@incollection{Deuflhard2003, author = {Deuflhard, Peter}, title = {From Molecular Dynamics to Conformational Dynamics in Drug Design}, booktitle = {Trends in Nonlinear Analysis}, editor = {et al. Kirkilionis, Markus}, publisher = {Springer Verlag Berlin}, pages = {269 -- 288}, year = {2003}, language = {en} } @misc{DeuflhardZachow2012, author = {Deuflhard, Peter and Zachow, Stefan}, title = {Mathematische Therapie- und Operationsplanung}, publisher = {Berliner Wirtschaftsgespr{\"a}che e.V.}, address = {Berlin}, pages = {89 -- 90}, year = {2012}, language = {en} } @incollection{DeuflhardDoesselLouisetal.2010, author = {Deuflhard, Peter and D{\"o}ssel, Olaf and Louis, Alfred and Zachow, Stefan}, title = {More Mathematics into Medicine!}, booktitle = {Production Factor Mathematics}, publisher = {Springer}, pages = {357 -- 378}, year = {2010}, language = {en} } @article{WeiserZachowDeuflhard2010, author = {Weiser, Martin and Zachow, Stefan and Deuflhard, Peter}, title = {Craniofacial Surgery Planning Based on Virtual Patient Models}, volume = {52}, journal = {it - Information Technology}, number = {5}, publisher = {Oldenbourg Verlagsgruppe}, doi = {10.1524/itit.2010.0600}, pages = {258 -- 263}, year = {2010}, language = {en} } @inproceedings{ZachowHierlErdmann2004, author = {Zachow, Stefan and Hierl, Thomas and Erdmann, Bodo}, title = {A quantitative evaluation of 3D soft tissue prediction in maxillofacial surgery planning}, booktitle = {Proc. 3. Jahrestagung der Deutschen Gesellschaft f{\"u}r Computer- und Roboter-assistierte Chirurgie e.V.}, address = {M{\"u}nchen}, year = {2004}, language = {en} } @inproceedings{WeiserScacchi2017, author = {Weiser, Martin and Scacchi, Simone}, title = {Spectral Deferred Correction methods for adaptive electro-mechanical coupling in cardiac simulation}, booktitle = {G. Russo et al.(eds.) Progress in Industrial Mathematics at ECMI 2014}, publisher = {Springer}, doi = {10.1007/978-3-319-23413-7_42}, pages = {321 -- 328}, year = {2017}, abstract = {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.}, language = {en} } @misc{LubkollSchielaWeiser2015, author = {Lubkoll, Lars and Schiela, Anton and Weiser, Martin}, title = {An affine covariant composite step method for optimization with PDEs as equality constraints}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53954}, year = {2015}, abstract = {We propose a composite step method, designed for equality constrained optimization with partial differential equations. Focus is laid on the construction of a globalization scheme, which is based on cubic regularization of the objective and an affine covariant damped Newton method for feasibility. We show finite termination of the inner loop and fast local convergence of the algorithm. We discuss preconditioning strategies for the iterative solution of the arising linear systems with projected conjugate gradient. Numerical results are shown for optimal control problems subject to a nonlinear heat equation and subject to nonlinear elastic equations arising from an implant design problem in craniofacial surgery.}, language = {en} } @misc{WeiserGhosh2016, author = {Weiser, Martin and Ghosh, Sunayana}, title = {Theoretically optimal inexact SDC methods}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53140}, year = {2016}, abstract = {In several inital value problems with particularly expensive right hand side computation, there is a trade-off between accuracy and computational effort in evaluating the right hand sides. We consider inexact spectral deferred correction (SDC) methods for solving such non-stiff 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 an error model bounding the total error in terms of the right hand side 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 tolerance selection is worked out by minimizing the total work subject to achieving the requested tolerance.}, language = {en} } @phdthesis{Goetschel2015, author = {G{\"o}tschel, Sebastian}, title = {Adaptive Lossy Trajectory Compression for Optimal Control of Parabolic PDEs}, year = {2015}, abstract = {Optimal control problems governed by nonlinear, time-dependent PDEs on three-dimensional spatial domains are an important tool in many fields, ranging from engineering applications to medicine. For the solution of such optimization problems, methods working on the reduced objective functional are often employed to avoid a full spatio-temporal discretization of the problem. The evaluation 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, requiring the storage of a full 4D data set. If Newton-CG methods are used, two additional trajectories have to be stored. To get numerical results that are accurate enough, in many cases very fine discretizations in time and space are necessary, leading to a significant amount of data to be stored and transmitted to mass storage. This thesis deals with the development and analysis of methods for lossy compression of such finite element solutions. The algorithms are based on a change of basis to reduce correlations in the data, combined with quantization. This is achieved by transforming the finite element coefficient vector from the nodal to the hierarchical basis, followed by rounding the coefficients to a prescribed precision. Due to the inexact reconstruction, and thus inexact data for the adjoint equation, the error induced in the reduced gradient, and reduced Hessian, has to be controlled, to not impede convergence of the optimization. Accuracy requirements of different optimization methods are analyzed, and computable error estimates for the influence of lossy trajectory storage are derived. These tools are used to adaptively control the accuracy of the compressed data. The efficiency of the algorithms is demonstrated on several numerical examples, ranging from a simple linear, scalar equation to a semi-linear system of reaction-diffusion equations. In all examples considerable reductions in storage space and bandwidth requirements are achieved, without significantly influencing the convergence behavior of the optimization methods. Finally, to go beyond pointwise error control, the hierarchical basis transform can be replaced by more sophisticated wavelet transforms. Numerical experiments indicate that choosing suitable norms for error control allows higher compression factors.}, language = {en} } @misc{Freytag2017, author = {Freytag, Yvonne}, title = {Optimal Experimental Design to Estimate the Time of Death in a Bayesian Context}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-62475}, year = {2017}, abstract = {This thesis is devoted to the interdisciplinary work between mathematicians and forensic experts: the modeling of the human body cooling process after death laying the foundation for the estimation of the time of death. An inverse problem needs to be solved. In this thesis the inverse problem computes the time of death given the measured body temperature and the Forward Model that simulates the body cooling process. The Forward Model is based on the heat equation established by Fourier. This differential equation is numerically solved by the discretization over space by the Finite Element Method and the discretization over time by the Implicit Euler Method. The applications in this thesis demand a fast computation time. A model reduction is achieved by the Proper Orthogonal Decomposition in combination with the Galerkin Method. For reasons of simplification the computations and the measurements are restricted to a cylindrical phantom that is made out of homogeneous polyethylene. The estimate of the time of death is accompanied by an uncertainty. The inverse problem is incorporated by Bayesian inference to interpret the quality of the estimate and the effciency of the experiment. The uncertainty of the estimate of the time of death is minimized by approaching the Optimal Design of the Experiment. An objective function measures the certainty of the data and lays the foundation of the optimization problem. Solving the optimization problem is successfully done by relaxing the complex discrete NP-hard problem and applying a gradient-based method. The results of this thesis clearly show that the design of an experiment has a great in- uence on the outcome of the quality of the estimate. The comparison of the estimate and its properties based on different designs and conditions reveals the effciency of the Design of Experiment in the context of the estimation of the time of death.}, language = {en} }