Parallelization of Robust Multigrid Technique Using OpenMP Technology

• Published in: Parallel Computing Technologies Vol. 12942; pp. 196 - 209
• Main Authors: Martynenko, Sergey, Zhou, Weixing, Gökalp, İskender, Bakhtin, Vladimir, Toktaliev, Pavel
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2021; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Boundary value problems; OpenMP; Parallel solvers; Robust multigrid technique
• ISBN: 9783030863586; 3030863581
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-86359-3_15

This article represents the parallel multigrid component analysis of Robust Multigrid Technique (RMT). The RMT has been developed for black-box solution of a large class of (non)linear boundary value problems in computational continuum mechanics. Parallel RMT can be constructed by combination of the algebraic and geometric approaches to parallelization. The geometric smoother-independent approach based on a decomposition of the given problem into 3κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3^\kappa _{}$$\end{document} (κ=1,2,…\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa =1,2,\ldots $$\end{document}) subproblems without an overlap should be used to overcome the problems of large communication overhead and idling processors on coarser levels. The algebraic grid-independent approach based on a decomposition of the given problem into C3κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C 3^\kappa _{}$$\end{document} (κ=1,2,…\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa =1,2,\ldots $$\end{document}) subproblems with an overlap (multicoloured Vanka-type smoother) should be used for parallel smoothing on finer levels. Standard programming model for shared memory parallel programming OpenMP has been used for parallel implementation of RMT on personal computer and computer cluster. This paper represents parallel multigrid cycle, algebraic and geometric approaches to parallelization, estimation of the parallel RMT efficiency and parallel multigrid component analysis.