Parallelization of Alternating Direction Implicit Methods for Three-Dimensional Domains

Abstract

The method of domain decomposition using a three-dimensional analogue of the Peaceman-Rachford algorithm is considered. In the proposed method, solution of a three-dimensional boundary value problem is performed with the use of iterations, each including two half-steps: at the first step “two-dimensional” problems are solved by the classical Peaceman-Rachford method in the planes perpendicular to the axis z, at the second – “one-dimensional” problems are solved on the lines parallel to the axis z. For the solution of one-dimensional problems, the block method of the even/odd reductions without “back step" is used, which is readily parallelized. Estimations of parallelization efficiency and results of numerical experiments on computers RM-600-E 30 (Siemens-Nixdorf) and MVS1000 (“Scientific Research Institute” Kvant – Moscow) for different grid domains and processor topologies are presented.

The work was supported by the RFBR, N 01-01-00819 and N 02-01-01176