Parallel iterative methods with factorized preconditioning matrices for discretized elliptic equations on nonuniform grids

Parallel versions of MICCG(O) are considered for solving finite-difference equations on nonuniform grids in rectangular domains on distributed-memory parallel computers, which are based on two special orderings of unknowns. Automatic methods for choosing parameters are suggested that ensure a slow increase in the number of iteration steps with the number of processors. The efncienty of the methods proposed is estimated by computing the model problems.