Domain decomposition with local mesh refinement. Research report

Technical Report · Tue Aug 01 00:00:00 EDT 1989

OSTI ID:7055114

Gropp, W D; Keyes, D E

A preconditioned Krylov iterative algorithm is based on domain decomposition for implicit linear systems 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.

• Research Organization: Yale Univ., New Haven, CT (USA). Dept. of Computer Science
• OSTI ID: 7055114
• Report Number(s): AD-A-215806/1/XAB; YALEU/DCS/RR-726
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
ITERATIVE METHODS
ALGORITHMS
COMPUTER CALCULATIONS
DATA BASE MANAGEMENT
MESH GENERATION
MIXING
NUMERICAL SOLUTION
PARALLEL PROCESSING
PARTIAL DIFFERENTIAL EQUATIONS
RESOLUTION
SPECIFICATIONS
TENSORS
DIFFERENTIAL EQUATIONS
EQUATIONS
MANAGEMENT
MATHEMATICAL LOGIC
PROGRAMMING
990200* - Mathematics & Computers