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 language | English (US) |
|---|---|
| Pages (from-to) | 135-142 |
| Number of pages | 8 |
| Journal | Journal of Computational Physics |
| Volume | 332 |
| DOIs | |
| State | Published - Mar 1 2017 |
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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
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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 journal › Article
TY - JOUR
T1 - Efficient relaxed-Jacobi smoothers for multigrid on parallel computers
AU - Yang, Xiang
AU - Mittal, Rajat
PY - 2017/3/1
Y1 - 2017/3/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85006351807&partnerID=8YFLogxK
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U2 - 10.1016/j.jcp.2016.12.010
DO - 10.1016/j.jcp.2016.12.010
M3 - Article
AN - SCOPUS:85006351807
VL - 332
SP - 135
EP - 142
JO - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
ER -