Towards Automatic Multigrid Algorithms for SPD,
Nonsymmetric and Indefinite Problems

Yair Shapira, Moshe Israeli, and Avram Sidi
Computer Science Department
Haifa 32000


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.

Contributed October 19, 1995.