Parallel Domain Decomposition And Iterative Refinement Algorithms

Algorithms for the solution of partial diierential equations based on a subdivision of the spatial domain, has received much interest in recent years. To a large extent this has been motivated by the new generation of parallel computers. This algorithmic approach can introduce independent parallel tasks of variable granularity, depending on the subdivision and can therefore be adapted to a wide range of parallel computers. We review some of the progress that has been made and report on numerical experiments that illustrate the convergence behavior. We also describe parallel implementations on both shared memory computers (Alliant FX/8) and on local memory systems (Intel iPSC/2 and network connected workstations).