Robust algebraic Schur complement preconditioners based on low rank corrections

Laura Grigori 1 Frédéric Nataf 1, 2 Soleiman Yousef 1
1 ALPINES - Algorithms and parallel tools for integrated numerical simulations
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, INSMI - Institut National des Sciences Mathématiques et de leurs Interactions
Abstract : In this paper we introduce LORASC, a robust algebraic preconditioner for solving sparse linear systems of equations involving symmetric and positive definite matrices. The graph of the input matrix is partitioned by using k-way partitioning with vertex separators into N disjoint domains and a separator formed by the vertices connecting the N domains. The obtained permuted matrix has a block arrow structure. The preconditioner relies on the Cholesky factorization of the first N diagonal blocks and on approximating the Schur complement corresponding to the separator block. The approximation of the Schur complement involves the factorization of the last diagonal block and a low rank correction obtained by solving a generalized eigenvalue problem or a randomized algorithm. The preconditioner can be build and applied in parallel. Numerical results on a set of matrices arising from the discretization by the finite element method of linear elasticity models illustrate the robusteness and the efficiency of our preconditioner.
Complete list of metadatas

Cited literature [24 references]  Display  Hide  Download

https://hal.inria.fr/hal-01017448
Contributor : Laura Grigori <>
Submitted on : Thursday, July 3, 2014 - 8:15:56 AM
Last modification on : Friday, September 20, 2019 - 4:34:04 PM
Long-term archiving on : Friday, October 3, 2014 - 10:50:52 AM

File

RR-8557.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01017448, version 1

Citation

Laura Grigori, Frédéric Nataf, Soleiman Yousef. Robust algebraic Schur complement preconditioners based on low rank corrections. [Research Report] RR-8557, INRIA. 2014, pp.18. ⟨hal-01017448⟩

Share

Metrics

Record views

1173

Files downloads

831