Block preconditioners for boundary control of elliptic PDE

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• Daniel Loghin (School of Mathematics, University of Birmingham)
• Thursday 12 October 2017, 12:00-13:00
• G13, Arts Building.

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

The discretization of weak formulations of optimal control of elliptic partial differential equations yields optimality conditions in the form of large sparse linear systems with block structure. For distributed control problems a successful approach is provided by Krylov methods equipped with block preconditioners. However, boundary control problems yield structures which pose specific challenges: rank deficient blocks, intractable Schur complements and generally a lack of a methodical strategy for preconditioner design. In this talk we introduce a novel approach based on a certain boundary preconditioning technique involving blocks of discrete fractional Sobolev norms on the boundary. We illustrate our approach on standard elliptic control problems. We present analysis which shows that the resulting iterative method converges independently of the size of the problem. We include numerical results which indicate that performance is only mildly dependent of the control regularisation parameter.

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

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• G13, Arts Building
• Optimisation and Numerical Analysis Seminars
• School of Mathematics Events

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