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 direct method describes an optimized parallel strategy to solve the initial problem, providing the exact solution, up to rounding errors. Moreover, it 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.