A Combined Preconditioning Strategy for Nonsymmetric Systems | Zendy

Blanca Ayuso de Dios | Zendy; Andrew T. Barker | Zendy; Panayot S. Vassilevski | Zendy

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A Combined Preconditioning Strategy for Nonsymmetric Systems

Author(s) -

Blanca Ayuso de Dios,

Andrew T. Barker,

Panayot S. Vassilevski

Publication year - 2014

Publication title -

siam journal on scientific computing

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.674

H-Index - 147

eISSN - 1095-7197

pISSN - 1064-8275

DOI - 10.1137/120888946

Subject(s) - preconditioner , mathematics , generalized minimal residual method , positive definite matrix , matrix (chemical analysis) , linear system , mathematical optimization , iterative method , mathematical analysis , eigenvalues and eigenvectors , physics , materials science , quantum mechanics , composite material

We present and analyze a class of nonsymmetric preconditioners within a normal (weighted least-squares) matrix form for use in GMRES to solve nonsymmetric matrix problems that typically arise in finite element discretizations. An example of the additive Schwarz method applied to nonsymmetric but definite matrices is presented for which the abstract assumptions are verified. A variable preconditioner, combining the original nonsymmetric one and a weighted least-squares version of it, is shown to be convergent and provides a viable strategy for using nonsymmetric preconditioners in practice. Numerical results are included to assess the theory and the performance of the proposed preconditioners

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