Incomplete decomposition of explicit group-2 matrices with 5 and 9 block diagonal

Abstract

Recent attempts has been achieved to group the elements of the unknowns (2 or more) and utilizing the 5-point molecular structure called explicit group-2 finite difference according to different numbering strategy, such that the resulting sparse block linear system solved iteratively and proved it is efficiency. The aim of this paper is to introduce the 9-point molecular structure for group-2 explicit finite difference and to generalize the incomplete matrix decomposition with 5 or 9 block diagonal. A comparison between different incomplete matrix decompositions with an iterative method confirm the reliability of the present approach.