Skip to Main content Skip to Navigation
New interface
Reports (Research report)

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 metadata

Cited literature [24 references]  Display  Hide  Download
Contributor : Laura Grigori Connect in order to contact the contributor
Submitted on : Thursday, July 3, 2014 - 8:15:56 AM
Last modification on : Wednesday, October 26, 2022 - 8:16:17 AM
Long-term archiving on: : Friday, October 3, 2014 - 10:50:52 AM


Files produced by the author(s)


  • HAL Id : hal-01017448, version 1


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⟩



Record views


Files downloads