Iterative Solution of High Order Compact Systems


                        W. F. Spotz* and G. F. Carey
                  Computational Fluid Dynamics Laboratory
                     The University of Texas at Austin

We have recently developed a class of finite difference methods which
provide higher accuracy and greater stability than standard central or
upwind difference methods, but still reside on a compact patch of grid
cells.   In the present study we investigate the performance of several
gradient-type iterative methods for solving the associated sparse systems. 
Both serial and parallel performance studies have been made. 
Representative examples are taken from elliptic PDE's for diffusion,
convection-diffusion, and viscous flow applications.