Abstract
In this article, to better implement the modified positive-definite and skew-Hermitian splitting preconditioners studied recently (Numer. Algor., 72 (2016) 243–258) for generalized saddle point problems, a class of inexact modified positive-definite and skew-Hermitian splitting preconditioners is proposed with improved computing efficiency. Some spectral properties, including the eigenvalue distribution, the eigenvector distribution, and an upper bound of the degree of the minimal polynomial of the inexact modified positive-definite and skew-Hermitian splitting preconditioned matrices are studied. In addition, a theoretical optimal inexact modified positive-definite and skew-Hermitian splitting preconditioner is obtained. Numerical experiments arising from a model steady incompressible Navier–Stokes problem are used to validate the theoretical results and illustrate the effectiveness of this new class of proposed preconditioners.
Highlights
In the solution of large, sparse generalized saddle point problems, finding efficient preconditioners is crucial to obtaining an iterative solution
We propose a class of inexact modified positive-definite and skew-Hermitian splitting (IMPSS)
The IMPSS preconditioner and implementation aspects will be presented in section ‘‘The inexact MPSS preconditioner.’’ In section ‘‘Spectral analysis of the IMPSS preconditioned matrix,’’ we study the spectral properties of the IMPSS preconditioned matrix and introduce the optimal modified positive-definite and skew-Hermitian splitting (OIMPSS) preconditioner
Summary
In the solution of large, sparse generalized saddle point problems, finding efficient preconditioners is crucial to obtaining an iterative solution. Keywords Generalized saddle point problem, matrix splitting preconditioner, eigenvalues, Krylov subspace method, Navier–Stokes equation
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