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

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.