Speaker: Matthias Heinkenschloss

Abstract

Domain Decomposition Methods (DDMs) are routinely used for the parallel solution of systems of partial differential equations (PDEs). More recently, they have been successfully applied to PDE constrained optimization problems. In the latter context, DDMs introduce parallelism at the optimization level, allow the design of preconditioners of so-called KKT systems arising within the optimization, but also offer opportunities for storage management and subdomain model reduction.

In this talk I will present DDMs for selected PDE constrained optimization model problems. While many of these DDMs are similar to DMMs that are well known for single PDEs, the optimization structure of the subdomain problems and their coupling used in the optimization level DDMs is quite different from the structure encountered in DMMs for PDEs. I will present numerical examples illustrating the performance of optimization level DDMs and I will discuss some theoretical results.

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