Abstract
The key goal of the current paper is to implement a parallel alternating-direction implicit, or ADI, method for solving linear and non-linear equations describing gravitational flow of ground water and realize it on a distributed-memory MIMD-computer under the MPI messagepassing system. Aside from that, the paper represents a comparison of the parallel algorithms for solving aforementioned equations and their evaluation in terms of relative efficiency and speedup. The obtained results show that for reasonably large discretization grids the parallel ADI method, both for the linear and non-linear equations, is effective enough on a large number of processors, and limM→∞ CcA/CcB = 1.05, where CcA and CcB are computational complexity of the algorithms for solving non-linear and linear equations respectively.
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