@article{WeiserGaenzlerSchiela2007, author = {Weiser, Martin and G{\"a}nzler, Tobias and Schiela, Anton}, title = {A control reduced primal interior point method for a class of control constrained optimal control problems}, series = {Comput. Optim. Appl.}, volume = {41}, journal = {Comput. Optim. Appl.}, number = {1}, pages = {127 -- 145}, year = {2007}, language = {en} } @article{WeihrauchWustWeiseretal.2007, author = {Weihrauch, Mirko and Wust, Peter and Weiser, Martin and Nadobny, Johanna and Eisenhardt, Steffen and Budach, Volker and Gellermann, Johanna}, title = {Adaptation of antenna profiles for control of MR guided hyperthermia (HT) in a hybrid MR-HT system}, series = {Medical Physics}, volume = {34}, journal = {Medical Physics}, number = {12}, pages = {4717 -- 4725}, year = {2007}, language = {en} } @article{MoldenhauerWeiserZachow, author = {Moldenhauer, Marian and Weiser, Martin and Zachow, Stefan}, title = {Adaptive Algorithms for Optimal Hip Implant Positioning}, series = {PAMM}, volume = {17}, journal = {PAMM}, number = {1}, doi = {10.1002/pamm.201710071}, pages = {203 -- 204}, abstract = {In an aging society where the number of joint replacements rises, it is important to also increase the longevity of implants. In particular hip implants have a lifetime of at most 15 years. This derives primarily from pain due to implant migration, wear, inflammation, and dislocation, which is affected by the positioning of the implant during the surgery. Current joint replacement practice uses 2D software tools and relies on the experience of surgeons. Especially the 2D tools fail to take the patients' natural range of motion as well as stress distribution in the 3D joint induced by different daily motions into account. Optimizing the hip joint implant position for all possible parametrized motions under the constraint of a contact problem is prohibitively expensive as there are too many motions and every position change demands a recalculation of the contact problem. For the reduction of the computational effort, we use adaptive refinement on the parameter domain coupled with the interpolation method of Kriging. A coarse initial grid is to be locally refined using goal-oriented error estimation, reducing locally high variances. This approach will be combined with multi-grid optimization such that numerical errors are reduced.}, language = {en} } @article{SemlerWeiser, author = {Semler, Phillip and Weiser, Martin}, title = {Adaptive Gaussian Process Regression for Efficient Building of Surrogate Models in Inverse Problems}, series = {Inverse Problems}, volume = {39}, journal = {Inverse Problems}, number = {12}, doi = {10.1088/1361-6420/ad0028}, pages = {125003}, abstract = {In a task where many similar inverse problems must be solved, evaluating costly simulations is impractical. Therefore, replacing the model y with a surrogate model y(s) that can be evaluated quickly leads to a significant speedup. The approximation quality of the surrogate model depends strongly on the number, position, and accuracy of the sample points. With an additional finite computational budget, this leads to a problem of (computer) experimental design. In contrast to the selection of sample points, the trade-off between accuracy and effort has hardly been studied systematically. We therefore propose an adaptive algorithm to find an optimal design in terms of position and accuracy. Pursuing a sequential design by incrementally appending the computational budget leads to a convex and constrained optimization problem. As a surrogate, we construct a Gaussian process regression model. We measure the global approximation error in terms of its impact on the accuracy of the identified parameter and aim for a uniform absolute tolerance, assuming that y(s) is computed by finite element calculations. A priori error estimates and a coarse estimate of computational effort relate the expected improvement of the surrogate model error to computational effort, resulting in the most efficient combination of sample point and evaluation tolerance. We also allow for improving the accuracy of already existing sample points by continuing previously truncated finite element solution procedures.}, language = {en} } @article{VolkweinWeiser2002, author = {Volkwein, S. and Weiser, Martin}, title = {Affine Invariant Convergence Analysis for Inexact Augmented Lagrangian SQP Methods}, series = {SIAM J. Control Optim.}, volume = {41}, journal = {SIAM J. Control Optim.}, number = {3}, pages = {875 -- 899}, year = {2002}, language = {en} } @article{LubkollSchielaWeiser, author = {Lubkoll, Lars and Schiela, Anton and Weiser, Martin}, title = {An affine covariant composite step method for optimization with PDEs as equality constraints}, series = {Optimization Methods and Software}, volume = {32}, journal = {Optimization Methods and Software}, number = {5}, doi = {10.1080/10556788.2016.1241783}, pages = {1132 -- 1161}, 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} } @article{LubkollSchielaWeiser, author = {Lubkoll, Lars and Schiela, Anton and Weiser, Martin}, title = {An optimal control problem in polyconvex hyperelasticity}, series = {SIAM J. Control Opt.}, volume = {52}, journal = {SIAM J. Control Opt.}, number = {3}, doi = {10.1137/120876629}, pages = {1403 -- 1422}, abstract = {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.}, language = {en} } @article{WeiserSchielaDeuflhard2005, author = {Weiser, Martin and Schiela, Anton and Deuflhard, Peter}, title = {Asymptotic Mesh Independence of Newton's Method Revisited}, series = {SIAM J. Num. Anal.}, volume = {42}, journal = {SIAM J. Num. Anal.}, number = {5}, pages = {1830 -- 1845}, year = {2005}, language = {en} } @article{SchenklMuggenthalerHubigetal.2017, author = {Schenkl, Sebastian and Muggenthaler, Holger and Hubig, Michael and Erdmann, Bodo and Weiser, Martin and Zachow, Stefan and Heinrich, Andreas and G{\"u}ttler, Felix Victor and Teichgr{\"a}ber, Ulf and Mall, Gita}, title = {Automatic CT-based finite element model generation for temperature-based death time estimation: feasibility study and sensitivity analysis}, series = {International Journal of Legal Medicine}, volume = {131}, journal = {International Journal of Legal Medicine}, number = {3}, doi = {doi:10.1007/s00414-016-1523-0}, pages = {699 -- 712}, year = {2017}, abstract = {Temperature based death time estimation is based either on simple phenomenological models of corpse cooling or on detailed physical heat transfer models. The latter are much more complex, but allow a higher accuracy of death time estimation as in principle all relevant cooling mechanisms can be taken into account. Here, a complete work flow for finite element based cooling simulation models is presented. The following steps are demonstrated on CT-phantoms: • CT-scan • Segmentation of the CT images for thermodynamically relevant features of individual geometries • Conversion of the segmentation result into a Finite Element (FE) simulation model • Computation of the model cooling curve • Calculation of the cooling time For the first time in FE-based cooling time estimation the steps from the CT image over segmentation to FE model generation are semi-automatically performed. The cooling time calculation results are compared to cooling measurements performed on the phantoms under controlled conditions. In this context, the method is validated using different CTphantoms. Some of the CT phantoms thermodynamic material parameters had to be experimentally determined via independent experiments. Moreover the impact of geometry and material parameter uncertainties on the estimated cooling time is investigated by a sensitivity analysis.}, language = {en} } @article{WilhelmsSeemannWeiseretal., author = {Wilhelms, Mathias and Seemann, Gunnar and Weiser, Martin and D{\"o}ssel, Olaf}, title = {Benchmarking Solvers of the Monodomain Equation in Cardiac Electrophysiological Modeling}, series = {Biomed. Engineer.}, volume = {55}, journal = {Biomed. Engineer.}, doi = {10.1515/BMT.2010.712}, pages = {99 -- 102}, language = {en} }