@article{DeuflhardErdmannRoitzschetal.2009, author = {Deuflhard, Peter and Erdmann, Bodo and Roitzsch, Rainer and Lines, Glenn Terje}, title = {Adaptive Finite Element Simulation of Ventricular Dynamics}, volume = {12}, journal = {J. Computing and Visualization in Science}, pages = {201 -- 205}, year = {2009}, language = {en} } @inproceedings{RoitzschLangErdmann1998, author = {Roitzsch, Rainer and Lang, Jens and Erdmann, Bodo}, title = {The Benefits of Modularization}, booktitle = {Proc. 14th GAMM-Seminar Kiel on 'Concepts of Numerical Software}, publisher = {did not appear}, year = {1998}, language = {en} } @article{HuisingaBestRoitzschetal.1999, author = {Huisinga, Wilhelm and Best, Christoph and Roitzsch, Rainer and Sch{\"u}tte, Christof and Cordes, Frank}, title = {From Simulation Data to Conformational Ensembles}, volume = {20}, journal = {J. Comp. Chem.}, number = {16}, doi = {10.1002/(SICI)1096-987X(199912)20:16<1760::AID-JCC8>3.0.CO;2-2}, pages = {1760 -- 1774}, year = {1999}, 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} } @misc{LourencoRosaCastroetal.1998, author = {Lourenco, Maria Jos{\´e} and Rosa, Samuel Costa S. and Castro, Carlos Alberto Nieto de and Albuquerque, C. and Erdmann, Bodo and Lang, Jens and Roitzsch, Rainer}, title = {Simulation of the Transient Heating in an Unsymmetrical Coated Hot--Strip Sensor with a Self--Adaptive Finite Element Method}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3656}, number = {SC-98-22}, year = {1998}, abstract = {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.}, language = {en} } @misc{LangErdmannRoitzsch1997, author = {Lang, Jens and Erdmann, Bodo and Roitzsch, Rainer}, title = {Adaptive Time-Space Discretization for Combustion Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3094}, number = {SC-97-40}, year = {1997}, abstract = {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.}, language = {en} } @misc{RoitzschErdmannLang1998, author = {Roitzsch, Rainer and Erdmann, Bodo and Lang, Jens}, title = {The Benefits of Modularization: from KASKADE to KARDOS}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3586}, number = {SC-98-15}, year = {1998}, abstract = {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.}, language = {en} } @misc{HuisingaBestCordesetal.1998, author = {Huisinga, Wilhelm and Best, Christoph and Cordes, Frank and Roitzsch, Rainer and Sch{\"u}tte, Christof}, title = {From Simulation Data to Conformational Ensembles: Structure and Dynamics based Methods}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3797}, number = {SC-98-36}, year = {1998}, abstract = {Statistical methods for analyzing large data sets of molecular configurations within the chemical concept of molecular conformations are described. The strategies are based on dependencies between configurations of a molecular ensemble; the article concentrates on dependencies induces by a) correlations between the molecular degrees of freedom, b) geometrical similarities of configurations, and c) dynamical relations between subsets of configurations. The statistical technique realizing aspect a) is based on an approach suggested by {\sc Amadei et al.} (Proteins, 17 (1993)). It allows to identify essential degrees of freedom of a molecular system and is extended in order to determine single configurations as representatives for the crucial features related to these essential degrees of freedom. Aspects b) and c) are based on statistical cluster methods. They lead to a decomposition of the available simulation data into {\em conformational ensembles} or {\em subsets} with the property that all configurations in one of these subsets share a common chemical property. In contrast to the restriction to single representative conformations, conformational ensembles include information about, e.g., structural flexibility or dynamical connectivity. The conceptual similarities and differences of the three approaches are discussed in detail and are illustrated by application to simulation data originating from a hybrid Monte Carlo sampling of a triribonucleotide.}, language = {en} } @misc{ErdmannLangRoitzsch2002, author = {Erdmann, Bodo and Lang, Jens and Roitzsch, Rainer}, title = {KARDOS - User"s Guide}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7096}, number = {02-42}, year = {2002}, abstract = {The adaptive finite element code {\sc Kardos} solves nonlinear parabolic systems of partial differential equations. It is applied to a wide range of problems from physics, chemistry, and engineering in one, two, or three space dimensions. The implementation is based on the programming language C. Adaptive finite element techniques are employed to provide solvers of optimal complexity. This implies a posteriori error estimation, local mesh refinement, and preconditioning of linear systems. Linearely implicit time integrators of {\em Rosenbrock} type allow for controlling the time steps adaptively and for solving nonlinear problems without using {\em Newton's} iterations. The program has proved to be robust and reliable. The user's guide explains all details a user of {\sc Kardos} has to consider: the description of the partial differential equations with their boundary and initial conditions, the triangulation of the domain, and the setting of parameters controlling the numerical algorithm. A couple of examples makes familiar to problems which were treated with {\sc Kardos}. We are extending this guide continuously. The latest version is available by network: {\begin{rawhtml} Downloads. \end{rawhtml}}}, language = {en} } @misc{NowakPoehleRoitzschetal.1996, author = {Nowak, Ulrich and P{\"o}hle, Uwe and Roitzsch, Rainer and Werk, Roland}, title = {ZGUI-Handbuch}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5397}, number = {TR-96-10}, year = {1996}, abstract = {In diesem Handbuch werden die Bausteine zum Aufbau einer graphischen Benutzeroberfl{\"a}che mit {\tt ZGUI} beschrieben. Auf der einen Seite stehen die Tcl/Tk--Prozeduren, die die graphischen Elemente definieren. Die Beschreibung der Anwendung der Prozeduren und der Interaktionen der Elemente bildet den ersten Teil des Handbuches. Auf der anderen Seite stehen die Anforderungen an Anwendungen, die mit einer {\tt ZGUI}--Benutzeroberlf{\"a}che gesteuert werden sollen. Hier findet man im Handbuch die Beschreibung der Anwendungsprogrammierschnittstelle (application programming interface, API).}, language = {de} } @misc{ErdmannLangRoitzsch1993, author = {Erdmann, Bodo and Lang, Jens and Roitzsch, Rainer}, title = {Kaskade Manual - Version 2.0.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4970}, number = {TR-93-05}, year = {1993}, abstract = {The KASKADE toolbox defines an interface to a set of C subroutines which can be used to implement adaptive multilevel Finite Element Methods solving systems of elliptic equations in two and three space dimensions. The manual contains the description of the data structures and subroutines. The main modules of the toolbox are a runtime environment, triangulation and node handling, assembling, direct and iterative solvers for the linear systems, error estimators, refinement strategies, and graphic utilities. Additionally, we included appendices on the basic command language interface, on file formats, and on the definition of the partial differential equations which can be solved. The software is available on the ZIB ftp--server {\tt elib} in the directory {\tt pub/kaskade}. TR 93--5 supersedes TR 89--4 and TR 89--05.}, language = {en} } @misc{BeckErdmannRoitzsch1995, author = {Beck, Rudolf and Erdmann, Bodo and Roitzsch, Rainer}, title = {KASKADE 3.0 User's Guide}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5269}, number = {TR-95-11}, year = {1995}, abstract = {KASKADE 3.x was developed for the solution of partial differential equations in one, two, or three space dimensions. Its object-oriented implementation concept is based on the programming language C++\$\,\$.~Adaptive finite element techniques are employed to provide solution procedures of optimal computational complexity. This implies a posteriori error estimation, local mesh refinement and multilevel preconditioning. The program was designed both as a platform for further developments of adaptive multilevel codes and as a tool to tackle practical problems. Up to now we have implemented scalar problem types like stationary or transient heat conduction. The latter one is solved with the Rothe method, enabling adaptivity both in space and time. Some nonlinear phenomena like obstacle problems or two-phase Stefan problems are incorporated as well. Extensions to vector-valued functions and complex arithmetic are provided. This report helps to work with KASKADE Especially we \begin{itemize} \setlength{\parskip}{0ex} \item [{\bf --}] study a set of examples, \item [{\bf --}] explain how to define a user's problem and \item [{\bf --}] introduce a graphical user interface. \end{itemize} We are extending this guide continuously. The latest version is available by network.}, language = {en} } @misc{BeckErdmannRoitzsch1995, author = {Beck, Rudolf and Erdmann, Bodo and Roitzsch, Rainer}, title = {KASKADE 3.0 - An Object Oriented Adaptive Finite Element Code}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5199}, number = {TR-95-04}, year = {1995}, abstract = {KASKADE 3.0 was developed for the solution of partial differential equations in one, two, or three space dimensions. Its object-oriented implementation concept is based on the programming language C++\$\,\$.~Adaptive finite element techniques are employed to provide solution procedures of optimal computational complexity. This implies a posteriori error estimation, local mesh refinement and multilevel preconditioning. The program was designed both as a platform for further developments of adaptive multilevel codes and as a tool to tackle practical problems. Up to now we have implemented scalar problem types like stationary or transient heat conduction. The latter one is solved with the Rothe method, enabling adaptivity both in space and time. Some nonlinear phenomena like obstacle problems or two-phase Stefan problems are incorporated as well. Extensions to vector-valued functions and complex arithmetic are provided. \%Such free boundary problems ... We have implemented several iterative solvers for both symmetric and unsymmetric systems together with multiplicative and additive multilevel preconditioners. Systems arising from the nonlinear problems can be solved with lately developed monotone multigrid methods. \%An object-oriented concept was chosen for KASKADE~3.0, based on the programming \%language C++\$\,\$. This should provide the desired extensibilty and clearly \%reflect the structure of the code. \%A direct sparse matrix solver (Harwell MA28) is included.}, language = {en} } @misc{Roitzsch1989, author = {Roitzsch, Rainer}, title = {KASKADE Programmer's Manual.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4617}, number = {TR-89-05}, year = {1989}, abstract = {The Programmers Manual contains the documentation of the C-KASKADE implementation. KASKADE is an adaptive finite element code (see SC ). The interfaces of all modules are described.}, language = {en} } @misc{Roitzsch1989, author = {Roitzsch, Rainer}, title = {KASKADE User's Manual.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4605}, number = {TR-89-04}, year = {1989}, abstract = {The Users Manual contains an introduction to the usage of the C-KASKADE implementation. KASKADE is an adaptive finite element code (see SC ). The manual includes a description of all commands, a simple recipe to define a new problem by changing the KASKADE source and a complete example.}, language = {en} } @misc{RoitzschKornhuber1990, author = {Roitzsch, Rainer and Kornhuber, Ralf}, title = {BOXES - a Program to Generate Triangulations from a Rectangular Domain Description.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4738}, number = {TR-90-09}, year = {1990}, abstract = {BOXES computes a triangulation from a 2D domain description which consists of an arbitrary set of rectangles. Each rectangle may have attributes to control the triangulating process, define subdomain classes, or specify boundary conditions. The output of the program can be used as a coarse grid for KASKADE or one of its variants. Additional features are extensive checking of the user input, graphical display, and simple editing.}, language = {en} } @misc{BornemannErdmannRoitzsch1991, author = {Bornemann, Folkmar A. and Erdmann, Bodo and Roitzsch, Rainer}, title = {KASKADE - Numerical Experiments.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4762}, number = {TR-91-01}, year = {1991}, abstract = {The C-implementation of KASKADE, an adaptive solver for linear elliptic differential equations in 2D, is object of a set of numerical experiments to analyze the use of resources (time and memory) with respect to numerical accuracy. We study the dependency of the reliability, robustness, and efficiency of the program from the parameters controlling the algorithm.}, language = {en} } @article{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}, volume = {101}, journal = {J. Chem. Phys.}, pages = {7643 -- 7650}, year = {1994}, language = {en} } @inproceedings{BeckErdmannRoitzsch1997, author = {Beck, Rudolf and Erdmann, Bodo and Roitzsch, Rainer}, title = {An Object-Oriented Adaptive Finite Element Code}, booktitle = {Modern Software Tools for Scientific Computing}, editor = {Arge, Erlend and Bruaset, Are Magnus and Langtangen, Hans Petter}, publisher = {Birkh{\"a}user, Boston}, pages = {105 -- 124}, year = {1997}, language = {en} } @misc{GalliatDeuflhardRoitzschetal.2000, author = {Galliat, Tobias and Deuflhard, Peter and Roitzsch, Rainer and Cordes, Frank}, title = {Automatic Identification of Metastable Conformations via Self-Organized Neural Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6197}, number = {00-51}, year = {2000}, abstract = {As has been shown recently, the identification of metastable chemical conformations leads to a Perron cluster eigenvalue problem for a reversible Markov operator. Naive discretization of this operator would suffer from combinatorial explosion. As a first remedy, a pre-identification of essential degrees of freedom out of the set of torsion angles had been applied up to now. The present paper suggests a different approach based on neural networks: its idea is to discretize the Markov operator via self-organizing (box) maps. The thus obtained box discretization then serves as a prerequisite for the subsequent Perron cluster analysis. Moreover, this approach also permits exploitation of additional structure within embedded simulations. As it turns out, the new method is fully automatic and efficient also in the treatment of biomolecules. This is exemplified by numerical results.}, language = {en} }