@misc{RoitzschErdmannLang, 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}, 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{LourencoRosaCastroetal., 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}, 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{LangWalter, author = {Lang, Jens and Walter, Artur}, title = {A Finite Element Method Adaptive in Space and Time for Nonlinear Reaction-Diffusion- Systems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-755}, number = {SC-92-05}, abstract = {Large scale combustion simulations show the need for adaptive methods. First, to save computation time and mainly to resolve local and instationary phenomena. In contrast to the widespread method of lines, we look at the reaction- diffusion equations as an abstract Cauchy problem in an appropriate Hilbert space. This means, we first discretize in time, assuming the space problems solved up to a prescribed tolerance. So, we are able to control the space and time error separately in an adaptive approach. The time discretization is done by several adaptive Runge-Kutta methods whereas for the space discretization a finite element method is used. The different behaviour of the proposed approaches are demonstrated on many fundamental examples from ecology, flame propagation, electrodynamics and combustion theory. {\bf Keywords:} initial boundary value problem, Rothe- method, adaptive Runge-Kutta method, finite elements, mesh refinement. {\bf AMS CLASSIFICATION:} 65J15, 65M30, 65M50.}, language = {en} } @misc{LangWalter, author = {Lang, Jens and Walter, Artur}, title = {An Adaptive Discontinuous Finite Element Method for the Transport Equation.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-579}, number = {SC-91-07}, abstract = {In this paper we introduce a discontinuous finite element method. In our approach, it is possible to combine the advantages of finite element and finite difference methods. The main ingredients are numerical flux approximation and local orthogonal basis functions. The scheme is defined on arbitrary triangulations and can be easily extended to nonlinear problems. Two different error indicators are derived. Especially the second one is closely connected to our approach and able to handle arbitrary variing flow directions. Numerical results are given for boundary value problems in two dimensions. They demonstrate the performance of the scheme, combined with the two error indicators. {\bf Key words:} neutron transport equation, discontinuous finite element, adaptive grid refinement. {\bf Subject classifications:} AMS(MOS) 65N30, 65M15.}, language = {en} } @misc{LangMerz, author = {Lang, Jens and Merz, Wilhelm}, title = {Two-Dimensional Adaptive Simulation of Dopant Diffusion in Silicon}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5716}, number = {00-03}, abstract = {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.}, language = {en} } @misc{LangMerz, author = {Lang, Jens and Merz, Wilhelm}, title = {Numerical Simulation of Single Species Dopant Diffusion in Silicon under Extrinsic Conditions}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3163}, number = {SC-97-47}, abstract = {In this article we consider a general model for phosphorus diffusion in silicon under extrinsic doping conditions. At such high concentrations we have to include the charged species and the internal electric field of the crystal, both of which can have profound effects on diffusion. In principle, this leads to a very large number of drift--diffusion--reaction equations: one for each charge state of every species, plus one Poisson equation to describe the internal electric field (in terms of the electron/hole concentration). The number of equations can be reduced substantially by making additional assumptions on the distribution of charge states and local equilibrium assumptions concerning the reaction terms. The resulting model turns out to be very interesting for numerical investigation. We solve the problem numerically in two space dimensions with the adaptive finite element program KARDOS and describe the numerical method used here to treat the resulting drift--diffusion--reaction problem.}, language = {en} } @misc{LangErdmannSeebass, author = {Lang, Jens and Erdmann, Bodo and Seebass, Martin}, title = {Impact of Nonlinear Heat Transfer on Temperature Control in Regional Hyperthermia}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3426}, number = {SC-97-73}, abstract = {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.}, language = {en} } @misc{LangErdmannRoitzsch, 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}, 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{LangErdmannRoitzsch, 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}, 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{LangErdmann, author = {Lang, Jens and Erdmann, Bodo}, title = {Adaptive Linearly Implicit Methods for Heat and Mass Transfer Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5892}, number = {00-21}, abstract = {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.}, language = {en} }