Parallel iterative methods using factorized preconditioning matrices for solving elliptic equations on triangular grids

Parallel analogs of the variants of the incomplete Cholesky-conjugate gradient method and the modified incomplete Cholesky-conjugate gradient method for solving elliptic equations on uniform triangular and unstructured triangular grids on parallel computer systems with the MIMD architecture are considered. The construction of parallel methods is based on the use of various variants of ordering the grid points depending on the decomposition of the computation domain. Results of the theoretic and experimental studies of the convergence rate of these methods are presented. The solution of model problems on a moderate number processors is used to examine the efficiency of the proposed parallel methods.