Improved Black Box Multigrid
                     for Definite and Indefinite Problems


                                 Yair Shapira
          Computer Science Department, Technion, Haifa 32000, Israel
                           e-mail: yairs@lanl.gov.


                                   Abstract

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 coefficients.  It motivates the definition of
improved versions of Black Box Multigrid for diffusion problems with
discontinuous coefficients and indefinite Helmholtz equations.  For
anisotropic problems, it helps in choosing suitable implementations for
frequency decomposition multigrid methods.  For highly indefinite problems, it
provides a way to choose a suitable mesh size for the coarsest grid used.
Numerical experiments confirm the analysis and show the advantage of the
present methods.