Abstract
We propose a new approximate factorization for solving linear systems with symmetric positive definite sparse matrices. In a nutshell the algorithm applies hierarchically block Gaussian elimination and additionally compresses the fill-in. The systems that have efficient compression of the fill-in mostly arise from discretization of partial differential equations. We show that the resulting factorization can be used as an efficient preconditioner and compare the proposed approach with the state-of-art direct and iterative solvers.
| Original language | English (US) |
|---|---|
| Pages (from-to) | A1742-A1762 |
| Journal | SIAM Journal on Scientific Computing |
| Volume | 40 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2018 |
Bibliographical note
Funding Information:∗Submitted to the journal’s Methods and Algorithms for Scientific Computing section March 30, 2016; accepted for publication (in revised form) February 16, 2018; published electronically June 14, 2018. http://www.siam.org/journals/sisc/40-3/M106848.html Funding: The work was supported by Russian Foundation of Basic Research grant 17-01-00854. †Skolkovo Institute of Science and Technology, Moscow, Russia ([email protected]). ‡Skolkovo Institute of Science and Technology, Moscow, Russia, 143025 and Institute of Numerical Mathematics Russian Academy of Sciences, Moscow, Russia, 119333 ([email protected]).
Publisher Copyright:
© 2018 Society for Industrial and Applied Mathematics.
Keywords
- Direct solver
- Hierarchical matrix
- Sparse matrix
- Symmetric positive definite matrix
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics