@misc{GoetschelWeiserSchiela2010, author = {G{\"o}tschel, Sebastian and Weiser, Martin and Schiela, Anton}, title = {Solving Optimal Control Problems with the Kaskade 7 Finite Element Toolbox}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11909}, number = {10-25}, year = {2010}, abstract = {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.}, language = {en} } @misc{MeyerPanizziSchiela2010, author = {Meyer, Christian and Panizzi, Lucia and Schiela, Anton}, title = {Uniqueness criteria for solutions of the adjoint equation in state-constrained optimal control}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11933}, number = {10-28}, year = {2010}, abstract = {The paper considers linear elliptic equations with regular Borel measures as inhomogeneity. Such equations frequently appear in state-constrained optimal control problems. By a counter-example of Serrin, it is known that, in the presence of non-smooth data, a standard weak formulation does not ensure uniqueness for such equations. Therefore several notions of solution have been developed that guarantee uniqueness. In this note, we compare different definitions of solutions, namely the ones of Stampacchia and the two notions of solutions of Casas and Alibert-Raymond, and show that they are the same. As side results, we reformulate the solution in the sense of Stampacchia, and prove the existence and uniqueness of solutions in in case of mixed boundary conditions.}, language = {en} } @misc{KlapprothSchielaDeuflhard2010, author = {Klapproth, Corinna and Schiela, Anton and Deuflhard, Peter}, title = {Adaptive Timestep Control for the Contact-Stabilized Newmark Method}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11714}, number = {10-09}, year = {2010}, abstract = {The aim of this paper is to devise an adaptive timestep control in the contact--stabilized Newmark method (CONTACX) for dynamical contact problems between two viscoelastic bodies in the framework of Signorini's condition. In order to construct a comparative scheme of higher order accuracy, we extend extrapolation techniques. This approach demands a subtle theoretical investigation of an asymptotic error expansion of the contact--stabilized Newmark scheme. On the basis of theoretical insight and numerical observations, we suggest an error estimator and a timestep selection which also cover the presence of contact. Finally, we give a numerical example.}, language = {en} } @misc{SchielaWeiser2010, author = {Schiela, Anton and Weiser, Martin}, title = {Barrier methods for a control problem from hyperthermia treatment planning}, journal = {Recent Advances in Optimization and its Applications in Engineering (Proceedings of 14th Belgian-French-German Conference on Optimization 2009)}, editor = {Diehl, M. and Glineur, F. and Jarlebring, E. and Michiels, W.}, publisher = {Springer}, pages = {419 -- 428}, year = {2010}, abstract = {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.}, language = {en} }