An Innovative Tool for Effectively Applying Highly Parallelized Hardware To Problems of Elasticity

Abstract

At present, the most efficient domain decomposition methods (DDM) are nonoverlapping methods. The improved efficiency of such methods is due to the significant independence achieved by local problems when the subdomains are non-overlapping. However, standard discretizations applied up to now in non-overlapping DDMs use systems of nodes in which some of the nodes are shared by more than one subdomain of the domain decomposition. This is a limiting feature of the present state-of-the-art in these techniques and apparently further increases of the independence of local problems should be expected if this limiting characteristic wase liminated. In previous work, I. Herrera and co-workers have developed a new approach to domain decomposition methods: the ‘DVS framework’ that addresses this problem introducing a new discretization method, the ‘non-overlapping discretization method’, in which a non-overlapping system of nodes is used in the discrete formulation of the problem. Although the DVS algorithms have already been developed significantly, to profit from such advances it is essential to have available effective codes that permit their efficient implementation. As a further contribution in this line of research, in this paper we present and test software of such characteristics. The results here reported indicate that the DVS algorithms are very suitable for developing software that permits to apply effectively the most advanced hardware in parallel available at present to the solution of partial differential equations. Although the software here reported specifically treats static elasticity only, the DVSalgorithms are very eclectic and can be applied to a great diversity of problems after they have been discretized. Additional research work is being carried out oriented to develop general purpose codes based on the DVS algorithms.