Name
Title | ||
|---|---|---|
Local Fourier analysis for multigrid with overlapping smoothers applied to systems of PDEs. |
Abstract | ||
|---|---|---|
Since their popularization in the late 1970s and early 1980s, multigrid methods have been a central tool in the numerical solution of the linear and nonlinear systems that arise from the discretization of many PDEs. In this paper, we present a local Fourier analysis (LFA, or local mode analysis) framework for analyzing the complementarity between relaxation and coarse-grid correction within multigrid solvers for systems of PDEs. Important features of this analysis framework include the treatment of arbitrary finite-element approximation subspaces, leading to discretizations with staggered grids, and overlapping multiplicative Schwarz smoothers. The resulting tools are demonstrated for the Stokes, curl-curl, and grad-div equations. Copyright (C) 2011 John Wiley & Sons, Ltd. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1002/nla.762 | NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS |
Keywords | Field | DocType |
multigrid,finite-element discretizations,local Fourier analysis | Complementarity (molecular biology),Discretization,Mathematical optimization,Nonlinear system,Multiplicative function,Mathematical analysis,Linear subspace,Local fourier analysis,Mathematics,Multigrid method | Journal |
Volume | Issue | ISSN |
18 | 4 | 1070-5325 |
Citations | PageRank | References |
6 | 0.51 | 19 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Scott MacLachlan | 1 | 78 | 8.09 |
| Cornelis W. Oosterlee | 2 | 217 | 34.41 |