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 leastsquares 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.
Ayuso De Dios, B., Barker, A., Vassilevski, P. (2014). A combined preconditioning strategy for nonsymmetric systems. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 36(6), A2533-A2556 [10.1137/120888946].
A combined preconditioning strategy for nonsymmetric systems
Ayuso De Dios, B
;
2014
Abstract
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 leastsquares 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.File | Dimensione | Formato | |
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