Abstract: 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.

Key words: solution of linear systems, block tridiagonal matrix, incomplete factorization, domain decomposition, additive Schwarz, parallel algorithm