A critical study of agglomerated multigrid methods for diffusion on highly-stretched grids

Agglomerated multigrid methods for unstructured grids are studied critically for solving a model diffusion equation on highly-stretched grids typical of practical viscous simulations, following a previous work focused on isotropic grids. Different primal elements, including prismatic and tetrahedral elements in three dimensions, are considered. The components of an efficient node-centered full-coarsening multigrid scheme are identified and assessed using quantitative analysis methods. Fast grid-independent convergence is demonstrated for mixed-element grids composed of tetrahedral elements in the isotropic regions and prismatic elements in the highly-stretched regions. Implicit lines natural to advancing-layer/advancing-front grid generation techniques are essential elements of both relaxation and agglomeration. On agglomerated grids, consistent average-least-square discretizations augmented with edge-directional gradients to increase h-ellipticity of the operator are used. Simpler (edge-terms-only) coarse-grid discretizations are also studied and shown to produce grid-dependent convergence – only effective on grids with minimal skewing.