@misc{WeiserGaenzlerSchiela, author = {Weiser, Martin and G{\"a}nzler, Tobias and Schiela, Anton}, title = {A Control Reduced Primal Interior Point Method for PDE Constrained Optimization}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8138}, number = {04-38}, abstract = {A primal interior point method for control constrained optimal control problems with PDE constraints is considered. Pointwise elimination of the control leads to a homotopy in the remaining state and dual variables, which is addressed by a short step pathfollowing method. The algorithm is applied to the continuous, infinite dimensional problem, where discretization is performed only in the innermost loop when solving linear equations. The a priori elimination of the least regular control permits to obtain the required accuracy with comparable coarse meshes. Convergence of the method and discretization errors are studied, and the method is illustrated at two numerical examples.}, language = {en} } @misc{Weiser, author = {Weiser, Martin}, title = {Pointwise Nonlinear Scaling for Reaction-Diffusion-Equations}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10493}, number = {07-45}, abstract = {Parabolic reaction-diffusion systems may develop sharp moving reaction fronts which pose a challenge even for adaptive finite element methods. We propose a method to transform the equation into an equivalent form that usually exhibits solutions which are easier to discretize, giving higher accuracy for a given number of degrees of freedom. The transformation is realized as an efficiently computable pointwise nonlinear scaling that is optimized for prototypical planar travelling wave solutions of the underlying reaction-diffusion equation. The gain in either performance or accuracy is demonstrated on different numerical examples.}, language = {en} } @misc{WeiserErdmannDeuflhard, author = {Weiser, Martin and Erdmann, Bodo and Deuflhard, Peter}, title = {On Efficiency and Accuracy in Cardioelectric Simulation}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10934}, number = {08-41}, abstract = {Reasons for the failure of adaptive methods to deliver improved efficiency when integrating monodomain models for myocardiac excitation are discussed. Two closely related techniques for reducing the computational complexity of linearly implicit integrators, deliberate sparsing and splitting, are investigated with respect to their impact on computing time and accuracy.}, language = {en} }