Group accelerated OverRelaxation methods on rotated grid

Abstract

In Martins et al. [M.M. Martins, W.S. Yousif, D.J. Evans, Explicit group AOR method for solving elliptic partial differential equations, Neural, Parallel and Science Computation 10(4) (2002) 411–422], a new explicit four-point group accelerated OverRelaxation (Group AOR) iterative method was presented where the computational superiority of this new technique was established when compared with the point AOR method developed by Evans and Martins [D.J. Evans, M.M. Martins, The AOR method For AX - XB = C , International Journal of Computer Mathematics 52 (1994) 75–82] and Martins et al. [M.M. Martins, D.J. Evans, M.E. Trigo, The AOR iterative method for new preconditioned linear systems, Journal of Computational and Applied Mathematics 132 (2001) 461–466]. In this work, we formulate an alternative group scheme from the AOR family derived from the rotated (skewed) five point formula [G. Dahlquist, A. Bjorck, Numerical Methods, Prentice-Hall, Englewood Cliffs, NJ, 1974, p. 320; Y. Saad, Iterative Methods For Sparse Linear Systems, second ed., PWS Publishing Company, Boston, 2000, p. 50]. The derivation of this new group scheme is presented and its performance is compared with the existing explicit four-point Group AOR. We include the analysis of the convergence results for the new group scheme. Numerical experiments are also presented to illustrate our results.