Algebraic multigrid for directed graph Laplacian linear systems (NS‐LAMG)
- Center for Applied Scientific Computing Lawrence Livermore National Laboratory Livermore CA 94551 USA
- Department of Applied Mathematics University of Colorado Boulder Boulder CO 80303 USA
Summary We propose nonsymmetric lean algebraic multigrid (NS‐LAMG), a new algebraic multigrid algorithm for directed graph Laplacian systems that combines ideas from undirected graph Laplacian multigrid solvers and multigrid algorithms for Markov chain stationary distribution systems. Low‐degree elimination, proposed in LAMG for undirected graphs, is generalized to directed graphs and is a key component of NS‐LAMG. In the setup phase, we propose a simple stationary‐aggregation multigrid algorithms for Markov chain stationary distribution systems solver enhanced by low‐degree elimination to find the right null‐space vector that is used for the intergrid transfer operators. Numerical results show that low‐degree elimination improves performance and that NS‐LAMG outperforms generalized minimal residual method with restart and stable bi‐conjugate gradient method for real‐world, directed graph Laplacian linear systems.
- Sponsoring Organization:
- USDOE
- Grant/Contract Number:
- (SC) DE-FC02-03ER25574; (NNSA) DE-NA0002376
- OSTI ID:
- 1418882
- Journal Information:
- Numerical Linear Algebra with Applications, Journal Name: Numerical Linear Algebra with Applications Vol. 25 Journal Issue: 3; ISSN 1070-5325
- Publisher:
- Wiley Blackwell (John Wiley & Sons)Copyright Statement
- Country of Publication:
- United Kingdom
- Language:
- English
Web of Science
Similar Records
FINAL REPORT (MILESTONE DATE 9/30/11) FOR SUBCONTRACT NO. B594099 NUMERICAL METHODS FOR LARGE-SCALE DATA FACTORIZATION
Exploring basal sliding with a fluidity‐based, ice‐sheet model using FOSLS