Distance-Two Interpolation for Parallel Algebraic Multigrid

Journal Article · Tue May 08 00:00:00 EDT 2007 · Numerical Linear Algebra with Applications, vol. 15, no. 2-3, December 3, 2007, pp. 115-139

DOI:https://doi.org/10.1088/1742-6596/78/1/012017· OSTI ID:940875

De Sterck, H; Falgout, R; Nolting, J; Yang, U M

Algebraic multigrid (AMG) is one of the most efficient and scalable parallel algorithms for solving sparse linear systems on unstructured grids. However, for large three-dimensional problems, the coarse grids that are normally used in AMG often lead to growing complexity in terms of memory use and execution time per AMG V-cycle. Sparser coarse grids, such as those obtained by the Parallel Modified Independent Set coarsening algorithm (PMIS) [7], remedy this complexity growth, but lead to non-scalable AMG convergence factors when traditional distance-one interpolation methods are used. In this paper we study the scalability of AMG methods that combine PMIS coarse grids with long distance interpolation methods. AMG performance and scalability is compared for previously introduced interpolation methods as well as new variants of them for a variety of relevant test problems on parallel computers. It is shown that the increased interpolation accuracy largely restores the scalability of AMG convergence factors for PMIS-coarsened grids, and in combination with complexity reducing methods, such as interpolation truncation, one obtains a class of parallel AMG methods that enjoy excellent scalability properties on large parallel computers.

• Research Organization: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 940875
• Report Number(s): UCRL-JRNL-230844; TRN: US200824%%371
• Journal Information: Numerical Linear Algebra with Applications, vol. 15, no. 2-3, December 3, 2007, pp. 115-139, Vol. 15, Issue 2-3
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ACCURACY
ALGORITHMS
COMPUTERS
CONVERGENCE
INTERPOLATION
PERFORMANCE