@misc{SchielaGuenther, author = {Schiela, Anton and G{\"u}nther, Andreas}, title = {Interior Point Methods in Function Space for State Constraints - Inexact Newton and Adaptivity}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11007}, number = {09-01}, abstract = {We consider an interior point method in function space for PDE constrained optimal control problems with state constraints. Our emphasis is on the construction and analysis of an algorithm that integrates a Newton path-following method with adaptive grid refinement. This is done in the framework of inexact Newton methods in function space, where the discretization error of each Newton step is controlled by adaptive grid refinement in the innermost loop. This allows to perform most of the required Newton steps on coarse grids, such that the overall computational time is dominated by the last few steps. For this purpose we propose an a-posteriori error estimator for a problem suited norm.}, language = {en} } @misc{GuentherLameckerWeiser, author = {G{\"u}nther, Andreas and Lamecker, Hans and Weiser, Martin}, title = {Direct LDDMM of Discrete Currents with Adaptive Finite Elements}, doi = {10.1007/s11263-012-0599-3}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-13090}, number = {11-22}, abstract = {We consider Large Deformation Diffeomorphic Metric Mapping of general \$m\$-currents. After stating an optimization algorithm in the function space of admissable morph generating velocity fields, two innovative aspects in this framework are presented and numerically investigated: First, we spatially discretize the velocity field with conforming adaptive finite elements and discuss advantages of this new approach. Second, we directly compute the temporal evolution of discrete \$m\$-current attributes.}, language = {en} } @article{SchielaGuenther2011, author = {Schiela, Anton and G{\"u}nther, Andreas}, title = {An Interior Point Algorithm with Inexact Step Computation in Function Space for State Constrained Optimal Control}, series = {Numer. Math.}, volume = {119}, journal = {Numer. Math.}, number = {2}, publisher = {Springer Berlin / Heidelberg}, doi = {10.1007/s00211-011-0381-4}, pages = {373 -- 407}, year = {2011}, language = {en} } @misc{GuentherLameckerWeiser, author = {G{\"u}nther, Andreas and Lamecker, Hans and Weiser, Martin}, title = {Direct LDDMM of Discrete Currents with Adaptive Finite Elements}, series = {Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Modelling Biological Shape Variability}, journal = {Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Modelling Biological Shape Variability}, editor = {Pennec, X. and Joshi, S. and Nielsen, M.}, pages = {1 -- 14}, abstract = {We consider Large Deformation Diffeomorphic Metric Mapping of general \$m\$-currents. After stating an optimization algorithm in the function space of admissable morph generating velocity fields, two innovative aspects in this framework are presented and numerically investigated: First, we spatially discretize the velocity field with conforming adaptive finite elements and discuss advantages of this new approach. Second, we directly compute the temporal evolution of discrete \$m\$-current attributes.}, language = {en} } @article{GuentherLameckerWeiser, author = {G{\"u}nther, Andreas and Lamecker, Hans and Weiser, Martin}, title = {Flexible Shape Matching with Finite Element Based LDDMM}, series = {International Journal of Computer Vision}, volume = {105}, journal = {International Journal of Computer Vision}, number = {2}, doi = {10.1007/s11263-012-0599-3}, pages = {128 -- 143}, abstract = {We consider Large Deformation Diffeomorphic Metric Mapping of general \$m\$-currents. After stating an optimization algorithm in the function space of admissable morph generating velocity fields, two innovative aspects in this framework are presented and numerically investigated: First, we spatially discretize the velocity field with conforming adaptive finite elements and discuss advantages of this new approach. Second, we directly compute the temporal evolution of discrete \$m\$-current attributes.}, language = {en} }