Black Box Multigrid with Coarsening by a Factor of Three

Joel E. Dendy

MS B284, Los Alamos National Laboratory, Los Alamos, NM 87544

J. David Moulton


Abstract

Black Box Multigrid (BoxMG) is a robust variational multigrid solver on logically structured grids. BoxMG standardly uses coarsening by a factor of two. It handles cell-centered discretizations on logically rectangular grids by treating the cell-centers as the unknowns to be coarsened. Such a strategy does not preserve the cell structure. That is, coarse-grid cells are not the union of fine grid cells. In some applications, such as local grid refinement, it is desirable that the cell structure be preserved. One such method was discussed at the last Copper Mountain Conference on Multigrid Methods, and it employed a strategy that preserves cell structure while coarsening by a factor of two. However, performance of this approach was unsatisfactory for certain checkerboard configurations of the diffusion coefficient.

The method discussed in this talk employs coarsening by a factor of three. It is a natural generalization of standard BoxMG, using operator-induced interpolation (which approximately preserves the continuity of the normal flux), restriction as the transpose of interpolation, and Galerkin coarsening. We present numerical results that demonstrate its robustness with respect to discontinuous diffusion coefficients. In addition, we explore its relationship with smoothed aggregation.