The Improved Robustness of Multigrid Elliptic Solvers Based on Multiple Semicoarsened Grids
Abstract
Multigrid convergence rates degenerate on problems with stretched grids or anisotropic operators, unless one uses line or plane relaxation. For three dimensional problems, only place relaxation suffices, in general. While line and plane relaxation algorithms are efficient on sequential machines, they are quite awkward and inefficient on parallel machines. This paper presents a new multigrid algorithm, based on the use of multiple coarse grids, that eliminates the need for line or plane relaxation in anisotropic problems. We develop this algorithm, and extend the standard multigrid theory to establish rapid convergence for this class of algorithms. The new algorithm uses only point relaxation, allowing easy and efficient parallel implementation, yet achieves robustness and convergence rates comparable to line and plane relaxation multigrid algorithms. The algorithm describes here is a variant of Mulder's multigrid algorithm for hyperbolic problems. The latter uses multiple coarse grid to achieve robustness, but is unsuitable for elliptic problems, since its V-cycle convergence rates goes to one as the number of levels increases. The new algorithm combines the contributions from the multiple coarse grids via a local 'switch,' based on the strength of the discrete operator in each coordinate direction. This improvement allows up to show that the V-cycle convergence rates is uniformly bounded away from one, on model anisotropic problem.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1991
- Accession Number
- ADA242373
Entities
People
- John Van Rosendale
- Naomi H. Naik