Accession Number:

ADA234723

Title:

Domain Decomposition with Local Mesh Refinement

Descriptive Note:

Contractor rept.

Corporate Author:

INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA

Personal Author(s):

Report Date:

1991-02-01

Pagination or Media Count:

33.0

Abstract:

We describe a preconditioned Krylov iterative algorithm based on domain decomposition for linear systems arising from implicit finite difference or finite element discretizations of partial differential equation problems requiring local mesh refinement. To keep data structures as simple as possible for parallel computing applications, we define the fundamental computational unit in the algorithm as a subregion of the domain spanned by a locally uniform tensor-product grid, called a tile. In the tile-based domain decomposition approach, two levels of discretization are considered at each point of the domain a global coarse grid defined by tile vertices only, and a local fine grid where the degree of resolution can vary from tile to tile. One global level and one local level provide the flexibility required to adaptively discretize a diverse collection of problems on irregular regions and solve them at convergence rates that deteriorate only logarithmically in the finest mesh parameter, with the coarse tessellation held fixed. A logarithmic departure from optimality seems to be a reasonable compromise for the simplicity of the composite grid data structure and concomitant regular data exchange patterns in a multiprocessor environment.

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE