Two-level spectral preconditioners for indefinite or non-symmetric problems

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• Victorita Dolean Maini (University of Strathclyde, Glasgow)
• Tuesday 28 November 2023, 14:00-15:00
• Nuffield G13.

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

Generalized eigenvalue problems on the overlap (GenEO) is a method for computing an operator-dependent spectral coarse space to be combined with local solves on subdomains to form a robust parallel domain decomposition preconditioner for elliptic PDEs. It has previously been proved, in the self-adjoint and positive-definite case, that this method, when used as a preconditioner for conjugate gradients, yields iteration numbers that are completely independent of the heterogeneity of the coefficient field of the partial differential operator. We extend this theory to the case of convection–diffusion–reaction problems, which may be nonself-adjoint and indefinite, and whose discretizations are solved with preconditioned GMRES . The GenEO coarse space is defined here using a generalized eigenvalue problem based on a self-adjoint and positive-definite subproblem. We prove estimates on GMRES iteration counts that are independent of the variation of the coefficient of the diffusion term in the operator and depend only very mildly on variations of the other coefficients. While the iteration number estimates do grow as the nonself-adjointness and indefiniteness of the operator increases, practical tests indicate the deterioration is much milder. Thus, we obtain an iterative solver that is efficient in parallel and very effective for a wide range of convection–diffusion–reaction problems.

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

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• Nuffield G13
• Optimisation and Numerical Analysis Seminars
• School of Mathematics events

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