TY - JOUR A1 - Weber, Marie-Christin A1 - Fischer, Lisa A1 - Damerau, Alexandra A1 - Ponomarev, Igor A1 - Pfeiffenberger, Moritz A1 - Gaber, Timo A1 - Götschel, Sebastian A1 - Lang, Jens A1 - Röblitz, Susanna A1 - Buttgereit, Frank A1 - Ehrig, Rainald A1 - Lang, Annemarie T1 - In vitro and in silico modeling of cellular and matrix-related changes during the early phase of osteoarthritis JF - BioRxiv N2 - Understanding the pathophysiological processes of osteoarthritis (OA) require adequate model systems. Although different in vitro or in vivo models have been described, further comprehensive approaches are needed to study specific parts of the disease. This study aimed to combine in vitro and in silico modeling to describe cellular and matrix-related changes during the early phase of OA. We developed an in vitro OA model based on scaffold-free cartilage-like constructs (SFCCs), which was mathematically modeled using a partial differential equation (PDE) system to resemble the processes during the onset of OA. SFCCs were produced from mesenchymal stromal cells and analyzed weekly by histology and qPCR to characterize the cellular and matrix-related composition. To simulate the early phase of OA, SFCCs were treated with interleukin-1β (IL-1β), tumor necrosis factor α (TNFα) and examined after 3 weeks or cultivated another 3 weeks without inflammatory cytokines to validate the regeneration potential. Mathematical modeling was performed in parallel to the in vitro experiments. SFCCs expressed cartilage-specific markers, and after stimulation an increased expression of inflammatory markers, matrix degrading enzymes, a loss of collagen II (Col-2) and a reduced cell density was observed which could be partially reversed by retraction of stimulation. Based on the PDEs, the distribution processes within the SFCCs, including those of IL-1β, Col-2 degradation and cell number reduction was simulated. By combining in vitro and in silico methods, we aimed to develop a valid, efficient alternative approach to examine and predict disease progression and new therapeutic strategies. Y1 - 2019 U6 - https://doi.org/10.1101/725317 ER - TY - JOUR A1 - Weber, Marie-Christin A1 - Fischer, Lisa A1 - Damerau, Alexandra A1 - Ponomarev, Igor A1 - Pfeiffenberger, Moritz A1 - Gaber, Timo A1 - Götschel, Sebastian A1 - Lang, Jens A1 - Röblitz, Susanna A1 - Buttgereit, Frank A1 - Ehrig, Rainald A1 - Lang, Annemarie T1 - Macroscale mesenchymal condensation to study cytokine-driven cellular and matrix-related changes during cartilage degradation JF - Biofabrication N2 - Understanding the pathophysiological processes of cartilage degradation requires adequate model systems to develop therapeutic strategies towards osteoarthritis (OA). Although different in vitro or in vivo models have been described, further comprehensive approaches are needed to study specific disease aspects. This study aimed to combine in vitro and in silico modeling based on a tissue-engineering approach using mesenchymal condensation to mimic cytokine-induced cellular and matrix-related changes during cartilage degradation. Thus, scaffold-free cartilage-like constructs (SFCCs) were produced based on self-organization of mesenchymal stromal cells (mesenchymal condensation) and i) characterized regarding their cellular and matrix composition or secondly ii) treated with interleukin-1β (IL-1β) and tumor necrosis factor α (TNFα) for 3 weeks to simulate OA-related matrix degradation. In addition, an existing mathematical model based on partial differential equations was optimized and transferred to the underlying settings to simulate distribution of IL-1β, type II collagen degradation and cell number reduction. By combining in vitro and in silico methods, we aim to develop a valid, efficient alternative approach to examine and predict disease progression and effects of new therapeutics. Y1 - 2020 U6 - https://doi.org/10.1088/1758-5090/aba08f VL - 12 IS - 4 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 - 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 - 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 - 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 - GEN A1 - Lang, Jens T1 - Adaptive FEM for Reaction-Diffusion Equations N2 - An integrated time--space adaptive finite element method for solving mixed systems of nonlinear parabolic, elliptic, and differential algebraic equations is presented. The approach is independent of the spatial dimension. For the discretization in time we use singly diagonally linearly implicit Runge--Kutta methods of Rosenbrock type. Local time errors for the step size control are defined by an embedded strategy. A multilevel finite element Galerkin method is subsequently applied for the discretization in space. A posteriori estimates of local spatial discretization errors are obtained solving local problems with higher order approximation. Superconvergence arguments allow to simplify the required computations. Two different strategies to obtain the start grid of the multilevel process are compared. The devised method is applied to a solid--solid combustion problem. T3 - ZIB-Report - SC-96-28 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2393 ER - TY - GEN A1 - Fröhlich, Jochen A1 - Lang, Jens T1 - Twodimensional Cascadic Finite Element Computations of Combustion Problems N2 - We present an integrated time--space adaptive finite element method for solving systems of twodimensional nonlinear parabolic systems in complex geometry. The partial differential system is first discretized in time using a singly linearly implicit Runge--Kutta method of order three. Local time errors for the step size control are defined by an embedding strategy. These errors are used to propose a new time step by a PI controller algorithm. A multilevel finite element method with piecewise linear functions on unstructured triangular meshes is subsequently applied for the discretization in space. The local error estimate of the finite element solution steering the adaptive mesh refinement is obtained solving local problems with quadratic trial functions located essentially at the edges of the triangulation. This two--fold adaptivity successfully ensures an a priori prescribed tolerance of the solution. The devised method is applied to laminar gaseous combustion and to solid--solid alloying reactions. We demonstrate that for such demanding applications the employed error estimation and adaption strategies generate an efficient and versatile algorithm. T3 - ZIB-Report - SC-96-05 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2167 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 - 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 - 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 - 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 - 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 - Erdmann, Bodo A1 - Lang, Jens A1 - Seebass, Martin T1 - Adaptive Solutions of Nonlinear Parabolic Equations with Application to Hyperthermia Treatments N2 - We present a self-adaptive finite element method to solve nonlinear evolution problems in 3D. An implicit time integrator of Rosenbrock type is coupled with a multilevel approach in space. The proposed method is applied to hyperthermia treatments to demonstrate its potential for the solving of complicated problems. T3 - ZIB-Report - SC-97-44 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3130 ER - TY - GEN A1 - Lang, Jens A1 - Merz, Wilhelm T1 - Numerical Simulation of Single Species Dopant Diffusion in Silicon under Extrinsic Conditions N2 - 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. T3 - ZIB-Report - SC-97-47 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3163 ER - TY - GEN A1 - Deuflhard, Peter A1 - Lang, Jens A1 - Nowak, Ulrich T1 - Adaptive Algorithms in Dynamical Process Simulation N2 - Dynamical simulation of industrially relevant processes strongly advises the use of algorithms, which are {\em adaptive} both in time and in space discretization. The paper presents two alternatives: (a) a fully adaptive method of lines approach, which is based on finite difference methods and essentially applicable to 1D problems; (b) a fully adaptive Rothe method, which is based on a fast multilevel finite element method and applicable to 1D up to 3D. T3 - ZIB-Report - SC-95-16 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1823 ER - TY - GEN A1 - Lourenco, Maria José A1 - Rosa, Samuel Costa S. A1 - Castro, Carlos Alberto Nieto de A1 - Albuquerque, C. A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Roitzsch, Rainer T1 - Simulation of the Transient Heating in an Unsymmetrical Coated Hot--Strip Sensor with a Self--Adaptive Finite Element Method N2 - 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. T3 - ZIB-Report - SC-98-22 Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3656 ER - TY - GEN A1 - Lang, Jens A1 - Erdmann, Bodo A1 - Roitzsch, Rainer T1 - Adaptive Time-Space Discretization for Combustion Problems N2 - 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. T3 - ZIB-Report - SC-97-40 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3094 ER - TY - GEN A1 - Lang, Jens A1 - Walter, Artur T1 - A Finite Element Method Adaptive in Space and Time for Nonlinear Reaction-Diffusion- Systems. N2 - 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. T3 - ZIB-Report - SC-92-05 KW - initial boundary value problem KW - Rothe method KW - adaptive Runge-Kutta method KW - finite elements KW - mesh refinement Y1 - 1992 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-755 ER - TY - GEN A1 - Lang, Jens A1 - Walter, Artur T1 - An Adaptive Discontinuous Finite Element Method for the Transport Equation. N2 - 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. T3 - ZIB-Report - SC-91-07 KW - neutron transport equation KW - discontinuous finite element KW - adaptive grid refinement Y1 - 1991 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-579 ER - TY - GEN A1 - Lang, Jens T1 - Two-Dimensional Fully Adaptive Solutions of Reaction-Diffusion Equations N2 - We present an adaptive Rothe method for two--dimensional problems combining an embedded Runge--Kutta scheme in time and a multilevel finite element discretization in space. The spatial discretization error is controlled by a posteriori error estimates based on interpolation techniques. A computational example for a thermodiffusive flame propagation model illustrates the high accuracy that is possible with the proposed method. T3 - ZIB-Report - SC-94-34 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1627 ER - TY - GEN A1 - Lang, Jens T1 - High-Resolution Selfadapative Computations on Chemical Reaction-Diffusion Problems with Internal Boundaries N2 - Large chemical computations show the need for full adaptivity supporting the development of robust and highly efficient programs. For solutions possessing sharp moving spatial transitions, as travelling wavefronts or emerging boundary and internal layers, an automatic adjustment of both the space and the time stepsize is generally accepted to be more successful in efficient resolving critical regions of high spatial and temporal activity. In contrast to the widespread discretization sequence first space then time the reversed sequence first time then space is employed. Full adaptivity of the proposed algorithm is realized by combining embedded time discretization and multilevel finite element space discretization. In this paper the algorithm is described for one--dimensional problems. The numerical results show the significantly new perspectives opened by this approach. T3 - ZIB-Report - SC-94-09 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1395 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 - 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 - 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 - 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 - CHAP A1 - Roitzsch, Rainer A1 - Lang, Jens A1 - Erdmann, Bodo T1 - The Benefits of Modularization T2 - Proc. 14th GAMM-Seminar Kiel on ’Concepts of Numerical Software Y1 - 1998 PB - did not appear ER - TY - CHAP A1 - Birkenheuer, Georg A1 - Blunk, Dirk A1 - Breuers, Sebastian A1 - Brinkmann, Andre A1 - Fels, Gregor A1 - Gesing, Sandra A1 - Grunzke, Richard A1 - Herres-Pawlis, Sonja A1 - Kohlbacher, Oliver A1 - Krüger, Jens A1 - Lang, Ulrich A1 - Packschies, Lars A1 - Müller-Pfefferkorn, Ralph A1 - Schäfer, Patrick A1 - Schuster, Johannes A1 - Steinke, Thomas A1 - Warzecha, Klaus Dieter A1 - Wewior, Martin T1 - MoSGrid: Progress of Workflow driven Chemical Simulations T2 - Proc. of Grid Workflow Workshop 2011, Cologne, Germany Y1 - 2011 UR - http://CEUR-WS.org/Vol-826/paper02.pdf VL - 826 PB - CEUR Workshop Proceedings 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 - JOUR A1 - Birkenheuer, Georg A1 - Blunk, Dirk A1 - Breuers, Sebastian A1 - Brinkmann, Andre A1 - dos Santos Vieira, Ines A1 - Fels, Gregor A1 - Gesing, Sandra A1 - Grunzke, Richard A1 - Herres-Pawlis, Sonja A1 - Kohlbacher, Oliver A1 - Krüger, Jens A1 - Lang, Ulrich 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 - A Molecular Simulation Grid as new tool for Computational Chemistry, Biology and Material Science JF - Journal of Cheminformatics 2011 Y1 - 2011 UR - http://www.jcheminf.com/content/3/S1/P14 U6 - https://doi.org/10.1186/1758-2946-3-S1-P14 VL - 3 IS - Suppl 1 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 - Erdmann, Bodo A1 - Lang, Jens A1 - Roitzsch, Rainer A1 - Lourenco, Maria José A1 - Rosa, S. A1 - de Castro, C.A. A1 - Albuquerque, C. ED - Kim, M. ED - Ro, S. T1 - Simulation of the Transient Heating in an Unsymmetrical Coated Hot-Strip Sensor With a Self-Adaptive Finite Element Method T2 - Proc. 5th Asian Thermophysical Properties Conference Y1 - 1998 VL - 1 SP - 91 EP - 94 CY - Seoul, South Corea ER - TY - CHAP A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Seebass, Martin ED - de Vahl Davis, G. ED - Leonardi, E. T1 - Adaptive Solutions of Nonlinear Parabolic Equations with Application to Hyperthermia Treatments T2 - CHT’97 Y1 - 1997 SP - 103 EP - 110 CY - Cesme, Turkey ER - TY - CHAP A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Seebass, Martin ED - Diller, K. T1 - Optimization of Temperature Distributions for Regional Hyperthermia based on a Nonlinear Heat Transfer Model T2 - Biotransport Y1 - 1998 VL - 858 SP - 36 EP - 46 ER - TY - JOUR A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Seebass, Martin T1 - The Impact of a Nonlinear Heat Transfer Model for Temperature Control in Regional Hyperthermia JF - IEEE Transactions on Biomedical Engineering Y1 - 1999 VL - 49 IS - 9 SP - 1129 EP - 1138 ER - TY - CHAP A1 - Erdmann, Bodo A1 - Kober, C. A1 - Lang, Jens A1 - Deuflhard, Peter A1 - Zeilhofer, J. A1 - Sader, Robert T1 - Efficient and Reliable Finite Element Methods for Simulation of the Human Mandible T2 - proceedings of 9th Workshop on The Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields Y1 - 2002 CY - Ulm, Germany 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 - CHAP A1 - Lang, Jens A1 - Erdmann, Bodo A1 - Roitzsch, Rainer ED - Sydow, Achim T1 - Adaptive Time-Space Discretization for Combustion Problems T2 - 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics, Vol. 2, Numerical Mathematics Y1 - 1997 SP - 49 EP - 155 PB - Wissenschaft und Technik Verlag, Berlin ER - TY - CHAP A1 - Lang, Jens A1 - Erdmann, Bodo A1 - Roitzsch, Rainer ED - Lewis, R. T1 - Three-Dimensional Fully Adaptive Solution of Thermo-Diffusive Flame Propagation Problems T2 - Numerical Methods in Thermal Problems Y1 - 1997 SP - 857 EP - 862 PB - Pineridge Press, Swansea, UK ER - TY - CHAP A1 - Lang, Jens A1 - Erdmann, Bodo A1 - Kober, Cornelia A1 - Deuflhard, Peter A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian ED - Alt, Walter ED - Hermann, Martin T1 - Effiziente und zuverlässige Finite-Elemente-Methoden zur Simulation des menschlichen Unterkiefers T2 - Berichte des IZWR - Interdisziplinäres Zentrum für Wissenschaftliches Rechnen Y1 - 2003 VL - 1 SP - 49 EP - 57 PB - Universität Jena CY - Germany ER - TY - CHAP A1 - Kober, C. A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian T1 - Sensitivity of the Temporomandibular Joint Capsule for the Structural Behaviour of the Human Mandible T2 - Proc. BMT 2004 Y1 - 2004 VL - 49-2 SP - 372 EP - 373 CY - Ilmenau, Deutschland ER - TY - CHAP A1 - Kober, C. 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 T2 - Proc. of 75th Annual Meeting of the GAMM Y1 - 2004 VL - 4 IS - 1 SP - 332 EP - 333 ER - TY - JOUR A1 - Birkenheuer, Georg A1 - Blunk, Dirk A1 - Breuers, Sebastian A1 - Brinkmann, André A1 - dos Santos Vieira, Ines A1 - Fels, Gregor A1 - Gesing, Sandra A1 - Grunzke, Richard A1 - Herres-Pawlis, Sonja A1 - Kohlbacher, Oliver A1 - Krüger, Jens A1 - Lang, Ulrich A1 - Packschies, Lars A1 - Müller-Pfefferkorn, Ralph A1 - Schäfer, Patrick A1 - Steinke, Thomas A1 - Warzecha, Klaus Dieter A1 - Wewior, Martin T1 - MoSGrid: efficient data management and a standardized data exchange format for molecular simulations in a grid environment JF - Journal of Cheminformatics Y1 - 2012 UR - http://www.jcheminf.com/content/4/S1/P21 U6 - https://doi.org/10.1186/1758-2946-4-S1-P21 VL - 4 IS - Suppl 1 SP - 21 ER - TY - JOUR A1 - Lang, Jens A1 - Erdmann, Bodo A1 - Seebaß, Martin T1 - Impact of Nonlinear Heat Tansfer on Temperature Control in Regional Hypertermia JF - IEEE Trans. Biomed. Engrg. Y1 - 1999 U6 - https://doi.org/10.1109/10.784145 VL - 46 SP - 1129 EP - 1138 ER - TY - GEN A1 - Franzone, Piero Colli 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 N2 - Adaptive numerical methods in space and time are introduced and studied for multiscale cardiac reaction-diffusion models in three dimensions. The evolution of a complete heartbeat, from the excitation to the recovery phase, is simulated with both the anisotropic Bidomain and Monodomain models, coupled with either a variant of the simple FitzHugh-Nagumo model or the more complex phase-I Luo-Rudy ionic model. The simulations are performed with the {\sc kardos} library, that employs adaptive finite elements in space and adaptive linearly implicit methods in time. The numerical results show that this adaptive method successfully solves these complex cardiac reaction-diffusion models on three-dimensional domains of moderate sizes. By automatically adapting the spatial meshes and time steps to the proper scales in each phase of the heartbeat, the method accurately resolves the evolution of the intra- and extra-cellular potentials, gating variables and ion concentrations during the excitation, plateau and recovery phases. T3 - ZIB-Report - 05-30 KW - reaction-diffusion equations KW - cardiac Bidomain and Monodomain models KW - adaptive finite elements KW - adaptive time integration Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8649 ER - 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 - Erdmann, Bodo A1 - Lang, Jens A1 - Matera, Sebastian A1 - Wilmanski, Krzysztof T1 - Adaptive Linearly Implicit Methods for Linear Poroelastic Equations N2 - Adaptive numerical methods in time and space are introduced and studied for linear poroelastic models in two and three space dimensions. We present equivalent models for linear poroelasticity and choose both the {\em displacement--pressure} and the {\em stress--pressure} formulation for our computations. Their discretizations are provided by means of linearly implicit schemes in time and linear finite elements in space. Our concept of adaptivity opens a way to a fast and reliable simulation of different loading cases defined by corresponding boundary conditions. We present some examples using our code {\sf Kardos} and show that the method works efficiently. In particular, it could be used in the simulation of some bone healing models. T3 - ZIB-Report - 06-37 KW - Poroelasticity KW - Biot's model KW - bone healing KW - adaptive finite elements KW - adaptive time integration KW - Rosenbrock methods Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9312 ER -