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Multiscale methods are usually developed for solving second-order elliptic problems in which coefcients are of multiscale heterogeneous nature. The Multiscale Mixed Method (MuMM) was introduced aiming at the efcient and accurate approximation of large ow problems in highly heterogeneous porous media. In the MuMM numerical solver, rst mixed multiscale basis functions are constructed, and next global domain decomposition iterations are performed to compute the discrete solution of the problems. However, this iterative procedure is a time-consuming step. In this paper, the authors improve the MuMM solver through the implementation of parallel computations in the step concerning the global iterative procedure. The parallel version of the solver employs the application programming interface Open Multi-Processing (OpenMP). The implementation with the OpenMP reduces signicantly the computational effort to perform the domain decomposition iterations, as indicated by the numerical results.

An OpenMP implementation of the MuMM solver for porous media flow problems