@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} } @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} } @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} } @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} }