Abstract
Multiscale methods are usually developed for solving second-order elliptic problems in which coef?cients are of multiscale heterogeneous nature. The Multiscale Mixed Method (MuMM) was introduced aiming at the ef?cient 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 signi?cantly the computational effort to perform the domain decomposition iterations, as indicated by the numerical results.
Highlights
The development of multiscale numerical methods for second-order elliptic differential equations arising in porous media flow problems has attracted the attention of several research groups
The authors focus on the Multiscale Mixed Method (M uM M ), a numerical solver that uses a non-overlapping domain decomposition iterative procedure in which the spatial discretization of local problems uses the hybridized mixed finite elements at fine scale and the Robin boundary condition at coarse scale (FRANCISCO et al, 2014)
5.2 Parallel Algorithm The goal of this paper is to evaluate the performance of the parallel M uM M in simulations of the flow problem in highly heterogeneous porous media
Summary
The development of multiscale numerical methods for second-order elliptic differential equations arising in porous media flow problems has attracted the attention of several research groups. The authors focus on the Multiscale Mixed Method (M uM M ), a numerical solver that uses a non-overlapping domain decomposition iterative procedure in which the spatial discretization of local problems uses the hybridized mixed finite elements at fine scale and the Robin boundary condition at coarse scale (FRANCISCO et al, 2014). Mixed multiscale basis functions are used to compute the discrete solutions in local problems. The analogous use of the concept of multiscale flux basis functions can be found in (GANIS; YOTOV, 2009). The M uM M solver provides fast and accurate approximation for second-order elliptic equations. The multiscale procedure can take the advantage of heterogeneous processing units, which are relatively inexpensive and have great computational power
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