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 - 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 - Schiela, Anton A1 - Weiser, Martin T1 - Superlinear convergence of the Control Reduced Interior Point Method for PDE Constrained Optimization JF - Computational Optimization and Applications Y1 - 2008 VL - 39 IS - 3 SP - 369 EP - 393 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 - Deuflhard, Peter A1 - Schiela, Anton A1 - Weiser, Martin T1 - Mathematical Cancer Therapy Planning in Deep Regional Hyperthermia JF - Acta Numerica N2 - This paper surveys the required mathematics for a typical challenging problem from computational medicine, the cancer therapy planning in deep regional hyperthermia. In the course of many years of close cooperation with clinics, the medical problem gave rise to quite a number of subtle mathematical problems, part of which had been unsolved when the common project started. Efficiency of numerical algorithms, i.e. computational speed and monitored reliability, play a decisive role for the medical treatment. Off-the-shelf software had turned out to be not sufficient to meet the requirements of medicine. Rather, new mathematical theory as well as new numerical algorithms had to be developed. In order to make our algorithms useful in the clinical environment, new visualization software, a virtual lab, including 3D geometry processing of individual virtual patients had to be designed and implemented. Moreover, before the problems could be attacked by numerical algorithms, careful mathematical modelling had to be done. Finally, parameter identification and constrained optimization for the PDEs had to be newly analyzed and realized over the individual patient's geometry. Our new techniques had an impact on the specificity of the individual patients' treatment and on the construction of an improved hyperthermia applicator. Y1 - 2012 VL - 21 SP - 307 EP - 378 ER - 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 - Lubkoll, Lars A1 - Schiela, Anton A1 - Weiser, Martin T1 - An affine covariant composite step method for optimization with PDEs as equality constraints JF - Optimization Methods and Software N2 - 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. Y1 - 2017 U6 - https://doi.org/10.1080/10556788.2016.1241783 VL - 32 IS - 5 SP - 1132 EP - 1161 ER - TY - JOUR A1 - Götschel, Sebastian A1 - Schiela, Anton A1 - Weiser, Martin T1 - Kaskade 7 - a Flexible Finite Element Toolbox JF - Computers and Mathematics with Applications N2 - Kaskade 7 is a finite element toolbox for the solution of stationary or transient systems of partial differential equations, aimed at supporting application-oriented research in numerical analysis and scientific computing. The library is written in C++ and is based on the \textsc{Dune} interface. The code is independent of spatial dimension and works with different grid managers. An important feature is the mix-and-match approach to discretizing systems of PDEs with different ansatz and test spaces for all variables. We describe the mathematical concepts behind the library as well as its structure, illustrating its use at several examples on the way. Y1 - 2021 U6 - https://doi.org/10.1016/j.camwa.2020.02.011 VL - 81 SP - 444 EP - 458 ER - TY - JOUR A1 - Schiela, Anton A1 - Stöcklein, Matthias A1 - Weiser, Martin T1 - A primal dual projection algorithm for efficient constraint preconditioning JF - SIAM Journal on Scientific Computing N2 - We consider a linear iterative solver for large scale linearly constrained quadratic minimization problems that arise, for example, in optimization with PDEs. By a primal-dual projection (PDP) iteration, which can be interpreted and analysed as a gradient method on a quotient space, the given problem can be solved by computing sulutions for a sequence of constrained surrogate problems, projections onto the feasible subspaces, and Lagrange multiplier updates. As a major application we consider a class of optimization problems with PDEs, where PDP can be applied together with a projected cg method using a block triangular constraint preconditioner. Numerical experiments show reliable and competitive performance for an optimal control problem in elasticity. Y1 - 2021 U6 - https://doi.org/10.1137/20M1380739 VL - 43 IS - 6 SP - A4095 EP - A4120 ER -