Application of D4 Ordering And Minimization In An Effective Partial Matrix Inverse Iterative Method

Abstract

ABSTRACT A new algorithm is presented for solving simulation problems which employs minimization and a partial decomposition of the matrix resulting from an alternate diagonal ordering. The method also maintains material balance in its formulation, important for severely ill-conditioned problems. The technique has been applied to problems in two and three dimensions with good results and examples are given to show the convergence of the method. Examples include heterogeneous, ill-conditioned problems as well as ones with negative and positive co-efficients. Comparisons are made with currently available methods such as SIP, ORTHOMIN, the semi-direct algorithm of Letkeman and the diagonal method of Watts. The results show that the new method achieves convergence with less work than the other methods. In two dimensions, Stone's heterogeneous model problem with homogeneous sub-regions was solved with seven equivalent SIP iterations compared with 20.5 for the diagonal method. Coats, problem 1 in three dimensions was solved in 21 equivalent SIP iterations. SIP did not converge for this problem. Unlike SIP and similar to the Watts’ diagonal method, a sequence of iteration parameters is not required and this feature together with the stability of the method makes it relatively easy to use.