Parallel multigrid solvers with block-wise smoothers for multiblock grids

Abstract

Several methods have been proposed in the multigrid literature to deal with anisotropic operators. Alternating-direction plane smoothers in combination with full coarsening have been found to be highly efficient and robust on single-block grids because of their optimal work per cycle and low convergence factor. The purpose of this chapter is to study whether the optimal properties of plane implicit smoothers deteriorate for general multi block grids. Notice that the multigrid method with a block-wise smoother is a priori more efficient than a domain decomposition method because the multigrid algorithm is applied over the whole domain. Its efficiency and an excellent parallelization potential have been already demonstrated for isotropic elliptic problems where point-wise red-black smoothers were used. This chapter analyzes two sources of anisotropy. The first case is anisotropic coefficients in the equation discretized on uniform grids and the second case is the isotropic coefficient equation discretized on stretched grids.