Domain decomposition and nested grids in a parallel environment

A new algorithm for domain decomposition to solve steady flow problems in randomly heterogeneous porous media has recently been proposed. In the present paper we explain the most significant results of its parallel implementation. In each macro-triangle three adjoint problems are solved by a finite element technique. These adjoint problems are completely independent and my be solved concurrently on a parallel computer. The results obtained are subsequently transferred over the boundaries of subdomains and conveniently assembled over the nodes of the macromesh. We obtain a nonsymmetric linear system wich gives the potential values over the nodes of the macromesh. The code has been implemented, using specific parallelization directives, on a Cray Y-MP8/432. The average parallel spedups obtained in the numerical experiments using 2, 3, and 4 processors are, respectively, 1.991, 2.978, and 3.973. These values demonstrate the excellent level of parallelization achieved by the code and the high efficiency of the proposed algorithm.