@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} }