A survey of domain decomposition techniques and their implementation

Abstract

The advent of powerful parallel architecture supercomputers has greatly revitalized the study and use of domain decomposition techniques. These methods can be used globally to treat different portions of the computational domain separately on different processors, or locally to resolve important local physical behavior. For large-scale simulation problems, domain decomposition offers significant capabilities in computational efficiency. Recent techniques for domain decomposition which possess convergence rates that are independent of the number of subdomains used are surveyed. Techniques which involve a relatively coarse macro-mesh with potential local refinement in each separate mesh are also discussed. The macro-mesh will be the basis for domain decomposition techniques and parallel solution algorithms. Uniform or logically structured meshing in the subdomains allows efficient vectorization as well as parallelization of the algorithms. Preconditioned iterative procedures are used to efficiently solve the full domain decomposition problem or the local refinement variation. Results of the use of domain decomposition techniques for large multiphase fluid flow applications in porous media are reported.