TY - JOUR A1 - Wilhelms, Mathias A1 - Seemann, Gunnar A1 - Weiser, Martin A1 - Dössel, Olaf T1 - Benchmarking Solvers of the Monodomain Equation in Cardiac Electrophysiological Modeling JF - Biomed. Engineer. Y1 - 2010 U6 - https://doi.org/10.1515/BMT.2010.712 VL - 55 SP - 99 EP - 102 ER - TY - JOUR A1 - Weiser, Martin A1 - Zachow, Stefan A1 - Deuflhard, Peter T1 - Craniofacial Surgery Planning Based on Virtual Patient Models JF - it - Information Technology Y1 - 2010 U6 - https://doi.org/10.1524/itit.2010.0600 VL - 52 IS - 5 SP - 258 EP - 263 PB - Oldenbourg Verlagsgruppe ER - TY - JOUR A1 - Weiser, Martin A1 - Schiela, Anton A1 - Deuflhard, Peter T1 - Asymptotic Mesh Independence of Newton’s Method Revisited JF - SIAM J. Num. Anal. Y1 - 2005 VL - 42 IS - 5 SP - 1830 EP - 1845 ER - TY - JOUR A1 - Weiser, Martin A1 - Schiela, Anton T1 - Function space interior point methods for PDE constrained optimization JF - PAMM Y1 - 2004 VL - 4 IS - 1 SP - 43 EP - 46 ER - TY - JOUR 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 JF - Heat and Mass Transfer 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. Y1 - 2010 VL - 46 IS - 11-12 SP - 1419 EP - 1428 ER - TY - JOUR A1 - Weiser, Martin A1 - Götschel, Sebastian T1 - State Trajectory Compression for Optimal Control with Parabolic PDEs JF - SIAM J. Sci. Comput. N2 - In optimal control problems with nonlinear time-dependent 3D PDEs, full 4D discretizations are usually prohibitive due to the storage requirement. For this reason gradient and quasi-Newton methods working on the reduced functional are often employed. The computation of the reduced gradient requires one solve of the state equation forward in time, and one backward solve of the adjoint equation. The state enters into the adjoint equation, again requiring the storage of a full 4D data set. We propose a lossy compression algorithm using an inexact but cheap predictor for the state data, with additional entropy coding of prediction errors. As the data is used inside a discretized, iterative algorithm, lossy coding maintaining an error bound is sufficient. Y1 - 2012 U6 - https://doi.org/10.1137/11082172X VL - 34 IS - 1 SP - A161 EP - A184 ER - TY - JOUR A1 - Weiser, Martin A1 - Gänzler, Tobias A1 - Schiela, Anton T1 - A control reduced primal interior point method for a class of control constrained optimal control problems JF - Comput. Optim. Appl. Y1 - 2007 VL - 41 IS - 1 SP - 127 EP - 145 ER - TY - JOUR A1 - Weiser, Martin A1 - Ghosh, Sunayana T1 - Theoretically optimal inexact SDC methods JF - Communications in Applied Mathematics and Computational Science N2 - In several inital value problems with particularly expensive right hand side evaluation or implicit step computation, there is a trade-off between accuracy and computational effort. We consider inexact spectral deferred correction (SDC) methods for solving such initial value problems. SDC methods are interpreted as fixed point iterations and, due to their corrective iterative nature, allow to exploit the accuracy-work-tradeoff for a reduction of the total computational effort. On one hand we derive error models bounding the total error in terms of the evaluation errors. On the other hand, we define work models describing the computational effort in terms of the evaluation accuracy. Combining both, a theoretically optimal local tolerance selection is worked out by minimizing the total work subject to achieving the requested tolerance. The properties of optimal local tolerances and the predicted efficiency gain compared to simpler heuristics, and a reasonable practical performance, are illustrated on simple numerical examples. Y1 - 2018 U6 - https://doi.org/10.2140/camcos.2018.13.53 IS - 13-1 SP - 53 EP - 86 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 - 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 -