Accession Number : ADA324495

Title :   A Note on Multi-Block Relaxation Schemes for Multigrid Solvers.

Descriptive Note : Contract rept.,

Corporate Author : INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA

Personal Author(s) : Jones, Jim E. ; Melson, N. D.

PDF Url : ADA324495

Report Date : FEB 1997

Pagination or Media Count : 13

Abstract : Efficient and robust multigrid solvers for anisotropic problems typically use either semi-coarsened grids or implicit smoothers - line relaxation in 2D and plane relaxation in 3D. However, both of these may be difficult to implement in codes using multi-block structured grids where there may be no natural definition of a global line or plane. These multi-block structured grids are often used in fluid dynamic applications to capture complex geometries and/or to facilitate parallel processing. In this paper, we investigate the performance of multigrid algorithms using implicit smoothers within the blocks of a such a grid. By looking at a model problem, the 2-D anisotropic diffusion equation, we show that true multigrid efficiency is achieved only when the block sizes are proportional to the strength of the anisotropy. Further, the blocks must overlap and the size of the overlap must again be proportional to the strength of the anisotropy.

Descriptors :   *ALGORITHMS, *PARALLEL PROCESSING, MATHEMATICAL MODELS, GRIDS, COMPUTATIONAL FLUID DYNAMICS, FINITE DIFFERENCE THEORY, POLYNOMIALS, PARTIAL DIFFERENTIAL EQUATIONS, APPLIED MATHEMATICS.

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE