An overlapping domain decomposition method for large scale problems

Discretization of dynamical models defined through Partial Differential Equations leads to large scale systems. Time depending condition involves an iterative integration of such kind of systems. In this paper a novel technique based on overlapped domain decomposition, without preconditioner and scalable, is presented. Due to the domain decomposition, subproblems are solved in parallel without communications, cutting off the computation time and optimizing the computational cost. This method takes into account both physical nature of the problem and deriving numerical properties of the system. It is highly-recommended in case of band matrices and a long time interval because of an increasing gain in terms of performance and computational cost with the number of integrations. A deep analysis of the computational cost concludes the paper.