Multigrid methods for 3-D definite and indefinite problems Original Research Article

A multigrid method for the solution of certain finite difference and finite volume schemes for elliptic PDEs is introduced. A parallelizable version of it, suitable for two-level and multi-level analysis, is also defined and serves as a theoretical tool for deriving suitable implementations for the main version. For indefinite equations, this analysis provides a prediction of a suitable mesh size for the coarsest grid used. Numerical experiments show the efficiency of the method for 3-D diffusion problems with discontinuous coefficients and highly indefinite Helmholtz equations.