Wed, 22 July, 2009, 09:00-10:00, C1
In this talk we give an overview on basically two fundamental ideas for efficiently solving large scale inverse problems in the context of PDEs, that are motivated by previously developed approaches for the forward solution of PDEs. One of them consists of multilevel strategies making use of an appropriate combination of fine grid smoothing and coarse grid correction in a hierarchical discretization and therewith shifting as much computation as possible to coarsly discretized and hence cheaply to solve problems. The other one is adaptive discretization based on error estimators that allows to efficiently refine and coarsen the computational grid for the PDE solution, or the seached for parameter, or even both of them in such a way that the accuracy requirements are met with a number of of degrees of freedom as small as possible. In both cases, special care has to be taken due to the ill-posedness of the underlying inverse problem in the sense that either stability has to be additionally incorporated or the stabilizing effect of discretization has to be approproately exploited. Therefore, key tasks in this context are on one hand to prove regularization properties for the resulting methods and on the other hand to show their efficiency for the solution of large scale inverse problems. We intend to give an at least partial overview on existing literature and report on our own research, which includes joint work with Hend Benameur, Anke Griesbaum, Josef Schicho, and Boris Vexler.
Presentation slides (pdf, 1.9 MB)
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