Abstract: 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.

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