Segmental Refinement: A Multigrid Technique for Data Locality
We investigate a technique - segmental refinement (SR) - proposed by Brandt in the 1970s as a low memory multigrid method. The technique is attractive for modern computer architectures because it provides high data locality, minimizes network communication, is amenable to loop fusion, and is naturally highly parallel and asynchronous. The network communication minimization property was recognized by Brandt and Diskin in 1994; we continue this work by developing a segmental refinement method for a finite volume discretization of the 3D Laplacian on massively parallel computers. An understanding of the asymptotic complexities, required to maintain textbook multigrid efficiency, are explored experimentally with a simple SR method. A two-level memory model is developed to compare the asymptotic communication complexity of a proposed SR method with traditional parallel multigrid. Performance and scalability are evaluated with a Cray XC30 with up to 64K cores. We achieve modest improvement in scalability from traditional parallel multigrid with a simple SR implementation.
- Columbia Univ., New York, NY (United States). Applied Physics and Applied Mathematics Dept.; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Publication Date:
- OSTI Identifier:
- DOE Contract Number:
- Resource Type:
- Technical Report
- Research Org:
- Columbia Univ., New York, NY (United States)
- Sponsoring Org:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
- Country of Publication:
- United States
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS multigrid technique; segmental refinement; data locality; low memory; loop fusion; 3D Laplacian
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