Domain Decomposition with Local Mesh Refinement.
Abstract
A preconditioned Krylov iterative algorithm is based on domain decomposition for implicit linear system arising from partial differential equation problems which require local mesh refinement. To keep data structures as simple as possible for parallel computing applications, the fundamental computational unit in the algorithm is a subregion of the domain spanned by a locally uniform tensor-product grid, called a 'tile'. This is in contrast to local refinement techniques whose fundamental computational unit is a grid at a given level of refinement. Bookkeeping requirements of grid algorithms are potentially substantial, since consistency of data must be enforced at points of space which may belong to several different grids and the grids are not necessarily of tensor-product type, but more generally, unions thereof. The tile-based domain decomposition approach condenses the number of levels in consideration at each point of the domain to two: a global coarse grid defined by tile vertices only and a local fine grid, where the degree of resolution of the fine grid can vary from tile to tile. Experimentally, it is shown that one global level and one local level provide sufficient flexibility to handle a diverse collection of problems which include irregular regions, non-simply connected regions, non-self adjoint operators, mixed boundary conditions, non-smooth coefficients, or non-smooth solutions. Tiles on problems containing up to 16K degrees of freedom. (EDC)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1989
- Accession Number
- ADA215806
Entities
People
- David E. Keyes
- William D. Gropp
Organizations
- Yale University