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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

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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… Click to show full abstract

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.

Keywords: true robust; solving large; class boundary; robust pseudomultigrid; pseudomultigrid technique; large class

Journal Title: Lobachevskii Journal of Mathematics
Year Published: 2018

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