Preconditioning Schur Complement Systems of Highly-Indefinite Linear Systems for a Parallel Hybrid Solver

Preconditioning Schur Complement Systems of Highly-Indefinite Linear Systems for a Parallel Hybrid Solver

Year:    2010

Numerical Mathematics: Theory, Methods and Applications, Vol. 3 (2010), Iss. 3 : pp. 352–366

Abstract

A parallel hybrid linear solver based on the Schur complement method has the potential to balance the robustness of direct solvers with the efficiency of preconditioned iterative solvers. However, when solving large-scale highly-indefinite linear systems, this hybrid solver often suffers from either slow convergence or large memory requirements to solve the Schur complement systems. To overcome this challenge, we in this paper discuss techniques to preprocess the Schur complement systems in parallel. Numerical results of solving large-scale highly-indefinite linear systems from various applications demonstrate that these techniques improve the reliability and performance of the hybrid solver and enable efficient solutions of these linear systems on hundreds of processors, which was previously infeasible using existing state-of-the-art solvers.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2010.33.5

Numerical Mathematics: Theory, Methods and Applications, Vol. 3 (2010), Iss. 3 : pp. 352–366

Published online:    2010-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    15

Keywords:    Schur complement method preconditioning matrix preprocessing.

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