A simple cell-centered multigrid method for 3D interface problems

A multigrid algorithm is presented for cell-centered discretizations of interface problems. Instead of constructing the coarse grid operators by means of the Galerkin approximation, the coarse grid operators are obtained by discretization on the coarse grids. The advantage of this approach is that we obtain M-matrices on all grids, and that the sparsity pattern of the fine grid matrix is retained on all grids. Moreover, the coarse grid operators are very easy to construct. Numerical results of several test problems are presented.