Based on two-dimensional domain decomposition with small overlapping,we provide a method in which local lower and upper triangular incomplete factors are combined into an effective approximation for global incomplete lower and upper triangular factors of coefficient matrix.Parallelization method is applicable to any preconditioner of incomplete type. Parallel performance metric of two-dimensional parallel preconditioner is compared to that of one-dimensional ones.Experiments show that it is more efficient than additive Schwarz technique and two-dimensional decomposition is better than corresponding one-dimensional decomposition as more processors are used for parallel computation.

Based on one-dimensional domain decomposition with small overlapping, we approximate local lower and upper triangular incomplete factors and combine these factors into an effective approximation for global incomplete factorization preconditioner of coefficient matrix. Two implementations are considered. One is based on exchange of total boundary values of overlapped domain. The other is based on carefully arranged computation process to reduce communication of whole overlapped domain in one line of grid points. The parallelization method can be used to any incomplete factorization preconditioner. Experiments show that it is more efficient than widely-used additive Schwarz technique.