Segmental Refinement: A Multigrid Technique for Data Locality
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Scalable Solvers Group
- Univ. of Colorado, Boulder, CO (United States). Dept. of Computer Science
- Rice Univ., Houston, TX (United States). Computational and Applied Mathematics
- King Abdullah Univ. of Science and Technology, Thuwal (Saudi Arabia)
In this paper, we investigate a domain decomposed multigrid technique, termed segmental refinement, for solving general nonlinear elliptic boundary value problems. We extend the method first proposed in 1994 by analytically and experimentally investigating its complexity. We confirm that communication of traditional parallel multigrid is eliminated on fine grids, with modest amounts of extra work and storage, while maintaining the asymptotic exactness of full multigrid. We observe an accuracy dependence on the segmental refinement subdomain size, which was not considered in the original analysis. Finally, we present a communication complexity analysis that quantifies the communication costs ameliorated by segmental refinement and report performance results with up to 64K cores on a Cray XC30.
- Research Organization:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- Grant/Contract Number:
- AC02-05CH11231
- OSTI ID:
- 1440915
- Journal Information:
- SIAM Journal on Scientific Computing, Vol. 38, Issue 4; ISSN 1064-8275
- Publisher:
- SIAMCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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