University of Birmingham > Talks@bham > Optimisation and Numerical Analysis Seminars > Domain Decomposition Preconditioners for Optimal Control of Elliptic PDE

Domain Decomposition Preconditioners for Optimal Control of Elliptic PDE

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If you have a question about this talk, please contact Sergey Sergeev.

The discretization of optimal control of elliptic partial differential equations problems yields optimality conditions in the form of large sparse linear systems with block structure. Correspondingly, when the solution method is a non-overlapping domain decomposition method, we need to solve interface problems which inherit the block structure. It is therefore natural to consider block preconditioners acting on the interface variables for the acceleration of Krylov methods with substructuring preconditioners.

In this talk I will describe a generic technique which employs a preconditioner block structure based on the fractional Sobolev norms corresponding to the domains of the boundary operators arising in the matrix interface problem, some of which may include a dependence on the control regularization parameter. I will illustrate this approach on standard elliptic control problems. I will also present analysis which shows that the resulting iterative method converges independently of the size of the problem. Finally, I will present numerical results which indicate that performance is also independent of the control regularization parameter and exhibits only a mild dependence on the number of the subdomains.

This talk is part of the Optimisation and Numerical Analysis Seminars series.

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