@misc{DeuflhardErdmannRoitzschetal.2006, author = {Deuflhard, Peter and Erdmann, Bodo and Roitzsch, Rainer and Lines, Glenn Terje}, title = {Adaptive Finite Element Simulation of Ventricular Fibrillation Dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9431}, number = {06-49}, year = {2006}, abstract = {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).}, language = {en} } @misc{LangErdmannRoitzsch1997, author = {Lang, Jens and Erdmann, Bodo and Roitzsch, Rainer}, title = {Three-Dimensional Fully Adaptive Solution of Thermo-Diffusive Flame Propagation Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2879}, number = {SC-97-18}, year = {1997}, abstract = {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.}, language = {en} } @misc{NowakPoehleRoitzsch1996, author = {Nowak, Ulrich and P{\"o}hle, Uwe and Roitzsch, Rainer}, title = {Eine graphische Oberfl{\"a}che f{\"u}r numerische Programme}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2242}, number = {SC-96-13}, year = {1996}, abstract = {Der Entwurf und die Implementierung des auf Tcl/Tk basierenden Werkzeugkastens ZGUI wird beschrieben und an einigen Beispielen erl{\"a}utert. ZGUI unterst{\"u}tzt die Entwicklung einer graphischen Benutzeroberfl{\"a}che (GUI) f{\"u}r 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 Steuergr{\"o}\ss en und Verfahrensvarianten,\vspace*{-2mm} \item einfache Eingabe neuer Probleme,\vspace*{-2mm} \item einfache Nutzung graphischer Ausgabem{\"o}glichkeiten und\vspace*{-2mm} \item einheitliche Darstellung gleicher oder {\"a}hnlicher Optionen. \end{itemize}}, language = {de} } @misc{FroehlichLangRoitzsch1996, author = {Fr{\"o}hlich, Jochen and Lang, Jens and Roitzsch, Rainer}, title = {Selfadaptive Finite Element Computations with Smooth Time Controller and Anisotropic Refinement}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2270}, number = {SC-96-16}, year = {1996}, abstract = {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.}, language = {en} } @misc{AckermannErdmannRoitzsch1994, author = {Ackermann, J{\"o}rg and Erdmann, Bodo and Roitzsch, Rainer}, title = {A self-adaptive multilevel finite element method for the stationary Schr{\"o}dinger equation in three space dimensions.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1403}, number = {SC-94-10}, year = {1994}, abstract = {An error controlled finite elemente method (FEM) for solving stationary Schr{\"o}dinger 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.}, language = {en} } @misc{AckermannRoitzsch1993, author = {Ackermann, J{\"o}rg and Roitzsch, Rainer}, title = {On a Two-Dimensional Multilevel Adaptive Finite Element Method for the Time-Independent Schr{\"o}dinger-Equation.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1086}, number = {SC-93-12}, year = {1993}, abstract = {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 Schr{\"o}dinger--eigenvalue problems. Numerical results for standard problems appearing in vibrational motion and molecular electronic structure calculations are given and discussed.}, language = {en} } @misc{KornhuberRoitzsch1989, author = {Kornhuber, Ralf and Roitzsch, Rainer}, title = {Adaptive Finite-Elemet- Methoden f{\"u}r konvektionsdominierte Randwertprobleme bei partiellen Differentialgleichungen.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-170}, number = {SC-88-09}, year = {1989}, abstract = {Ausgangspunkt bei der Behandlung konvektiv dominierter, elliptischer Probleme sind die bekannten hierarchischen Finite-Element-Methoden f{\"u}r den rein elliptischen Fall. Als stabile Erweiterung des Standard-Galerkin-Verfahrens wird das Stromlinien-Diffusions-Verfahren durch physikalische {\"U}berlegungen 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 erh{\"a}lt man eine erheblich stabilere, genauere und schnellere Aufl{\"o}sung von Grenzschichten als mit herk{\"o}mmlichen Methoden.}, language = {de} } @misc{KornhuberRoitzsch1991, author = {Kornhuber, Ralf and Roitzsch, Rainer}, title = {Self Adaptive Computation of the Breakdown Voltage of Planar pn-Junctions with Multistep Field Plates.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-525}, number = {SC-91-02}, year = {1991}, abstract = {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.}, language = {en} } @misc{KornhuberRoitzsch1989, author = {Kornhuber, Ralf and Roitzsch, Rainer}, title = {On Adaptive Grid Refinement in the Presence of Internal or Boundary Layers.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-230}, number = {SC-89-05}, year = {1989}, abstract = {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.}, language = {en} } @misc{KornhuberRoitzsch1990, author = {Kornhuber, Ralf and Roitzsch, Rainer}, title = {Self Adaptive FEM Simulation of Reverse Biased pn-Junctions.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-389}, number = {SC-90-10}, year = {1990}, abstract = {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.}, language = {en} }