Towards Automatic Multigrid Algorithms
                for SPD, Nonsymmetric and Indefinite Problems


                  Yair Shapira, Moshe Israeli and Avram Sidi

                   Computer Science Department, Technion, 
                            Haifa $32000$, Israel
                            email: yairs@lanl.gov

                                   Abstract

A new multigrid algorithm is constructed for the solution of linear systems of
equations which arise from the discretization of elliptic PDEs.  It is defined
in terms of the difference scheme on the fine grid only, and no
rediscretization of the PDE is required.  Numerical experiments show that this
algorithm gives high convergence rates for several classes of problems:
symmetric, nonsymmetric and problems with discontinuous coefficients,
non-uniform grids and non-rectangular domains.  When supplemented with an
acceleration method, good convergence is achieved also for pure convection
problems and indefinite Helmholtz equations.