Volume 3, Issue 3
Preconditioning Schur Complement Systems of Highly-Indefinite Linear Systems for a Parallel Hybrid Solver

I. Yamazaki, X. S. Li & E. G. Ng

Numer. Math. Theor. Meth. Appl., 3 (2010), pp. 352-366.

Published online: 2010-03

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  • 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.

  • Keywords

Schur complement method, preconditioning, matrix preprocessing.

  • AMS Subject Headings

65F10, 15A12, 65N55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-3-352, author = {}, title = {Preconditioning Schur Complement Systems of Highly-Indefinite Linear Systems for a Parallel Hybrid Solver}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2010}, volume = {3}, number = {3}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2010.33.5}, url = {http://global-sci.org/intro/article_detail/nmtma/6003.html} }
TY - JOUR T1 - Preconditioning Schur Complement Systems of Highly-Indefinite Linear Systems for a Parallel Hybrid Solver JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 352 EP - 366 PY - 2010 DA - 2010/03 SN - 3 DO - http://doi.org/10.4208/nmtma.2010.33.5 UR - https://global-sci.org/intro/article_detail/nmtma/6003.html KW - Schur complement method, preconditioning, matrix preprocessing. AB -

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.

I. Yamazaki, X. S. Li & E. G. Ng. (2020). Preconditioning Schur Complement Systems of Highly-Indefinite Linear Systems for a Parallel Hybrid Solver. Numerical Mathematics: Theory, Methods and Applications. 3 (3). 352-366. doi:10.4208/nmtma.2010.33.5
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