@misc{WeiserErdmannDeuflhard2008, author = {Weiser, Martin and Erdmann, Bodo and Deuflhard, Peter}, title = {On Efficiency and Accuracy in Cardioelectric Simulation}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10934}, number = {08-41}, year = {2008}, abstract = {Reasons for the failure of adaptive methods to deliver improved efficiency when integrating monodomain models for myocardiac excitation are discussed. Two closely related techniques for reducing the computational complexity of linearly implicit integrators, deliberate sparsing and splitting, are investigated with respect to their impact on computing time and accuracy.}, language = {en} } @misc{WeiserRoelligArndtetal.2008, author = {Weiser, Martin and R{\"o}llig, Mathias and Arndt, Ralf and Erdmann, Bodo}, title = {Development and test of a numerical model for pulse thermography in civil engineering}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10980}, number = {08-45}, year = {2008}, abstract = {Pulse thermography of concrete structures is used in civil engineering for detecting voids, honeycombing and delamination. The physical situation is readily modeled by Fourier's law. Despite the simplicity of the PDE structure, quantitatively realistic numerical 3D simulation faces two major obstacles. First, the short heating pulse induces a thin boundary layer at the heated surface which encapsulates all information and therefore has to be resolved faithfully. Even with adaptive mesh refinement techniques, obtaining useful accuracies requires an unsatisfactorily fine discretization. Second, bulk material parameters and boundary conditions are barely known exactly. We address both issues by a semi-analytic reformulation of the heat transport problem and by parameter identification. Numerical results are compared with measurements of test specimens.}, language = {en} } @misc{FranzoneDeuflhardErdmannetal.2005, author = {Franzone, Piero Colli and Deuflhard, Peter and Erdmann, Bodo and Lang, Jens and Pavarino, Luca Franco}, title = {Adaptivity in Space and Time for Reaction-Diffusion Systems in Electrocardiology}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8649}, number = {05-30}, year = {2005}, abstract = {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.}, language = {en} } @misc{ErdmannLangMateraetal.2006, author = {Erdmann, Bodo and Lang, Jens and Matera, Sebastian and Wilmanski, Krzysztof}, title = {Adaptive Linearly Implicit Methods for Linear Poroelastic Equations}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9312}, number = {06-37}, year = {2006}, abstract = {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.}, language = {en} } @misc{WeiserDeuflhardErdmann2004, author = {Weiser, Martin and Deuflhard, Peter and Erdmann, Bodo}, title = {Affine conjugate adaptive Newton methods for nonlinear elastomechanics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7768}, number = {04-01}, year = {2004}, abstract = {The paper extends affine conjugate Newton methods from convex to nonconvex minimization, with particular emphasis on PDE problems originating from compressible hyperelasticity. Based on well-known schemes from finite dimensional nonlinear optimization, three different algorithmic variants are worked out in a function space setting, which permits an adaptive multilevel finite element implementation. These algorithms are tested on two well-known 3D test problems and a real-life example from surgical operation planning.}, language = {en} } @misc{DeuflhardErdmannRoitzschetal.2006, author = {Deuflhard, Peter and Erdmann, Bodo and Roitzsch, Rainer and Lines, Glenn Terje}, title = {Adaptive Finite Element Simulation of Ventricular Fibrillation Dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9431}, number = {06-49}, year = {2006}, abstract = {The dynamics of ventricular fibrillation caused by irregular excitation is simulated in the frame of the monodomain model with an action potential model due to Aliev-Panfilov for a human 3D geometry. The numerical solution of this multiscale reaction-diffusion problem is attacked by algorithms which are fully adaptive in both space and time (code library {\sc Kardos}). The obtained results clearly demonstrate an accurate resolution of the cardiac potential during the excitation and the plateau phases (in the regular cycle) as well as after a reentrant excitation (in the irregular cycle).}, language = {en} } @inproceedings{ZachowErdmannHegeetal.2004, author = {Zachow, Stefan and Erdmann, Bodo and Hege, Hans-Christian and Deuflhard, Peter}, title = {Advances in 3D osteotomy planning with 3D soft tissue prediction}, booktitle = {Proc. 2nd International Symposium on Computer Aided Surgery around the Head, Abstract}, address = {Bern}, pages = {31}, year = {2004}, language = {en} } @article{LangErdmannSeebass1999, author = {Lang, Jens and Erdmann, Bodo and Seebaß, Martin}, title = {Impact of Nonlinear Heat Tansfer on Temperature Control in Regional Hypertermia}, volume = {46}, journal = {IEEE Trans. Biomed. Engrg.}, doi = {10.1109/10.784145}, pages = {1129 -- 1138}, year = {1999}, language = {en} } @article{HellmichKoberErdmann2008, author = {Hellmich, Christian and Kober, Cornelia and Erdmann, Bodo}, title = {Micromechanics-based conversion of CT data into anisotropic elasticity tensors, applied to FE simulations of a mandible}, volume = {36}, journal = {Annals of Biomedical Engineering}, number = {1}, doi = {10.1007/s10439-007-9393-8}, pages = {108 -- 122}, year = {2008}, language = {en} } @inproceedings{ErdmannKoberLangetal.2002, author = {Erdmann, Bodo and Kober, C. and Lang, Jens and Deuflhard, Peter and Zeilhofer, J. and Sader, Robert}, title = {Efficient and Reliable Finite Element Methods for Simulation of the Human Mandible}, booktitle = {proceedings of 9th Workshop on The Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields}, address = {Ulm, Germany}, year = {2002}, language = {en} } @article{ErdmannLjubijankicNytschGeusen2007, author = {Erdmann, Bodo and Ljubijankic, M. and Nytsch-Geusen, C.}, title = {Entwicklung einer Toolbox zur zwei- und dreidimensionalen instation{\"a}ren thermischen Bauteilsimulation mit KARDOS}, volume = {29}, journal = {Bauphsik}, number = {1}, pages = {33 -- 39}, year = {2007}, language = {en} } @inproceedings{ErdmannLangRoitzschetal.1998, author = {Erdmann, Bodo and Lang, Jens and Roitzsch, Rainer and Lourenco, Maria Jos{\´e} and Rosa, S. and de Castro, C.A. and Albuquerque, C.}, title = {Simulation of the Transient Heating in an Unsymmetrical Coated Hot-Strip Sensor With a Self-Adaptive Finite Element Method}, volume = {1}, booktitle = {Proc. 5th Asian Thermophysical Properties Conference}, editor = {Kim, M. and Ro, S.}, address = {Seoul, South Corea}, pages = {91 -- 94}, year = {1998}, language = {en} } @inproceedings{ErdmannLangSeebass1997, author = {Erdmann, Bodo and Lang, Jens and Seebass, Martin}, title = {Adaptive Solutions of Nonlinear Parabolic Equations with Application to Hyperthermia Treatments}, booktitle = {CHT'97}, editor = {de Vahl Davis, G. and Leonardi, E.}, address = {Cesme, Turkey}, pages = {103 -- 110}, year = {1997}, language = {en} } @inproceedings{ErdmannLangSeebass1998, author = {Erdmann, Bodo and Lang, Jens and Seebass, Martin}, title = {Optimization of Temperature Distributions for Regional Hyperthermia based on a Nonlinear Heat Transfer Model}, volume = {858}, booktitle = {Biotransport}, editor = {Diller, K.}, pages = {36 -- 46}, year = {1998}, language = {en} } @article{ErdmannLangSeebass1999, author = {Erdmann, Bodo and Lang, Jens and Seebass, Martin}, title = {The Impact of a Nonlinear Heat Transfer Model for Temperature Control in Regional Hyperthermia}, volume = {49}, journal = {IEEE Transactions on Biomedical Engineering}, number = {9}, pages = {1129 -- 1138}, year = {1999}, language = {en} } @inproceedings{LangErdmannRoitzsch1997, author = {Lang, Jens and Erdmann, Bodo and Roitzsch, Rainer}, title = {Adaptive Time-Space Discretization for Combustion Problems}, booktitle = {15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics, Vol. 2, Numerical Mathematics}, editor = {Sydow, Achim}, publisher = {Wissenschaft und Technik Verlag, Berlin}, pages = {49 -- 155}, year = {1997}, language = {en} } @inproceedings{LangErdmannRoitzsch1997, author = {Lang, Jens and Erdmann, Bodo and Roitzsch, Rainer}, title = {Three-Dimensional Fully Adaptive Solution of Thermo-Diffusive Flame Propagation Problems}, booktitle = {Numerical Methods in Thermal Problems}, editor = {Lewis, R.}, publisher = {Pineridge Press, Swansea, UK}, pages = {857 -- 862}, year = {1997}, language = {en} } @incollection{LangErdmannKoberetal.2003, author = {Lang, Jens and Erdmann, Bodo and Kober, Cornelia and Deuflhard, Peter and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Effiziente und zuverl{\"a}ssige Finite-Elemente-Methoden zur Simulation des menschlichen Unterkiefers}, volume = {1}, booktitle = {Berichte des IZWR - Interdisziplin{\"a}res Zentrum f{\"u}r Wissenschaftliches Rechnen}, editor = {Alt, Walter and Hermann, Martin}, publisher = {Universit{\"a}t Jena}, address = {Germany}, pages = {49 -- 57}, year = {2003}, language = {en} } @article{KoberStuebingerErdmannetal.2006, author = {Kober, C. and St{\"u}binger, S. and Erdmann, Bodo and Hellmich, Christian and Radtke, Thomas and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Finite element simulation of the human mandible}, journal = {Int. Poster J. Dent. Oral Med.}, year = {2006}, language = {en} } @inproceedings{KoberErdmannHellmichetal.2005, author = {Kober, C. and Erdmann, Bodo and Hellmich, Christian and Geiger, M. and Sader, Robert and Zeilhofer, Hans-Florian}, title = {How does the periodontal ligament influence overall stress/strain profiles of a partially edentulous mandible?}, booktitle = {Proc. of 8th Int. Conference on Biological Mechanisms of Tooth Eruption, Resorption and Movement, Phuket, Thailand}, editor = {Davidovitch, Z. and Mah, J. and Suthanarak, S.}, address = {Harvard Society of the Advancement of Orthodontics, Boston, Massachusetts, USA}, year = {2005}, language = {en} } @inproceedings{KoberErdmannHellmichetal.2004, author = {Kober, C. and Erdmann, Bodo and Hellmich, Christian and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Anisotropic Simulation of the Human Mandible}, booktitle = {Proc. of 17th ASCE Engineering Mechanics Conference}, publisher = {Univ. of Delaware}, year = {2004}, language = {en} } @inproceedings{KoberErdmannHellmichetal.2005, author = {Kober, C. and Erdmann, Bodo and Hellmich, Christian and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Consideration of Bone Inhomogeneity and Anisotropy in Deformation Analysis of a Human Mandible}, volume = {1}, booktitle = {Proc. of BMT2005, 39th Annual Congress of the German Society of Biomedical Engineering, Nuremberg, Germany}, editor = {Boenick, U. and Bolz, A.}, publisher = {VDE}, address = {Nuremberg, Germany}, pages = {814 -- 815}, year = {2005}, language = {en} } @inproceedings{KoberErdmannHellmichetal.2005, author = {Kober, C. and Erdmann, Bodo and Hellmich, Christian and Sader, Robert and Zeilhofer, Hans-Florian}, title = {The Influence of the Periodontal Ligament on Overall Stress/Strain Profiles of a Human Mandible}, booktitle = {Proc. of 23rd CADFEM Users' Meeting, Int. Congress on FEM Technology, Biomechanics}, editor = {CADFEM GmbH, Grafing}, address = {Bonn, Germany}, pages = {1 -- 10}, year = {2005}, language = {en} } @article{KoberErdmannHellmichetal.2006, author = {Kober, C. and Erdmann, Bodo and Hellmich, Christian and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Consideration of anisotropic elasticity minimizes volumetric rather than shear deformation in human mandible}, volume = {9(2)}, journal = {Comp. Meth. Biomech. Biomed. Eng.}, pages = {91 -- 101}, year = {2006}, language = {en} } @article{KoberErdmannHellmichetal.2006, author = {Kober, C. and Erdmann, Bodo and Hellmich, Christian and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Validation of interdependency between inner structure visualization and structural mechanics simulation}, journal = {Int. Poster J. Dent. Oral Med.}, year = {2006}, language = {en} } @article{KoberErdmannHellmichetal.2006, author = {Kober, C. and Erdmann, Bodo and Hellmich, Christian and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Validation of interdependency between inner structure visualization and structural mechanics simulation}, journal = {Int. Poster J. Dent. Oral Med.}, year = {2006}, language = {en} } @inproceedings{KoberErdmannLangetal.2004, author = {Kober, C. and Erdmann, Bodo and Lang, Jens and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Sensitivity of the Temporomandibular Joint Capsule for the Structural Behaviour of the Human Mandible}, volume = {49-2}, booktitle = {Proc. BMT 2004}, address = {Ilmenau, Deutschland}, pages = {372 -- 373}, year = {2004}, language = {en} } @article{DeuflhardErdmannRoitzschetal.2009, author = {Deuflhard, Peter and Erdmann, Bodo and Roitzsch, Rainer and Lines, Glenn Terje}, title = {Adaptive Finite Element Simulation of Ventricular Dynamics}, volume = {12}, journal = {J. Computing and Visualization in Science}, pages = {201 -- 205}, year = {2009}, language = {en} } @inproceedings{KoberErdmannLangetal.2004, author = {Kober, C. and Erdmann, Bodo and Lang, Jens and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Adaptive Finite Element Simulation of the Human Mandible Using a New Physiological Model of the Masticatory Muscles}, volume = {4}, booktitle = {Proc. of 75th Annual Meeting of the GAMM}, number = {1}, pages = {332 -- 333}, year = {2004}, language = {en} } @inproceedings{KoberErdmannSaderetal.2003, author = {Kober, C. and Erdmann, Bodo and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Simulation of the Human Mandible}, booktitle = {Proceedings of 10th Workshop on The Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields}, address = {Ulm, Germany}, year = {2003}, language = {en} } @article{KoberErdmannSaderetal.2003, author = {Kober, C. and Erdmann, Bodo and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Belastungssimulation beim menschlichen Biss im Vergleich mit der Dichtestruktur im Unterkieferknochen}, volume = {48}, journal = {Biomedizinische Technik}, number = {Erg{\"a}nzungsband 1}, pages = {268 -- 269}, year = {2003}, language = {en} } @inproceedings{KoberErdmannSaderetal.2004, author = {Kober, C. and Erdmann, Bodo and Sader, Robert and Zeilhofer, Hans-Florian}, title = {An Application of Adaptive Finite Element Techniques in Biomechanics}, booktitle = {22. CAD-FEM Users Meeting - Internationale FEM Technologietage}, address = {Dresden, Germany}, year = {2004}, language = {en} } @article{KoberStuebingerErdmannetal.2006, author = {Kober, C. and St{\"u}binger, S. and Erdmann, Bodo and Hellmich, Christian and Radtke, Thomas and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Finite element simulation of the human mandible}, journal = {Int. Poster J. Dent. Oral Med.}, year = {2006}, language = {en} } @inproceedings{RoitzschLangErdmann1998, author = {Roitzsch, Rainer and Lang, Jens and Erdmann, Bodo}, title = {The Benefits of Modularization}, booktitle = {Proc. 14th GAMM-Seminar Kiel on 'Concepts of Numerical Software}, publisher = {did not appear}, year = {1998}, language = {en} } @article{WeiserDeuflhardErdmann2007, author = {Weiser, Martin and Deuflhard, Peter and Erdmann, Bodo}, title = {Affine conjugate adaptive Newton methods for nonlinear elastomechanics}, volume = {22}, journal = {Opt. Meth. Softw.}, number = {3}, pages = {413 -- 431}, year = {2007}, language = {en} } @article{SchenklMuggenthalerHubigetal.2017, author = {Schenkl, Sebastian and Muggenthaler, Holger and Hubig, Michael and Erdmann, Bodo and Weiser, Martin and Zachow, Stefan and Heinrich, Andreas and G{\"u}ttler, Felix Victor and Teichgr{\"a}ber, Ulf and Mall, Gita}, title = {Automatic CT-based finite element model generation for temperature-based death time estimation: feasibility study and sensitivity analysis}, volume = {131}, journal = {International Journal of Legal Medicine}, number = {3}, doi = {doi:10.1007/s00414-016-1523-0}, pages = {699 -- 712}, year = {2017}, abstract = {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.}, language = {en} } @article{WeiserFreytagErdmannetal.2018, author = {Weiser, Martin and Freytag, Yvonne and Erdmann, Bodo and Hubig, Michael and Mall, Gita}, title = {Optimal Design of Experiments for Estimating the Time of Death in Forensic Medicine}, volume = {34}, journal = {Inverse Problems}, number = {12}, doi = {10.1088/1361-6420/aae7a5}, pages = {125005}, year = {2018}, abstract = {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.}, language = {en} } @misc{WeiserFreytagErdmannetal.2018, author = {Weiser, Martin and Freytag, Yvonne and Erdmann, Bodo and Hubig, Michael and Mall, Gita}, title = {Optimal Design of Experiments for Estimating the Time of Death in Forensic Medicine}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-67247}, year = {2018}, abstract = {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.}, language = {en} } @article{WeiserErdmannSchenkletal.2018, author = {Weiser, Martin and Erdmann, Bodo and Schenkl, Sebastian and Muggenthaler, Holger and Hubig, Michael and Mall, Gita and Zachow, Stefan}, title = {Uncertainty in Temperature-Based Determination of Time of Death}, volume = {54}, journal = {Heat and Mass Transfer}, number = {9}, publisher = {Springer}, doi = {10.1007/s00231-018-2324-4}, pages = {2815 -- 2826}, year = {2018}, abstract = {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.}, language = {en} } @misc{LangErdmannRoitzsch1997, 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}, year = {1997}, 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{AckermannErdmannRoitzsch1994, author = {Ackermann, J{\"o}rg and Erdmann, Bodo and Roitzsch, Rainer}, title = {A self-adaptive multilevel finite element method for the stationary Schr{\"o}dinger equation in three space dimensions.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1403}, number = {SC-94-10}, year = {1994}, abstract = {An error controlled finite elemente method (FEM) for solving stationary Schr{\"o}dinger 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.}, language = {en} } @misc{BornemannErdmannKornhuber1993, author = {Bornemann, Folkmar A. and Erdmann, Bodo and Kornhuber, Ralf}, title = {A Posteriori Error Estimates for Elliptic Problems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1257}, number = {SC-93-29}, year = {1993}, abstract = {{\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.}}, language = {en} } @misc{ErdmannHoppeKornhuber1993, author = {Erdmann, Bodo and Hoppe, Ronald H. W. and Kornhuber, Ralf}, title = {Adaptive Multilevel-Methods for Obstacle Problems in Three Space Dimensions.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1049}, number = {SC-93-08}, year = {1993}, abstract = {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.}, language = {en} } @misc{BornemannErdmannKornhuber1992, author = {Bornemann, Folkmar A. and Erdmann, Bodo and Kornhuber, Ralf}, title = {Adaptive Multilevel-Methods in 3-Space Dimensions.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-843}, number = {SC-92-14}, year = {1992}, abstract = {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.}, language = {en} } @misc{ErdmannLangSeebass1997, author = {Erdmann, Bodo and Lang, Jens and Seebass, Martin}, title = {Adaptive Solutions of Nonlinear Parabolic Equations with Application to Hyperthermia Treatments}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3130}, number = {SC-97-44}, year = {1997}, abstract = {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.}, language = {en} } @misc{LourencoRosaCastroetal.1998, 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}, year = {1998}, 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{LangErdmannRoitzsch1997, 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}, year = {1997}, 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{RoitzschErdmannLang1998, 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}, year = {1998}, 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{ErdmannLangRoitzsch2002, author = {Erdmann, Bodo and Lang, Jens and Roitzsch, Rainer}, title = {KARDOS - User"s Guide}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7096}, number = {02-42}, year = {2002}, abstract = {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}}}, language = {en} } @misc{KoberErdmannSaderetal.2003, author = {Kober, Cornelia and Erdmann, Bodo and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Simulation of the Human Mandible: Comparison of Bone Mineral Density and Stress/Strain Profiles due to Masticatory Muscles' Traction}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7458}, number = {03-23}, year = {2003}, abstract = {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.}, language = {en} } @misc{ErdmannLangRoitzsch1993, author = {Erdmann, Bodo and Lang, Jens and Roitzsch, Rainer}, title = {Kaskade Manual - Version 2.0.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4970}, number = {TR-93-05}, year = {1993}, abstract = {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.}, language = {en} } @misc{BeckErdmannRoitzsch1995, author = {Beck, Rudolf and Erdmann, Bodo and Roitzsch, Rainer}, title = {KASKADE 3.0 User's Guide}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5269}, number = {TR-95-11}, year = {1995}, abstract = {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.}, language = {en} } @misc{BeckErdmannRoitzsch1995, author = {Beck, Rudolf and Erdmann, Bodo and Roitzsch, Rainer}, title = {KASKADE 3.0 - An Object Oriented Adaptive Finite Element Code}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5199}, number = {TR-95-04}, year = {1995}, abstract = {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.}, language = {en} } @misc{BornemannErdmannRoitzsch1991, author = {Bornemann, Folkmar A. and Erdmann, Bodo and Roitzsch, Rainer}, title = {KASKADE - Numerical Experiments.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4762}, number = {TR-91-01}, year = {1991}, abstract = {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.}, language = {en} } @misc{LangErdmannSeebass1998, 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}, year = {1998}, 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{ErdmannLangSeebass1997, author = {Erdmann, Bodo and Lang, Jens and Seebass, Martin}, title = {Optimization of Temperature Distributions for Regional Hyperthermia Based on a Nonlinear Heat Transfer Model}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3283}, number = {SC-97-59}, year = {1997}, abstract = {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 .}, language = {en} } @misc{KoberErdmannHellmichetal.2004, author = {Kober, Cornelia and Erdmann, Bodo and Hellmich, Christian and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Anisotropic Simulation of the Human Mandible}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7873}, number = {04-12}, year = {2004}, abstract = {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''.}, language = {en} } @misc{KoberErdmannLangetal.2004, author = {Kober, Cornelia and Erdmann, Bodo and Lang, Jens and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Adaptive Finite Element Simulation of the Human Mandible Using a New Physiological Model of the Masticatory Muscles}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7917}, number = {04-16}, year = {2004}, abstract = {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.}, language = {en} } @article{AckermannErdmannRoitzsch1994, author = {Ackermann, J{\"o}rg and Erdmann, Bodo and Roitzsch, Rainer}, title = {A self-adaptive multilevel finite element method for the stationary Schr{\"o}dinger equation in three space dimensions}, volume = {101}, journal = {J. Chem. Phys.}, pages = {7643 -- 7650}, year = {1994}, language = {en} } @inproceedings{BeckErdmannRoitzsch1997, author = {Beck, Rudolf and Erdmann, Bodo and Roitzsch, Rainer}, title = {An Object-Oriented Adaptive Finite Element Code}, booktitle = {Modern Software Tools for Scientific Computing}, editor = {Arge, Erlend and Bruaset, Are Magnus and Langtangen, Hans Petter}, publisher = {Birkh{\"a}user, Boston}, pages = {105 -- 124}, year = {1997}, language = {en} } @article{ColliFranzoneDeuflhardErdmannetal.2006, author = {Colli Franzone, Piero and Deuflhard, Peter and Erdmann, Bodo and Lang, Jens and Pavarino, Luca Franco}, title = {Adaptivity in Space and Time for Reaction-Diffusion Systems in Electrocardiology}, volume = {28}, journal = {SIAM J. Sc. Comp.}, pages = {942 -- 962}, year = {2006}, language = {en} } @inproceedings{ZachowHierlErdmann2004, author = {Zachow, Stefan and Hierl, Thomas and Erdmann, Bodo}, title = {A quantitative evaluation of 3D soft tissue prediction in maxillofacial surgery planning}, booktitle = {Proc. 3. Jahrestagung der Deutschen Gesellschaft f{\"u}r Computer- und Roboter-assistierte Chirurgie e.V.}, address = {M{\"u}nchen}, year = {2004}, language = {en} } @inproceedings{ZachowHierlErdmann2004, author = {Zachow, Stefan and Hierl, Thomas and Erdmann, Bodo}, title = {On the Predictability of tissue changes after osteotomy planning in maxillofacial surgery}, booktitle = {Computer Assisted Radiology and Surgery (CARS)}, address = {Chicago, USA}, doi = {10.1016/j.ics.2004.03.043}, pages = {648 -- 653}, year = {2004}, language = {en} } @inproceedings{ZachowHierlErdmann2004, author = {Zachow, Stefan and Hierl, Thomas and Erdmann, Bodo}, title = {{\"U}ber die Genauigkeit einer 3D Weichgewebepr{\"a}diktion in der MKG-Cirurgie}, booktitle = {Workshop 'Bildverarbeitung f{\"u}r die Medizin' (BVM)}, address = {Berlin, Germany}, pages = {75 -- 79}, year = {2004}, language = {en} } @misc{WeiserErdmannSchenkletal.2017, author = {Weiser, Martin and Erdmann, Bodo and Schenkl, Sebastian and Muggenthaler, Holger and Hubig, Michael and Mall, Gita and Zachow, Stefan}, title = {Uncertainty in Temperature-Based Determination of Time of Death}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-63818}, year = {2017}, abstract = {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.}, language = {en} } @misc{WeiserErdmannDeuflhard2010, author = {Weiser, Martin and Erdmann, Bodo and Deuflhard, Peter}, title = {On Efficiency and Accuracy in Cardioelectric Simulation}, journal = {Progress in Industrial Mathematics at ECMI 2008}, editor = {Wilson, E. and Fitt, A. and Ockendon, H. and Norbury, J.}, publisher = {Springer}, pages = {371 -- 376}, year = {2010}, abstract = {Reasons for the failure of adaptive methods to deliver improved efficiency when integrating monodomain models for myocardiac excitation are discussed. Two closely related techniques for reducing the computational complexity of linearly implicit integrators, deliberate sparsing and splitting, are investigated with respect to their impact on computing time and accuracy.}, language = {en} } @article{WeiserRoelligArndtetal.2010, author = {Weiser, Martin and R{\"o}llig, Mathias and Arndt, Ralf and Erdmann, Bodo}, title = {Development and test of a numerical model for pulse thermography in civil engineering}, volume = {46}, journal = {Heat and Mass Transfer}, number = {11-12}, pages = {1419 -- 1428}, year = {2010}, abstract = {Pulse thermography of concrete structures is used in civil engineering for detecting voids, honeycombing and delamination. The physical situation is readily modeled by Fourier's law. Despite the simplicity of the PDE structure, quantitatively realistic numerical 3D simulation faces two major obstacles. First, the short heating pulse induces a thin boundary layer at the heated surface which encapsulates all information and therefore has to be resolved faithfully. Even with adaptive mesh refinement techniques, obtaining useful accuracies requires an unsatisfactorily fine discretization. Second, bulk material parameters and boundary conditions are barely known exactly. We address both issues by a semi-analytic reformulation of the heat transport problem and by parameter identification. Numerical results are compared with measurements of test specimens.}, language = {en} } @misc{LangErdmann2000, 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}, year = {2000}, 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} } @misc{ErdmannKoberLangetal.2001, author = {Erdmann, Bodo and Kober, Cornelia and Lang, Jens and Sader, Robert and Zeilhofer, Hans-Florian and Deuflhard, Peter}, title = {Efficient and Reliable Finite Element Methods for Simulation of the Human Mandible}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6403}, number = {01-14}, year = {2001}, abstract = {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.}, language = {en} }