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 - 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 - 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 - Kober, Cornelia A1 - Erdmann, Bodo A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian T1 - Simulation of the Human Mandible: Comparison of Bone Mineral Density and Stress/Strain Profiles due to Masticatory Muscles' Traction N2 - The correlation of the inner architecture of bone and its functional loading was already stated by Wolff in 1892. Our objective is to demonstrate this interdependence in the case of the human mandible. For this purpose, stress/strain profiles occuring at a human lateral bite were simulated. Additionally, by a combination of computer graphics modules, a three--dimensional volumetric visualization of bone mineral density could be given. Qualitative correspondences between the density profile of the jaw and the simulated stress/strain profiles could be pointed out. In the long run, this might enable the use of the simulation for diagnosis and prognosis. The solution of the underlying partial differential equations describing linear elastic material behaviour was provided by an adaptive finite element method. Estimates of the discretization errors, local grid refinement, and multilevel techniques guaranteed the reliability and efficiency of the method. T3 - ZIB-Report - 03-23 KW - linear elasticity KW - finite element method KW - adaptive grid refinement KW - stress/strain analysis KW - human mandible Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7458 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 - Beck, Rudolf A1 - Erdmann, Bodo A1 - Roitzsch, Rainer T1 - KASKADE 3.0 User's Guide N2 - 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. T3 - ZIB-Report - TR-95-11 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5269 ER - TY - GEN A1 - Beck, Rudolf A1 - Erdmann, Bodo A1 - Roitzsch, Rainer T1 - KASKADE 3.0 - An Object Oriented Adaptive Finite Element Code N2 - 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. T3 - ZIB-Report - TR-95-04 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5199 ER - TY - GEN A1 - Bornemann, Folkmar A. A1 - Erdmann, Bodo A1 - Roitzsch, Rainer T1 - KASKADE - Numerical Experiments. N2 - 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. T3 - ZIB-Report - TR-91-01 Y1 - 1991 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4762 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 - Hellmich, Christian A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian T1 - Anisotropic Simulation of the Human Mandible N2 - We focus on the role of anisotropic elasticity in the simulation of the load distribution in a human mandible due to a lateral bite on the leftmost premolar. Based on experimental evidence, we adopt ``local''" orthotropy of the elastic properties of the bone tissue. Since the trajectories of anisotropic elasticity are not accessible from Computer Tomographic (CT) data, they will be reconstructed from (i) the organ's geometry and (ii) from coherent structures which can be recognized from the spatial distribution of the CT values. A sensitivity analysis comprising various 3D FE simulations reveals the relevance of elastic anisotropy for the load carrying behavior of a human mandible: Comparison of the load distributions in isotropic and anisotropic simulations indicates that anisotropy seems to ``spare''" the mandible from loading. Moreover, a maximum degree of anisotropy leads to kind of an load minimization of the mandible, expressed by a minimum of different norms of local strain, evaluated throughout the organ. Thus, we may suggest that anisotropy is not only relevant, but also in some sense ``optimal''. T3 - ZIB-Report - 04-12 KW - anisotropy KW - elasticity KW - bony organ simulation KW - human mandible KW - visualization of tissue quality KW - finite element analysis Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7873 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 - Ackermann, Jörg A1 - Erdmann, Bodo A1 - Roitzsch, Rainer T1 - A self-adaptive multilevel finite element method for the stationary Schrödinger equation in three space dimensions JF - J. Chem. Phys. Y1 - 1994 VL - 101 SP - 7643 EP - 7650 ER - TY - CHAP A1 - Beck, Rudolf A1 - Erdmann, Bodo A1 - Roitzsch, Rainer ED - Arge, Erlend ED - Bruaset, Are Magnus ED - Langtangen, Hans Petter T1 - An Object-Oriented Adaptive Finite Element Code T2 - Modern Software Tools for Scientific Computing Y1 - 1997 SP - 105 EP - 124 PB - Birkhäuser, Boston 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 - Zachow, Stefan A1 - Hierl, Thomas A1 - Erdmann, Bodo T1 - A quantitative evaluation of 3D soft tissue prediction in maxillofacial surgery planning T2 - Proc. 3. Jahrestagung der Deutschen Gesellschaft für Computer- und Roboter-assistierte Chirurgie e.V. Y1 - 2004 CY - München ER - TY - CHAP A1 - Zachow, Stefan A1 - Hierl, Thomas A1 - Erdmann, Bodo T1 - On the Predictability of tissue changes after osteotomy planning in maxillofacial surgery T2 - Computer Assisted Radiology and Surgery (CARS) Y1 - 2004 U6 - https://doi.org/10.1016/j.ics.2004.03.043 SP - 648 EP - 653 CY - Chicago, USA ER - TY - CHAP A1 - Zachow, Stefan A1 - Hierl, Thomas A1 - Erdmann, Bodo T1 - Über die Genauigkeit einer 3D Weichgewebeprädiktion in der MKG-Cirurgie T2 - Workshop ’Bildverarbeitung für die Medizin’ (BVM) Y1 - 2004 SP - 75 EP - 79 CY - Berlin, Germany ER - TY - GEN A1 - Weiser, Martin A1 - Erdmann, Bodo A1 - Schenkl, Sebastian A1 - Muggenthaler, Holger A1 - Hubig, Michael A1 - Mall, Gita A1 - Zachow, Stefan T1 - Uncertainty in Temperature-Based Determination of Time of Death N2 - Temperature-based estimation of time of death (ToD) can be per- formed either with the help of simple phenomenological models of corpse cooling or with detailed mechanistic (thermodynamic) heat transfer mod- els. The latter are much more complex, but allow a higher accuracy of ToD estimation as in principle all relevant cooling mechanisms can be taken into account. The potentially higher accuracy depends on the accuracy of tissue and environmental parameters as well as on the geometric resolution. We in- vestigate the impact of parameter variations and geometry representation on the estimated ToD based on a highly detailed 3D corpse model, that has been segmented and geometrically reconstructed from a computed to- mography (CT) data set, differentiating various organs and tissue types. From that we identify the most crucial parameters to measure or estimate, and obtain a local uncertainty quantifcation for the ToD. T3 - ZIB-Report - 17-18 KW - forensic medicine KW - determination of time of death KW - heat transfer equation KW - sensitivity i.r.t. thermal parameters KW - sensitivity i.r.t. geometric resolution Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-63818 SN - 1438-0064 ER -