TY - JOUR A1 - Kober, C. A1 - Erdmann, Bodo A1 - Hellmich, Christian A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian T1 - Validation of interdependency between inner structure visualization and structural mechanics simulation JF - Int. Poster J. Dent. Oral Med. Y1 - 2006 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 - JOUR A1 - Deuflhard, Peter A1 - Erdmann, Bodo A1 - Roitzsch, Rainer A1 - Lines, Glenn Terje T1 - Adaptive Finite Element Simulation of Ventricular Dynamics JF - J. Computing and Visualization in Science Y1 - 2009 VL - 12 SP - 201 EP - 205 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 - CHAP A1 - Kober, C. A1 - Erdmann, Bodo A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian T1 - Simulation of the Human Mandible T2 - Proceedings of 10th Workshop on The Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields Y1 - 2003 CY - Ulm, Germany ER - TY - JOUR A1 - Kober, C. A1 - Erdmann, Bodo A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian T1 - Belastungssimulation beim menschlichen Biss im Vergleich mit der Dichtestruktur im Unterkieferknochen JF - Biomedizinische Technik Y1 - 2003 VL - 48 IS - Ergänzungsband 1 SP - 268 EP - 269 ER - TY - CHAP A1 - Kober, C. A1 - Erdmann, Bodo A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian T1 - An Application of Adaptive Finite Element Techniques in Biomechanics T2 - 22. CAD-FEM Users Meeting - Internationale FEM Technologietage Y1 - 2004 CY - Dresden, Germany ER - TY - JOUR A1 - Kober, C. A1 - Stübinger, S. A1 - Erdmann, Bodo A1 - Hellmich, Christian A1 - Radtke, Thomas A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian T1 - Finite element simulation of the human mandible JF - Int. Poster J. Dent. Oral Med. Y1 - 2006 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 - JOUR A1 - Weiser, Martin A1 - Deuflhard, Peter A1 - Erdmann, Bodo T1 - Affine conjugate adaptive Newton methods for nonlinear elastomechanics JF - Opt. Meth. Softw. Y1 - 2007 VL - 22 IS - 3 SP - 413 EP - 431 ER - TY - JOUR A1 - Schenkl, Sebastian A1 - Muggenthaler, Holger A1 - Hubig, Michael A1 - Erdmann, Bodo A1 - Weiser, Martin A1 - Zachow, Stefan A1 - Heinrich, Andreas A1 - Güttler, Felix Victor A1 - Teichgräber, Ulf A1 - Mall, Gita T1 - Automatic CT-based finite element model generation for temperature-based death time estimation: feasibility study and sensitivity analysis JF - International Journal of Legal Medicine N2 - Temperature based death time estimation is based either on simple phenomenological models of corpse cooling or on detailed physical heat transfer models. The latter are much more complex, but allow a higher accuracy of death time estimation as in principle all relevant cooling mechanisms can be taken into account. Here, a complete work flow for finite element based cooling simulation models is presented. The following steps are demonstrated on CT-phantoms: • CT-scan • Segmentation of the CT images for thermodynamically relevant features of individual geometries • Conversion of the segmentation result into a Finite Element (FE) simulation model • Computation of the model cooling curve • Calculation of the cooling time For the first time in FE-based cooling time estimation the steps from the CT image over segmentation to FE model generation are semi-automatically performed. The cooling time calculation results are compared to cooling measurements performed on the phantoms under controlled conditions. In this context, the method is validated using different CTphantoms. Some of the CT phantoms thermodynamic material parameters had to be experimentally determined via independent experiments. Moreover the impact of geometry and material parameter uncertainties on the estimated cooling time is investigated by a sensitivity analysis. KW - temperature based death time estimation KW - finite element method KW - CT segmentation KW - sensitivity analysis Y1 - 2017 U6 - https://doi.org/doi:10.1007/s00414-016-1523-0 VL - 131 IS - 3 SP - 699 EP - 712 ER - TY - JOUR A1 - Weiser, Martin A1 - Freytag, Yvonne A1 - Erdmann, Bodo A1 - Hubig, Michael A1 - Mall, Gita T1 - Optimal Design of Experiments for Estimating the Time of Death in Forensic Medicine JF - Inverse Problems N2 - Estimation of time of death based on a single measurement of body core temperature is a standard procedure in forensic medicine. Mechanistic models using simulation of heat transport promise higher accuracy than established phenomenological models in particular in nonstandard situations, but involve many not exactly known physical parameters. Identifying both time of death and physical parameters from multiple temperature measurements is one possibility to reduce the uncertainty significantly. In this paper, we consider the inverse problem in a Bayesian setting and perform both local and sampling-based uncertainty quantification, where proper orthogonal decomposition is used as model reduction for fast solution of the forward model. Based on the local uncertainty quantification, optimal design of experiments is performed in order to minimize the uncertainty in the time of death estimate for a given number of measurements. For reasons of practicability, temperature acquisition points are selected from a set of candidates in different spatial and temporal locations. Applied to a real corpse model, a significant accuracy improvement is obtained already with a small number of measurements. Y1 - 2018 U6 - https://doi.org/10.1088/1361-6420/aae7a5 VL - 34 IS - 12 SP - 125005 ER - TY - GEN A1 - Weiser, Martin A1 - Freytag, Yvonne A1 - Erdmann, Bodo A1 - Hubig, Michael A1 - Mall, Gita T1 - Optimal Design of Experiments for Estimating the Time of Death in Forensic Medicine N2 - Estimation of time of death based on a single measurement of body core temperature is a standard procedure in forensic medicine. Mechanistic models using simulation of heat transport promise higher accuracy than established phenomenological models in particular in nonstandard situations, but involve many not exactly known physical parameters. Identifying both time of death and physical parameters from multiple temperature measurements is one possibility to reduce the uncertainty significantly. In this paper, we consider the inverse problem in a Bayesian setting and perform both local and sampling-based uncertainty quantification, where proper orthogonal decomposition is used as model reduction for fast solution of the forward model. Based on the local uncertainty quantification, optimal design of experiments is performed in order to minimize the uncertainty in the time of death estimate for a given number of measurements. For reasons of practicability, temperature acquisition points are selected from a set of candidates in different spatial and temporal locations. Applied to a real corpse model, a significant accuracy improvement is obtained already with a small number of measurements. T3 - ZIB-Report - 18-08 Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-67247 SN - 1438-0064 ER - TY - JOUR 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 JF - Heat and Mass Transfer 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. Y1 - 2018 U6 - https://doi.org/10.1007/s00231-018-2324-4 VL - 54 IS - 9 SP - 2815 EP - 2826 PB - Springer 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 - 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. N2 - An error controlled finite elemente method (FEM) for solving stationary Schrödinger 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. T3 - ZIB-Report - SC-94-10 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1403 ER - TY - GEN A1 - Bornemann, Folkmar A. A1 - Erdmann, Bodo A1 - Kornhuber, Ralf T1 - A Posteriori Error Estimates for Elliptic Problems. N2 - {\def\enorm {\mathop{\mbox{\boldmath{$|\!|$}}}\nolimits} Let $u \in H$ be the exact solution of a given self--adjoint elliptic boundary value problem, which is approximated by some $\tilde{u} \in {\cal S}$, $\cal S$ being a suitable finite element space. Efficient and reliable a posteriori estimates of the error $\enorm u - \tilde{u}\enorm $, measuring the (local) quality of $\tilde{u}$, play a crucial role in termination criteria and in the adaptive refinement of the underlying mesh. A well--known class of error estimates can be derived systematically by localizing the discretized defect problem using domain decomposition techniques. In the present paper, we provide a guideline for the theoretical analysis of such error estimates. We further clarify the relation to other concepts. Our analysis leads to new error estimates, which are specially suited to three space dimensions. The theoretical results are illustrated by numerical computations.} T3 - ZIB-Report - SC-93-29 Y1 - 1993 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1257 ER - TY - GEN A1 - Erdmann, Bodo A1 - Hoppe, Ronald H. W. A1 - Kornhuber, Ralf T1 - Adaptive Multilevel-Methods for Obstacle Problems in Three Space Dimensions. N2 - We consider the discretization of obstacle problems for second order elliptic differential operators in three space dimensions by piecewise linear finite elements. Linearizing the discrete problems by suitable active set strategies, the resulting linear sub--problems are solved iteratively by preconditioned cg--iterations. We propose a variant of the BPX preconditioner and prove an $O(j)$ estimate for the resulting condition number. To allow for local mesh refinement we derive semi--local and local a posteriori error estimates. The theoretical results are illustrated by numerical computations. T3 - ZIB-Report - SC-93-08 Y1 - 1993 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1049 ER - TY - GEN A1 - Bornemann, Folkmar A. A1 - Erdmann, Bodo A1 - Kornhuber, Ralf T1 - Adaptive Multilevel-Methods in 3-Space Dimensions. N2 - We consider the approximate solution of selfadjoint elliptic problems in three space dimensions by piecewise linear finite elements with respect to a highly non-uniform tetrahedral mesh which is generated adaptively. The arising linear systems are solved iteratively by the conjugate gradient method provided with a multilevel preconditioner. Here, the accuracy of the iterative solution is coupled with the discretization error. as the performance of hierarchical bases preconditioners deteriorate in three space dimensions, the BPX preconditioner is used, taking special care of an efficient implementation. Reliable a-posteriori estimates for the discretization error are derived from a local comparison with the approximation resulting from piecewise quadratic elements. To illustrate the theoretical results, we consider a familiar model problem involving reentrant corners and a real-life problem arising from hyperthermia, a recent clinical method for cancer therapy. T3 - ZIB-Report - SC-92-14 Y1 - 1992 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-843 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 - 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 -