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- Title
The generalized double shift-splitting preconditioner for nonsymmetric generalized saddle point problems from the steady Navier-Stokes equations.
- Authors
Fan, Hong-Tao; Zhu, Xin-Yun; Zheng, Bing
- Abstract
In this paper, a generalized double shift-splitting (GDSS) preconditioner induced by a new matrix splitting method is proposed and implemented for nonsymmetric generalized saddle point problems having a nonsymmetric positive definite (1,1)-block and a positive definite (2,2)-block. Detailed theoretical analysis of the iteration matrix is provided to show the GDSS method, which corresponds to the GDSS preconditioner, is unconditionally convergent. Additionally, a deteriorated GDSS (DGDSS) method is proposed. It is shown that, with suitable choice of parameter matrix, the DGDSS preconditioned matrix has an eigenvalue at 1 with multiplicity n, and the other m eigenvalues are of the form 1-λ<inline-graphic></inline-graphic> with |λ|<1<inline-graphic></inline-graphic>, independently of the Schur complement matrix related. Finally, numerical experiments arising from a model Navier-Stokes problem are provided to validate and illustrate the effectiveness of the proposed preconditioner, with which a faster convergence for Krylov subspace iteration methods can be achieved.
- Subjects
NAVIER-Stokes equations; EIGENVALUE equations; KRYLOV subspace; STOCHASTIC convergence; MATRICES (Mathematics)
- Publication
Computational & Applied Mathematics, 2018, Vol 37, Issue 3, p3256
- ISSN
0101-8205
- Publication type
Article
- DOI
10.1007/s40314-017-0510-5