Experimental Optimization of Parallel 3D Overlapping Domain Decomposition Schemes?

Abstract. Overlapping domain decomposition is a technique for solving complex problems described by Partial Differential Equations in a parallel framework. The performance of this approach strongly depends on the size and the position of the overlap since on the one hand more overlap increases the computational costs for the single subdomain but on the other hand it accelerates the iterative procedure of the global decomposition solving. In this paper we test the overlapping domain decomposition method on the finite element discretization of a diffusion reaction problem in both idealized and real 3D geometries. Results confirm that the detection of the optimal overlapping in real cases is not trivial but has the potential to significantly reduce the computational costs of the entire solution process.