Improved Black Box Multigrid for Definite and Indefinite Problems

A two-level analysis method for certain separable problems is introduced. Unlike standard two-level analysis methods, based on Fourier analysis, it is based on spectral analysis, hence applicable to non-normal problems and to certain problems with variable coeecients. It motivates the deenition of improved versions of Black Box Multigrid for diiusion problems with discontinuous coeecients and indeenite Helmholtz equations. For anisotropic problems, it helps in choosing suitable implementations for frequency decomposition multigrid methods. For highly indeenite problems, it provides a way to choose a suitable mesh size for the coarsest grid used. Numerical experiments connrm the analysis and show the advantage of the present methods.