TY - JOUR A1 - Lubkoll, Lars A1 - Schiela, Anton A1 - Weiser, Martin T1 - An optimal control problem in polyconvex hyperelasticity JF - SIAM J. Control Opt. N2 - We consider a shape implant design problem that arises in the context of facial surgery. We introduce a reformulation as an optimal control problem, where the control acts as a boundary force. The state is modelled as a minimizer of a polyconvex hyperelastic energy functional. We show existence of optimal solutions and derive - on a formal level - first order optimality conditions. Finally, preliminary numerical results are presented. Y1 - 2014 U6 - https://doi.org/10.1137/120876629 VL - 52 IS - 3 SP - 1403 EP - 1422 ER - TY - JOUR A1 - Götschel, Sebastian A1 - Nagaiah, Chamakuri A1 - Kunisch, Karl A1 - Weiser, Martin T1 - Lossy Compression in Optimal Control of Cardiac Defibrillation JF - J. Sci. Comput. N2 - This paper presents efficient computational techniques for solving an optimization problem in cardiac defibrillation governed by the monodomain equations. Time-dependent electrical currents injected at different spatial positions act as the control. Inexact Newton-CG methods are used, with reduced gradient computation by adjoint solves. In order to reduce the computational complexity, adaptive mesh refinement for state and adjoint equations is performed. To reduce the high storage and bandwidth demand imposed by adjoint gradient and Hessian-vector evaluations, a lossy compression technique for storing trajectory data is applied. An adaptive choice of quantization tolerance based on error estimates is developed in order to ensure convergence. The efficiency of the proposed approach is demonstrated on numerical examples. Y1 - 2014 U6 - https://doi.org/10.1007/s10915-013-9785-x VL - 60 IS - 1 SP - 35 EP - 59 ER - TY - GEN A1 - Deuflhard, Peter A1 - Kornhuber, Ralf A1 - Sander, Oliver A1 - Schiela, Anton A1 - Weiser, Martin ED - Deuflhard, Peter ED - Grötschel, Martin ED - Hömberg, Dietmar ED - Horst, Ulrich ED - Kramer, Jürg ED - Mehrmann, Volker ED - Polthier, Konrad ED - Schmidt, Frank ED - Schütte, Christof ED - Skutella, Martin ED - Sprekels, Jürgen T1 - Mathematics cures virtual patients T2 - MATHEON-Mathematics for Key Technologies Y1 - 2014 VL - 1 SP - 7 EP - 25 PB - European Mathematical Society ER - TY - GEN A1 - Weiser, Martin A1 - Scacchi, Simone T1 - Spectral Deferred Correction methods for adaptive electro-mechanical coupling in cardiac simulation N2 - We investigate spectral deferred correction (SDC) methods for time stepping and their interplay with spatio-temporal adaptivity, applied to the solution of the cardiac electro-mechanical coupling model. This model consists of the Monodomain equations, a reaction-diffusion system modeling the cardiac bioelectrical activity, coupled with a quasi-static mechanical model describing the contraction and relaxation of the cardiac muscle. The numerical approximation of the cardiac electro-mechanical coupling is a challenging multiphysics problem, because it exhibits very different spatial and temporal scales. Therefore, spatio-temporal adaptivity is a promising approach to reduce the computational complexity. SDC methods are simple iterative methods for solving collocation systems. We exploit their flexibility for combining them in various ways with spatio-temporal adaptivity. The accuracy and computational complexity of the resulting methods are studied on some numerical examples. T3 - ZIB-Report - 14-22 Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-50695 SN - 1438-0064 ER -