Efficient relaxed-Jacobi smoothers for multigrid on parallel computers

Xiang Yang, Rajat Mittal

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this Technical Note, we present a family of Jacobi-based multigrid smoothers suitable for the solution of discretized elliptic equations. These smoothers are based on the idea of scheduled-relaxation Jacobi proposed recently by Yang & Mittal (2014) [18] and employ two or three successive relaxed Jacobi iterations with relaxation factors derived so as to maximize the smoothing property of these iterations. The performance of these new smoothers measured in terms of convergence acceleration and computational workload, is assessed for multi-domain implementations typical of parallelized solvers, and compared to the lexicographic point Gauss–Seidel smoother. The tests include the geometric multigrid method on structured grids as well as the algebraic grid method on unstructured grids. The tests demonstrate that unlike Gauss–Seidel, the convergence of these Jacobi-based smoothers is unaffected by domain decomposition, and furthermore, they outperform the lexicographic Gauss–Seidel by factors that increase with domain partition count.

Original languageEnglish (US)
Pages (from-to)135-142
Number of pages8
JournalJournal of Computational Physics
Volume332
DOIs
StatePublished - Mar 1 2017

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parallel computers
Decomposition
iteration
multigrid methods
smoothing
partitions
grids
decomposition

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

Cite this

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abstract = "In this Technical Note, we present a family of Jacobi-based multigrid smoothers suitable for the solution of discretized elliptic equations. These smoothers are based on the idea of scheduled-relaxation Jacobi proposed recently by Yang & Mittal (2014) [18] and employ two or three successive relaxed Jacobi iterations with relaxation factors derived so as to maximize the smoothing property of these iterations. The performance of these new smoothers measured in terms of convergence acceleration and computational workload, is assessed for multi-domain implementations typical of parallelized solvers, and compared to the lexicographic point Gauss–Seidel smoother. The tests include the geometric multigrid method on structured grids as well as the algebraic grid method on unstructured grids. The tests demonstrate that unlike Gauss–Seidel, the convergence of these Jacobi-based smoothers is unaffected by domain decomposition, and furthermore, they outperform the lexicographic Gauss–Seidel by factors that increase with domain partition count.",
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Efficient relaxed-Jacobi smoothers for multigrid on parallel computers. / Yang, Xiang; Mittal, Rajat.

In: Journal of Computational Physics, Vol. 332, 01.03.2017, p. 135-142.

Research output: Contribution to journalArticle

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