Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Univ. of Minnesota, Twin Cities, MN (United States)
This study presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits domain decomposition (DD) and low-rank corrections. The DD approach decouples the matrix and, once inverted, a low-rank approximation is applied by exploiting the Sherman--Morrison--Woodbury formula, which yields two variants of the preconditioning methods. The low-rank expansion is computed by the Lanczos procedure with reorthogonalizations. Numerical experiments indicate that, when combined with Krylov subspace accelerators, this preconditioner can be efficient and robust for solving symmetric sparse linear systems. Comparisons with pARMS, a DD-based parallel incomplete LU (ILU) preconditioning method, are presented for solving Poisson's equation and linear elasticity problems.
- Research Organization:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE
- Grant/Contract Number:
- AC52-07NA27344
- OSTI ID:
- 1438714
- Report Number(s):
- LLNL-JRNL-727122
- Journal Information:
- SIAM Journal on Matrix Analysis and Applications, Vol. 38, Issue 3; ISSN 0895-4798
- Publisher:
- SIAMCopyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
An ensemble Kalman filter approach based on operator splitting for solving nonlinear Hammerstein type ill-posed operator equations
|
journal | October 2018 |
Similar Records
An Algebraic Multilevel Preconditioner with Low-Rank Corrections for Sparse Symmetric Matrices
Approximate inverse preconditioners for general sparse matrices