MULTIGRID TECHNIQUES FOR HIGHLY INDEFINITE EQUATIONS

                                 Yair Shapira
                         Computer Science Department
                                   Technion
                                 Haifa 32000
                                    Israel


                                   SUMMARY

A multigrid method for the solution of finite difference approximations of
elliptic PDEs is introduced.  A parallelizable version of it, suitable for two
and multi level analysis, is also defined, and serves as a theoretical tool
for deriving an optimal implementation for the main version.  For indefinite
Helmholtz equations, this analysis provides a prediction of the optimal mesh
size for the coarsest grid used.  Numerical experiments show that the method
is applicable to diffusion equations with discontinuous coefficients and to
highly indefinite Helmholtz equations.