REVENGE OF THE SEMICOARSENING FREQUENCY DECOMPOSITION        
                              MULTIGRID METHOD 

                               J. E. Dendy, Jr.
                        Theoretical Division, MS-B284
                        Los Alamos National Laboratory
                         Los Alamos, New Mexico 87545


The frequency decomposition multigrid method was previously considered and
modified so as to obtain robustness for problems with discontinuous
coefficients while retaining robustness for problems with anisotropic
coefficients.  The application of this modified method to a problem arising in
global ocean modeling was also considered.  For this problem it was shown that
the discretization employed gives rise to an operator with a nontrivial null
space, for which point relaxation is not robust.  In fact alternating line
relaxation is required for robustness, negating the main advantage of the
frequency decomposition method:  robustness for anisotropic operators using
only point relaxation.  In this talk a semicoarsening variant, which requires
line relaxation in one direction only, is considered, and it is shown that
this variant works well for the global ocean modeling problem.