TY - GEN A1 - Weiser, Martin A1 - Götschel, Sebastian T1 - State Trajectory Compression for Optimal Control with Parabolic PDEs N2 - In optimal control problems with nonlinear time-dependent 3D PDEs, full 4D discretizations are usually prohibitive due to the storage requirement. For this reason gradient and quasi-Newton methods working on the reduced functional are often employed. The computation of the reduced gradient requires one solve of the state equation forward in time, and one backward solve of the adjoint equation. The state enters into the adjoint equation, again requiring the storage of a full 4D data set. We propose a lossy compression algorithm using an inexact but cheap predictor for the state data, with additional entropy coding of prediction errors. As the data is used inside a discretized, iterative algorithm, lossy coding maintaining an error bound is sufficient. T3 - ZIB-Report - 10-05 KW - optimal control KW - adjoint gradient computation KW - trajectory storage Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11676 SN - 1438-0064 ER - TY - GEN A1 - Götschel, Sebastian A1 - Weiser, Martin A1 - Schiela, Anton T1 - Solving Optimal Control Problems with the Kaskade 7 Finite Element Toolbox N2 - 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. T3 - ZIB-Report - 10-25 KW - partial differential equations KW - optimal control KW - finite elements KW - generic programming KW - adaptive methods Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11909 SN - 1438-0064 ER -