An Optimal Iterative Solver for Symmetric Indefinite Systems Stemming from Mixed Approximation

被引：16

作者：

Silvester, David J. ^{[1
]}

Simoncini, Valeria ^{[2
]}

机构：

[1] Univ Manchester, Sch Math, Manchester M13 9PL, Lancs, England

[2] Univ Bologna, Dept Matemat, I-40127 Bologna, Italy

来源：

ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE | 2011年 / 37卷 / 04期

关键词：

Algorithms; Design; Finite elements; incompressible flow; iterative solvers; stopping criteria; EST_MINRES; MATLAB; STOPPING CRITERIA; ERROR ESTIMATION; H(DIV); STOKES; NORM;

D O I：

10.1145/1916461.1916466

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We discuss the design and implementation of a suite of functions for solving symmetric indefinite linear systems associated with mixed approximation of systems of PDEs. The novel feature of our iterative solver is the incorporation of error control in the natural "energy" norm in combination with an a posteriori estimator for the PDE approximation error. This leads to a robust and optimally efficient stopping criterion: the iteration is terminated as soon as the algebraic error is insignificant compared to the approximation error. We describe a "proof of concept" MATLAB implementation of this algorithm, which we call EST_MINRES, and we illustrate its effectiveness when integrated into the Incompressible Flow Iterative Solution Software (IFISS) package (cf. ACM Transactions on Mathematical Software 33, Article 14, 2007).

引用

页数：22

共 29 条

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