Second‐order treatment of the interface of domain decomposition method for parabolic problems

Abstract

Estimations for the values on interface lines are necessary in a domain decomposition method. However, the accuracy of the estimations is of the first order for most of unconditionally stable domain decomposition schemes. In this paper, a second order of accuracy for the estimations on interface lines is presented. With the new scheme, the optimal number of decomposed subdomains has been observed and proposed. Moreover when the SOR iterative method is used, the optimal over-relaxation parameter is also studied. A matrix A of order N has Property A if there exist two disjoint subsets S 1 and S 2 of W , the set of the first N positive integers, such that S 1 + S 2 = W and such that if i = j and if either a i, j = 0 or a j,i = 0, then i ∈ S 1 and j ∈ S 2 or else i ∈ S 2 and j ∈ S 1 .