Parallel iterative methods with factorized preconditioning matrices for elliptic equations on unstructed triangular grid

Parallel versions of two iterative methods are proposed for solving discretized elliptic equations on unstructed triangular grid on distributed-memory parallel computers. The conjugate gradient methods with incomplete factorization type preconditioning and modified incomplete factorization type preconditioning are considered. The construction of the parallel versions of the methods is based on the special orderings of nodes of a grid. The rate of convergence and efficientcy of proposed methods are investigated both teoretically and by means of calculations of model problem.