A parallel strongly implicit algorithm for solving of diffusion equations

Abstract

We present a parallel algorithm for the solution of partial differential equations representing a 3-D diffusion process of the underground water by a finite difference method. The algorithm belongs to a class of the incomplete LU factorization methods, where corresponding system of linear algebraic equations is solved by a quasi LU decomposition in every time step. A code realizing the algorithm was written in Fortran 90 programming language using the MPI message passing interface system and was tested on a SGI Origin 2000 parallel computer.