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AbstractWe 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. 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.
CitationAdams MF, Brown J, Knepley M, Samtaney R (2016) Segmental Refinement: A Multigrid Technique for Data Locality. SIAM Journal on Scientific Computing 38: C426–C440. Available: http://dx.doi.org/10.1137/140975127.
SponsorsThis material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, and performed under the auspices of the U.S. Department of Energy by Lawrence Berkeley National Laboratory under contract DE-AC02-05CH11231. This research used resources of the National Energy Research Scientific Computing Center, which is a DOE Office of Science User Facility. Authors from Lawrence Berkeley National Laboratory were supported by the U.S. Department of Energy's Advanced Scientific Computing Research Program under contract DEAC02-05CH11231.