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 of problems: symmetric, nonsymmetric and problems with discontinuous coefficients, nonuniform grids, and nonrectangular domains. When supplemented with an acceleration method, good convergence is achieved also for pure convection problems and indefinite Helmholtz equations.