Parallelization of porous media solver

Abstract

We have developed three parallel algorithms which are typical fJSf, implementation ofMfsolverC + + methods. All of them solve a parabolic 3D problem^-with nonlocal boundary condition. Thefirst one implements explicit Euler scheme. The ,iSt| second algorithm is based on the backward Eider scheme. At each time step a ;ar^e S^ system of linear equations is solved. We use the Conjugate Gradient iterative method, since matrix of the system is symmetrical. This algorithm enables MS to test the^'SJSf efficiency of collective data sending methods, implemented in Parallel C++ Army .gf Objects tool. The last algorithm is built on Locally One Dimensional approximation of,% the three-dimensional problem. The Wang factorization algorithm is used to solve a. ^fei|| large number of three-diagonal systems of linear equations. A modification of the |%| algorithm is done to include non-local boundary conditions.