ausprobieren anhand vordefinierter Testprobleme,\vspace*{-2mm} \item Kennenlernen numerischer Steuergrö\ss en und Verfahrensvarianten,\vspace*{-2mm} \item einfache Eingabe neuer Probleme,\vspace*{-2mm} \item einfache Nutzung graphischer Ausgabemöglichkeiten und\vspace*{-2mm} \item einheitliche Darstellung gleicher oder ähnlicher Optionen. \end{itemize} T3 - ZIB-Report - SC-96-13 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2242 ER - TY - GEN A1 - Fröhlich, Jochen A1 - Lang, Jens A1 - Roitzsch, Rainer T1 - Selfadaptive Finite Element Computations with Smooth Time Controller and Anisotropic Refinement N2 - We present Multilevel Finite Element computations for twodimensional reaction-diffusion systems modelling laminar flames. These systems are prototypes for extreme stiffness in time and space. The first of these two rather general features is accounted for by an improved control mechanism for the time step. The second one is reflected through very thin travelling reaction fronts for which we propose an anisotropic discretization by local directional refinement. T3 - ZIB-Report - SC-96-16 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2270 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 - Ackermann, Jörg A1 - Roitzsch, Rainer T1 - On a Two-Dimensional Multilevel Adaptive Finite Element Method for the Time-Independent Schrödinger-Equation. N2 - The subject of this study is a multilevel Finite Element Method based on an error estimator and step by step grid refinement as an universal tool for solving time--independent Schrödinger--eigenvalue problems. Numerical results for standard problems appearing in vibrational motion and molecular electronic structure calculations are given and discussed. T3 - ZIB-Report - SC-93-12 Y1 - 1993 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1086 ER - TY - GEN A1 - Kornhuber, Ralf A1 - Roitzsch, Rainer T1 - Adaptive Finite-Elemet- Methoden für konvektionsdominierte Randwertprobleme bei partiellen Differentialgleichungen. N2 - Ausgangspunkt bei der Behandlung konvektiv dominierter, elliptischer Probleme sind die bekannten hierarchischen Finite-Element-Methoden für den rein elliptischen Fall. Als stabile Erweiterung des Standard-Galerkin-Verfahrens wird das Stromlinien-Diffusions-Verfahren durch physikalische Überlegungen motiviert und kurz diskutiert. Anschließend zeigen wir, daß diese Methode erst in Verbindung mit einer hier erstmals vorgestellten lokalen Ausrichtung der Kanten wirksam eingesetzt werden kann. Zusammen mit einer ebenfalls neu entwickelten richtungsorientierten Verfeinerungsstrategie erhält man eine erheblich stabilere, genauere und schnellere Auflösung von Grenzschichten als mit herkömmlichen Methoden. T3 - ZIB-Report - SC-88-09 Y1 - 1989 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-170 ER - TY - GEN A1 - Kornhuber, Ralf A1 - Roitzsch, Rainer T1 - Self Adaptive Computation of the Breakdown Voltage of Planar pn-Junctions with Multistep Field Plates. N2 - The breakdown voltage highly depends on the electric field in the depletion area whose computation is the most time consuming part of the simulation. We present a self adaptive Finite Element Method which reduces dramatically the required computation time compared to usual Finite Difference Methods. A numerical example illustrates the efficiency and reliability of the algorithm. T3 - ZIB-Report - SC-91-02 Y1 - 1991 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-525 ER - TY - GEN A1 - Kornhuber, Ralf A1 - Roitzsch, Rainer T1 - On Adaptive Grid Refinement in the Presence of Internal or Boundary Layers. N2 - We propose an anisotropic refinement strategy which is specially designed for the efficient numerical resolution of internal and boundary layers. This strategy is based on the directed refinement of single triangles together with adaptive multilevel grid orientation. It is demonstrated by several numerical examples that compared to usual methods, the new anisotropic refinement ends up in more stable and more accurate solutions at much less computational cost. {\bf Keywords:} Adaptive finite elements, directed refinement, adaptive grid orientation, convection diffusion equation, internal and boundary layers. T3 - ZIB-Report - SC-89-05 KW - adaptive finite elements KW - directed refinement KW - adaptive grid orientation KW - convection diffusion equation KW - internal and boundary layers Y1 - 1989 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-230 ER - TY - GEN A1 - Kornhuber, Ralf A1 - Roitzsch, Rainer T1 - Self Adaptive FEM Simulation of Reverse Biased pn-Junctions. N2 - The potential distribution of reverse biased pn-junctions can be described by a double obstacle problem for the Laplacian. This problem is solved by a self adaptive Finite Element Method involving automatic termination criteria for the iterative solver, local error estimation and local mesh refinement. Special attention is paid to the efficient resolution of the geometries typically arising in semiconductor device simulation. The algorithm is applied to a reverse biased pn- junction with multi-step field plate and stop- electrode to illustrate its efficiency and reliability. T3 - ZIB-Report - SC-90-10 Y1 - 1990 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-389 ER -