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2010.37: An Optimal Iterative Solver for Symmetric Indefinite Systems stemming from Mixed Approximation

2010.37: David J. Silvester and Valeria Simoncini (2011) An Optimal Iterative Solver for Symmetric Indefinite Systems stemming from Mixed Approximation. ACM Transactions on Mathematical Software, 37 (4). ISSN 1749-9097

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DOI: 10.1145/1916461.1916466


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 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).

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Uncontrolled Keywords:Finite elements, incompressible flow, iterative solvers, stopping criteria, EST_MINRES, MATLAB
Subjects:MSC 2000 > 65 Numerical analysis
MIMS number:2010.37
Deposited By:professor david silvester
Deposited On:23 April 2011

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