Towards Automatic Multigrid Algorithms for SPD, Nonsymmetric and Indefinite Problems

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 ofproblems: symmetric, nonsymmetdc and problems with discontinuous coefficients, nonuniform grids, and l;tonrectangular domains. When supplemented with an acceleration method, good convergence is achieved also for pure convection problems and indefinite Helmholtz equations. Key words, convection-diffusion equation, discontinuous coefficients, elliptic PDEs, indefinite Helmholtz equation, automatic multigrid method AMS subject classifications. 65F10, 65N22, 65N55