Experimental Optimization of Parallel 3D Overlapping Domain Decomposition Schemes

Overlapping domain decomposition is a possible convenient 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 the overlapping has a positive impact on the number of iterations required by the numerical scheme and the relatively flexible and judicious choice of the interface may lead to a reduction of the communication time. 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.