Partitioning Regular Domains on Modern Parallel Computers

Abstract

It has become apparent in recent years that the performance of current high performance computers, from powerful workstations to massively parallel processors, is strongly dependent on the behaviour of the memory hierarchy. In fact, it does not only affect the computation time but the time consumed in performing communications. In this research, the impact of the memory hierarchy usage on the partitioning of multidimensional regular domain problems is studied. We use as an example the numerical solution of a three-dimensional partial differential equation in a regular mesh, by means of a multigrid-like iterative method. Experimental results contradict the traditional regular partitioning techniques on some present parallel computers like the Cray T3E or the SGI Origin 2000: a linear decomposition is more efficient than a three dimensional one due to the better exploitation of the spatial data locality. For similar reasons, computation-communication overlapping increases also execution time.