On Distributed Gauss-Seidel Relaxation

                                  A. J. Meir
                          Department of Mathematics
                              Auburn University
                           Auburn, AL 36849, U.S.A.


Multigrid methods have proven to be efficient methods for solving partial
differential equations (especially those of elliptic type).  There is also
growing experience with multigrid solvers for fluids problems, e.g., the
Stokes and Navier Stokes equations (using both finite element and finite
difference discretizations).

It is also well known that at the heart of any multigrid method is the
smoother.  In this work we look at a smoother introduced by Brandt and Dinar,
we examine some of its properties and consider some possible modifications to
it.

It is well known that multigrid performance using DGS relaxation is sensitive
to the treatment of boundaries; this issue is addressed.