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 - TY - GEN A1 - Lang, Jens T1 - Adaptive Incompressible Flow Computations with Linearly Implicit Time Discretization and Stabilized Finite Elements N2 - Fully adaptive solutions of imcompressible flow problems employing the discretization sequence first in time then in space are presented. The time discretization is done by linearly implicit one--step methods possibly of high order with automatic step size control. A posteriori error estimates for the stabilized finite element discretization in space are obtained by solving local Dirichlet problems with higher accuracy. Once those estimates have been computed, we are able to control time and space grids with respect to required tolerances and necessary computational work. The devised method is applied to two benchmark problems in 2D. T3 - ZIB-Report - SC-98-16 KW - Incompressible Flow KW - Adaptive Stabilized Finite Element KW - Linearly Implicit Time Discretization Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3599 ER - TY - GEN A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Roitzsch, Rainer T1 - KARDOS - User"s Guide N2 - 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}} T3 - ZIB-Report - 02-42 KW - nonlinear parabolic systems KW - Rosenbrock methods KW - adaptivity in time and space Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7096 ER - TY - GEN A1 - Lang, Jens T1 - KARDOS - KAskade Reaction Diffusion One-dimensional System. N2 - A software package for the adaptive solution of time--dependent reaction--diffusion systems and linear elliptic systems in one space dimension is presented. The used algorithm is based on fundamental arguments in J.~Lang, A.~Walter: {\it A Finite Element Method Adaptive in Space and Time for Nonlinear Reaction--Diffusion Systems.} IMPACT of Computing in Science and Engineering, 4, p.~269--314 (1992). Here, only brief outlines of the algorithm are given. This software package is based on the KASKADE toolbox B.~Erdmann, J.~Lang, R.~Roitzsch: {\it KASKADE -- Manual.} To appear as Technical Report TR 93--5, Konrad--Zuse--Zentrum (ZIB) (1993). T3 - ZIB-Report - TR-93-09 Y1 - 1993 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5019 ER - TY - GEN A1 - Lang, Jens A1 - Merz, Wilhelm T1 - Two-Dimensional Adaptive Simulation of Dopant Diffusion in Silicon N2 - One important step in the fabrication of silicon-based integrated circuits is the creation of semiconducting areas by diffusion of dopant impurities into silicon. Complex models have been developed to investigate the redistribution of dopants and point defects. In general, numerical analysis of the resulting PDEs is the central tool to assess the modelling process. We present an adaptive approach which is able to judge the quality of the numerical approximation and which provides an automatic mesh improvement. Using linearly implicit methods in time and multilevel finite elements in space, we are able to integrate efficiently the arising reaction-drift-diffusion equations with high accuracy. Two different diffusion processes of practical interest are simulated. T3 - ZIB-Report - 00-03 KW - Semiconductor devices KW - nonlinear reaction-drift-diffusion equations KW - mesh control KW - multilevel finite elements KW - Rosenbrock methods Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5716 ER - TY - GEN A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Roitzsch, Rainer T1 - Kaskade Manual - Version 2.0. N2 - 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. T3 - ZIB-Report - TR-93-05 Y1 - 1993 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4970 ER - TY - GEN A1 - Seewald, Frank A1 - Pollei, Anja A1 - Kraume, Matthias A1 - Mittelbach, Walter A1 - Lang., Jens T1 - Numerical Calculation of the Heat Transfer in an Adsorption Energy Storage with KARDOS N2 - A new seasonal energy storage for thermal solar systems has been developed on the basis of an adsorption-desorption process. Design and optimization of this storage will be supported by numerical simulations of heat and mass transfer with KARDOS. This paper focuses on the unsteady heat transfer during the major operating step of energetic discharge of the storage, which is characterized by conductive heat transfer in the fixed bed and a strong heat source caused by the adsorption enthalpy. Results are interpreted concerning the influence of variations in the parameter set. The method of implementation of the differential equation will be shown as well as the post-processing and gridwriting programs. T3 - ZIB-Report - SC-99-04 Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3927 ER - TY - GEN A1 - Lang, Jens T1 - An Adaptive Finite Element Method for Convection-Diffusion Problems by Interpolation Techniques. N2 - For adaptive solution of convection- difussion problems with the streamline-diffusion finite element method, an error estimator based on interpolation techniques is developed. It can be shown that for correctness of this error estimator a restriction of the maximum angle is to be sufficient. Compared to usual methods, the adaptive process leads to more accurate solutions at much less computational cost. Numerical tests are enclosed. {\bf Keywords: } Adaptive finite elements, convection- diffusion equation, internal and boundary layers, streamline-diffusion. {\bf Subject Classifications:} AMS(MOS): 65N15, 65N30 T3 - ZIB-Report - TR-91-04 Y1 - 1991 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4795 ER - TY - GEN A1 - Lang, Jens A1 - Erdmann, Bodo A1 - Seebass, Martin T1 - Impact of Nonlinear Heat Transfer on Temperature Control in Regional Hyperthermia N2 - We describe an optimization process specially designed for regional hyperthermia of deep seated tumors in order to achieve desired steady--state temperature distributions. A nonlinear three--dimensional heat transfer model based on temperature--dependent blood perfusion is applied to predict the temperature. Using linearly implicit methods in time and adaptive multilevel finite elements in space, we are able to integrate efficiently the instationary nonlinear heat equation with high accuracy. Optimal heating is obtained by minimizing an integral object function which measures the distance between desired and model predicted temperatures. A sequence of minima is calculated from successively improved constant--rate perfusion models employing a damped Newton method in an inner iteration. We compare temperature distributions for two individual patients calculated on coarse and fine spatial grids and present numerical results of optimizations for a Sigma 60 Applicator of the BSD 2000 Hyperthermia System. T3 - ZIB-Report - SC-97-73 Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3426 ER - TY - GEN A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Seebass, Martin T1 - Optimization of Temperature Distributions for Regional Hyperthermia Based on a Nonlinear Heat Transfer Model N2 - We describe an optimization process specially designed for regional hyperthermia of deap seated tumors in order to achieve desired steady--state temperature distributions. A nonlinear three--dimensional heat--transfer model based on temperature--dependent blood perfusion is applied to predict the temperature. Optimal heating is obtained by minimizing an integral object function which measures the distance between desired and model predicted temperatures. Sequential minima are calculated from successively improved constant--rate perfusion models employing a damped Newton method in an inner iteration. Numerical results for a Sigma 60 applicator are presented. This work has been supported by Deutsche Forschungsgemeinschaft (DFG) within the Sonderforschungsbereich 273 \glqq Hyperthermie: Methodik und Klinik \grqq . T3 - ZIB-Report - SC-97-59 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3283 ER - TY - GEN A1 - Kober, Cornelia A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian T1 - Adaptive Finite Element Simulation of the Human Mandible Using a New Physiological Model of the Masticatory Muscles N2 - Structural mechanics simulation of bony organs is of general medical and biomechanical interest, because of the interdependence of the inner architecture of bone and its functional loading already stated by Wolff in 1892. This work is part of a detailed research project concerning the human mandible. By adaptive finite element techniques, stress/strain profiles occurring in the bony structure under biting were simulated. Estimates of the discretization errors, local grid refinement, and multilevel techniques guarantee the reliability and efficiency of the method. In general, our simulation requires a representation of the organ's geometry, an appropriate material description, and the load case due to teeth, muscle, or joint forces. In this paper, we want to focus on the influence of the masticatory system. Our goal is to capture the physiological situation as far as possible. By means of visualization techniques developed by the group, we are able to extract individual muscle fibres from computed tomography data. By a special algorithm, the fibres are expanded to fanlike (esp. for the musc. temporalis) coherent vector fields similar to the anatomical reality. The activity of the fibres can be adapted according to compartmentalisation of the muscles as measured by electromyological experiments. A refined sensitivity analysis proved remarkable impact of the presented approach on the simulation results. T3 - ZIB-Report - 04-16 KW - adaptive finite elements KW - error estimation KW - local grid refinement KW - isotropic linear elasticity KW - human mandible KW - masticatory muscles Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7917 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 - Birkenheuer, Georg A1 - Blunk, Dirk A1 - Breuers, Sebastian A1 - Brinkmann, André A1 - d. Santos Vieira, I. A1 - Fels, Gregor A1 - Gesing, Sandra A1 - Grunzke, Richard A1 - Herres-Pawlis, Sonja A1 - Kohlbacher, Oliver A1 - Kruber, Nico A1 - Krüger, Jens A1 - Lang, U. A1 - Packschies, Lars A1 - Müller-Pfefferkorn, Ralph A1 - Schäfer, Patrick A1 - Schmalz, Hans-Günther A1 - Steinke, Thomas A1 - Warzecha, Klaus Dieter A1 - Wewior, Martin T1 - MoSGrid – A Molecular Simulation Grid as a new tool in Computational Chemistry, Biology and Material Science T2 - 6. German Conference on Chemoinformatics Y1 - 2010 N1 - Free software session and poster ER - TY - CHAP A1 - Krüger, Jens A1 - Birkenheuer, Georg A1 - Blunk, Dirk A1 - Breuers, Sebastian A1 - Brinkmann, André A1 - Fels, Gregor A1 - Gesing, Sandra A1 - Grunzke, Richard A1 - Herres-Pawlis, Sonja A1 - Kohlbacher, Oliver A1 - Kruber, Nico A1 - Lang, U. A1 - Packschies, Lars A1 - Müller-Pfefferkorn, Ralph A1 - Schäfer, Patrick A1 - Schmalz, Hans-Günther A1 - Steinke, Thomas A1 - Warzecha, Klaus Dieter A1 - Wewior, Martin T1 - Molecular Simulation Grid T2 - 6. German Conference on Chemoinformatics Y1 - 2010 PB - Gesellschaft Deutscher Chemiker (GDCh) ER - TY - THES A1 - Lang, Jens T1 - Adaptive Multilevel Solution of Nonlinear Parabolic PDE Systems. Theory, Algorithm, and Applications N2 - This monograph has been written to illustrate the interlocking of theory, algorithm, and application in developing solution techniques for complex PDE systems. A deep theoretical understanding is necessary to produce a powerful idea leading to a successful algorithm. Efficient and robust implementation is the key to make the algorithm perform satisfactorily. The extra insight obtained by solving real--life problems brings out the structure of the method more clearly and suggests often ways to improve the numerical algorithm. It is my intention to impart the beauty and complexity found in both the theoretical investigation of the adaptive algorithm proposed here, i.e., the coupling of Rosenbrock methods in time and multilevel finite elements in space, and its realization. I hope that this method will find many more interesting applications. T3 - ZIB-Report - SC-99-20 KW - Adaptive multilevel finite elements KW - Rosenbrock methods KW - a posteriori error estimates KW - Rothe method Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4089 ER - TY - GEN A1 - Lang, Jens A1 - Erdmann, Bodo T1 - Adaptive Linearly Implicit Methods for Heat and Mass Transfer Problems N2 - Dynamical process simulation of complex real-life problems often requires the use of modern algorithms, which automatically adapt both the time and space discretization in order to get error-controlled approximations of the solution. In this paper, a combination of linearly implicit time integrators of Rosenbrock type and adaptive multilevel finite elements based on a posteriori error estimates is presented. This approach has proven to work quite satisfactorily for a wide range of challenging practical problems. We show the performance of our adaptive method for two applications that arise in the study of flame balls and brine transport in porous media. T3 - ZIB-Report - 00-21 KW - Nonlinear time-dependent PDEs KW - Rosenbrock methods KW - multilevel finite elements KW - local refinement KW - a posteriori error estimates Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5892 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 -