TY - GEN A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Seebass, Martin T1 - Adaptive Solutions of Nonlinear Parabolic Equations with Application to Hyperthermia Treatments N2 - We present a self-adaptive finite element method to solve nonlinear evolution problems in 3D. An implicit time integrator of Rosenbrock type is coupled with a multilevel approach in space. The proposed method is applied to hyperthermia treatments to demonstrate its potential for the solving of complicated problems. T3 - ZIB-Report - SC-97-44 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3130 ER - TY - GEN A1 - Götschel, Sebastian A1 - von Tycowicz, Christoph A1 - Polthier, Konrad A1 - Weiser, Martin T1 - Reducing Memory Requirements in Scientific Computing and Optimal Control N2 - In high accuracy numerical simulations and optimal control of time-dependent processes, often both many time steps and fine spatial discretizations are needed. Adjoint gradient computation, or post-processing of simulation results, requires the storage of the solution trajectories over the whole time, if necessary together with the adaptively refined spatial grids. In this paper we discuss various techniques to reduce the memory requirements, focusing first on the storage of the solution data, which typically are double precision floating point values. We highlight advantages and disadvantages of the different approaches. Moreover, we present an algorithm for the efficient storage of adaptively refined, hierarchic grids, and the integration with the compressed storage of solution data. T3 - ZIB-Report - 13-64 KW - optimal control KW - trajectory storage KW - mesh compression KW - compression Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42695 SN - 1438-0064 ER -