TY - GEN A1 - Weiser, Martin A1 - Götschel, Sebastian T1 - State Trajectory Compression for Optimal Control with Parabolic PDEs 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. T3 - ZIB-Report - 10-05 KW - optimal control KW - adjoint gradient computation KW - trajectory storage Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11676 SN - 1438-0064 ER - TY - GEN A1 - Götschel, Sebastian A1 - Weiser, Martin A1 - Schiela, Anton T1 - Solving Optimal Control Problems with the Kaskade 7 Finite Element Toolbox N2 - This paper presents concepts and implementation of the finite element toolbox Kaskade 7, a flexible C++ code for solving elliptic and parabolic PDE systems. Issues such as problem formulation, assembly and adaptivity are discussed at the example of optimal control problems. Trajectory compression for parabolic optimization problems is considered as a case study. T3 - ZIB-Report - 10-25 KW - partial differential equations KW - optimal control KW - finite elements KW - generic programming KW - adaptive methods Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11909 SN - 1438-0064 ER - TY - GEN A1 - Schiela, Anton A1 - Weiser, Martin ED - Diehl, M. ED - Glineur, F. ED - Jarlebring, E. ED - Michiels, W. T1 - Barrier methods for a control problem from hyperthermia treatment planning T2 - Recent Advances in Optimization and its Applications in Engineering (Proceedings of 14th Belgian-French-German Conference on Optimization 2009) N2 - We consider an optimal control problem from hyperthermia treatment planning and its barrier regularization. We derive basic results, which lay the groundwork for the computation of optimal solutions via an interior point path-following method. Further, we report on a numerical implementation of such a method and its performance at an example problem. Y1 - 2010 SP - 419 EP - 428 PB - Springer 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 - GEN A1 - Weiser, Martin A1 - Erdmann, Bodo A1 - Deuflhard, Peter ED - Wilson, E. ED - Fitt, A. ED - Ockendon, H. ED - Norbury, J. T1 - On Efficiency and Accuracy in Cardioelectric Simulation T2 - Progress in Industrial Mathematics at ECMI 2008 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. Y1 - 2010 SP - 371 EP - 376 PB - Springer ER - 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 - GEN A1 - Wust, Peter A1 - Weihrauch, Mirko A1 - Weiser, Martin A1 - Gellermann, Johanna A1 - Eisenhardt, Steffen A1 - Chobrok, Thorsten A1 - Budach, Volker ED - Dössel, O. ED - Schlegel, W. ED - Magjarevic, R. T1 - Optimization of clinical radiofrequency hyperthermia by use of MR-thermography in a hybrid system T2 - World Congress on Medical Physics and Biomedical Engineering, September 2009, Munich, Germany Y1 - 2010 SP - 174 EP - 175 PB - Springer ER - TY - JOUR A1 - Götschel, Sebastian A1 - Weiser, Martin T1 - State Trajectory Compression in Optimal Control JF - PAMM N2 - In optimal control problems with nonlinear time-dependent 3D PDEs, the computation of the reduced gradient by adjoint methods requires one solve of the state equation forward in time, and one backward solve of the adjoint equation. Since the state enters into the adjoint equation, the storage of a 4D discretization is necessary. We propose a lossy compression algorithm using a cheap predictor for the state data, with additional entropy coding of prediction errors. Analytical and numerical results indicate that compression factors around 30 can be obtained without exceeding the FE discretization error. Y1 - 2010 U6 - https://doi.org/10.1002/pamm.201010282 VL - 10 IS - 1 SP - 579 EP - 580 ER - TY - GEN A1 - Weiser, Martin T1 - Delayed Residual Compensation for Bidomain Equations T2 - AIP Conference Proceedings N2 - The biodomain model of cardioelectric excitation consists of a reaction‐diffusion equation, an elliptic algebraic constraint, and a set of pointwise ODEs. Fast reaction enforces small time steps, such that for common mesh sizes the reaction‐diffusion equation is easily solved implicitly due to a dominating mass matrix. In contrast, the elliptic constraint does not benefit from small time steps and requires a comparably expensive solution. We propose a delayed residual compensation that improves the solution of the elliptic constraint and thus alleviates the need for long iteration times. Y1 - 2010 U6 - https://doi.org/10.1063/1.3498495 VL - 1281 SP - 419 EP - 422 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 -