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Structure of highly parallel, efficient, scalable, true robust pseudomultigrid technique for black-box solving a large class of the boundary value problems on high performance computing systems. (English) Zbl 1483.65201

Summary: In this paper, we discuss the true robust pseudomultigrid technique (RMT) for blackbox solving a large class of the boundary value problems on high performance computing systems. RMT has the same number of the problem-dependent components as Gauss-Seidel method and close-to-optimal algorithmic complexity. First, an algebraic approach to parallelization is introduced for a parallel smoothing on the fine levels. The algebraic approach is based on a decomposition of the given problem into a number of subproblems with an overlap. Second, a geometric approach to parallelization is introduced for a parallel smoothing on the coarse levels to avoid communication overhead and idling processes on the very coarse grids. The geometric approach is based on a decomposition of the given problem into a number of subproblems without an overlap. After that we discuss a combination of the algebraic and the geometric approaches for parallel RMT.

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65Y05 Parallel numerical computation
65Y10 Numerical algorithms for specific classes of architectures
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References:

[1] S. I. Martynenko, The RobustMultigrid Technique. For Black-box Software (de Gruyter, Berlin, 2017). · Zbl 1382.65450 · doi:10.1515/9783110539264
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