A Low-Rank Multigrid Method for the Stochastic Steady-State Diffusion Problem
Journal Article
·
· SIAM Journal on Matrix Analysis and Applications
- Univ. of Maryland, College Park, MD (United States); University of Maryland, Department of Computer Science
- Univ. of Maryland, College Park, MD (United States)
We study a multigrid method for solving large linear systems of equations with tensor product structure here. Such systems are obtained from stochastic finite element discretization of stochastic partial differential equations such as the steady-state diffusion problem with random coefficients. When the variance in the problem is not too large, the solution can be well approximated by a low-rank object. In the proposed multigrid algorithm, the matrix iterates are truncated to low rank to reduce memory requirements and computational effort. The technique is proved convergent with an analytic error bound. Numerical experiments show its effectiveness in solving the Galerkin systems compared to the original multigrid solver, especially when the number of degrees of freedom associated with the spatial discretization is large.
- Research Organization:
- Univ. of Maryland, College Park, MD (United States)
- Sponsoring Organization:
- National Science Foundation (NSF); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
- Grant/Contract Number:
- SC0009301
- OSTI ID:
- 1598337
- Alternate ID(s):
- OSTI ID: 1541729
- Journal Information:
- SIAM Journal on Matrix Analysis and Applications, Journal Name: SIAM Journal on Matrix Analysis and Applications Journal Issue: 1 Vol. 39; ISSN 0895-4798
- Publisher:
- SIAMCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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