TY - GEN A1 - Weiser, Martin A1 - Erdmann, Bodo A1 - Deuflhard, Peter T1 - On Efficiency and Accuracy in Cardioelectric Simulation N2 - 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. T3 - ZIB-Report - 08-41 KW - elektrische Herzanregung KW - Diskretisierungsfehler KW - splitting KW - mass lumping KW - cardioelectric excitation KW - discretization error KW - splitting KW - mass lumping Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10934 SN - 1438-0064 ER - TY - GEN A1 - Weiser, Martin A1 - Röllig, Mathias A1 - Arndt, Ralf A1 - Erdmann, Bodo T1 - Development and test of a numerical model for pulse thermography in civil engineering N2 - 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. T3 - ZIB-Report - 08-45 KW - finite element model KW - KARDOS KW - pulse thermography KW - civil engineering KW - inverse solution Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10980 SN - 1438-0064 ER - TY - GEN A1 - Franzone, Piero Colli 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 N2 - 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. T3 - ZIB-Report - 05-30 KW - reaction-diffusion equations KW - cardiac Bidomain and Monodomain models KW - adaptive finite elements KW - adaptive time integration Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8649 ER - TY - GEN A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Matera, Sebastian A1 - Wilmanski, Krzysztof T1 - Adaptive Linearly Implicit Methods for Linear Poroelastic Equations N2 - 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. T3 - ZIB-Report - 06-37 KW - Poroelasticity KW - Biot's model KW - bone healing KW - adaptive finite elements KW - adaptive time integration KW - Rosenbrock methods Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9312 ER - TY - GEN A1 - Weiser, Martin A1 - Deuflhard, Peter A1 - Erdmann, Bodo T1 - Affine conjugate adaptive Newton methods for nonlinear elastomechanics N2 - 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. T3 - ZIB-Report - 04-01 KW - affine conjugate Newton methods KW - nonconvex minimization KW - nonlinear elastomechnics KW - cranio-maxillofacial surgery KW - soft tissue simulation KW - multilev Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7768 ER - TY - GEN A1 - Deuflhard, Peter A1 - Erdmann, Bodo A1 - Roitzsch, Rainer A1 - Lines, Glenn Terje T1 - Adaptive Finite Element Simulation of Ventricular Fibrillation Dynamics N2 - 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). T3 - ZIB-Report - 06-49 KW - reaction-diffusion equations KW - Aliev-Panfilov model KW - electrocardiology KW - adaptive finite elements KW - adaptive time integration KW - adaptive Rothe method Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9431 ER - TY - CHAP A1 - Zachow, Stefan A1 - Erdmann, Bodo A1 - Hege, Hans-Christian A1 - Deuflhard, Peter T1 - Advances in 3D osteotomy planning with 3D soft tissue prediction T2 - Proc. 2nd International Symposium on Computer Aided Surgery around the Head, Abstract Y1 - 2004 SP - 31 CY - Bern ER - TY - JOUR A1 - Lang, Jens A1 - Erdmann, Bodo A1 - Seebaß, Martin T1 - Impact of Nonlinear Heat Tansfer on Temperature Control in Regional Hypertermia JF - IEEE Trans. Biomed. Engrg. Y1 - 1999 U6 - https://doi.org/10.1109/10.784145 VL - 46 SP - 1129 EP - 1138 ER - TY - JOUR A1 - Hellmich, Christian A1 - Kober, Cornelia A1 - Erdmann, Bodo T1 - Micromechanics-based conversion of CT data into anisotropic elasticity tensors, applied to FE simulations of a mandible JF - Annals of Biomedical Engineering Y1 - 2008 U6 - https://doi.org/10.1007/s10439-007-9393-8 VL - 36 IS - 1 SP - 108 EP - 122 ER - TY - CHAP A1 - Erdmann, Bodo A1 - Kober, C. A1 - Lang, Jens A1 - Deuflhard, Peter A1 - Zeilhofer, J. A1 - Sader, Robert T1 - Efficient and Reliable Finite Element Methods for Simulation of the Human Mandible T2 - proceedings of 9th Workshop on The Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields Y1 - 2002 CY - Ulm, Germany ER - TY - JOUR A1 - Erdmann, Bodo A1 - Ljubijankic, M. A1 - Nytsch-Geusen, C. T1 - Entwicklung einer Toolbox zur zwei- und dreidimensionalen instationären thermischen Bauteilsimulation mit KARDOS JF - Bauphsik Y1 - 2007 VL - 29 IS - 1 SP - 33 EP - 39 ER - TY - CHAP A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Roitzsch, Rainer A1 - Lourenco, Maria José A1 - Rosa, S. A1 - de Castro, C.A. A1 - Albuquerque, C. ED - Kim, M. ED - Ro, S. T1 - Simulation of the Transient Heating in an Unsymmetrical Coated Hot-Strip Sensor With a Self-Adaptive Finite Element Method T2 - Proc. 5th Asian Thermophysical Properties Conference Y1 - 1998 VL - 1 SP - 91 EP - 94 CY - Seoul, South Corea ER - TY - CHAP A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Seebass, Martin ED - de Vahl Davis, G. ED - Leonardi, E. T1 - Adaptive Solutions of Nonlinear Parabolic Equations with Application to Hyperthermia Treatments T2 - CHT’97 Y1 - 1997 SP - 103 EP - 110 CY - Cesme, Turkey ER - TY - CHAP A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Seebass, Martin ED - Diller, K. T1 - Optimization of Temperature Distributions for Regional Hyperthermia based on a Nonlinear Heat Transfer Model T2 - Biotransport Y1 - 1998 VL - 858 SP - 36 EP - 46 ER - TY - JOUR A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Seebass, Martin T1 - The Impact of a Nonlinear Heat Transfer Model for Temperature Control in Regional Hyperthermia JF - IEEE Transactions on Biomedical Engineering Y1 - 1999 VL - 49 IS - 9 SP - 1129 EP - 1138 ER - TY - CHAP A1 - Lang, Jens A1 - Erdmann, Bodo A1 - Roitzsch, Rainer ED - Sydow, Achim T1 - Adaptive Time-Space Discretization for Combustion Problems T2 - 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics, Vol. 2, Numerical Mathematics Y1 - 1997 SP - 49 EP - 155 PB - Wissenschaft und Technik Verlag, Berlin ER - TY - CHAP A1 - Lang, Jens A1 - Erdmann, Bodo A1 - Roitzsch, Rainer ED - Lewis, R. T1 - Three-Dimensional Fully Adaptive Solution of Thermo-Diffusive Flame Propagation Problems T2 - Numerical Methods in Thermal Problems Y1 - 1997 SP - 857 EP - 862 PB - Pineridge Press, Swansea, UK ER - TY - CHAP A1 - Lang, Jens A1 - Erdmann, Bodo A1 - Kober, Cornelia A1 - Deuflhard, Peter A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian ED - Alt, Walter ED - Hermann, Martin T1 - Effiziente und zuverlässige Finite-Elemente-Methoden zur Simulation des menschlichen Unterkiefers T2 - Berichte des IZWR - Interdisziplinäres Zentrum für Wissenschaftliches Rechnen Y1 - 2003 VL - 1 SP - 49 EP - 57 PB - Universität Jena CY - 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 - Kober, C. A1 - Erdmann, Bodo A1 - Hellmich, Christian A1 - Geiger, M. A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian ED - Davidovitch, Z. ED - Mah, J. ED - Suthanarak, S. T1 - How does the periodontal ligament influence overall stress/strain profiles of a partially edentulous mandible? T2 - Proc. of 8th Int. Conference on Biological Mechanisms of Tooth Eruption, Resorption and Movement, Phuket, Thailand Y1 - 2005 CY - Harvard Society of the Advancement of Orthodontics, Boston, Massachusetts, USA ER - TY - CHAP A1 - Kober, C. A1 - Erdmann, Bodo A1 - Hellmich, Christian A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian T1 - Anisotropic Simulation of the Human Mandible T2 - Proc. of 17th ASCE Engineering Mechanics Conference Y1 - 2004 PB - Univ. of Delaware ER -