Coarse grid approximation governed by local

Solving discrete boundary value problems with the help of an appropriate multigrid method [1, 3, 4, 5] necessitates the construction of a sequence of coarse grids with corresponding coarse grid approximations for the given fine grid discretization. Popular choices in this context are the Galerkin coarse grid approximation (GCA) and the use of...

Multigrid for high dimensional elliptic partial differential equations on non-equidistant grids

This work presents techniques, theory and numbers for multigrid in a general d-dimensional setting. The main focus is the multigrid convergence for high-dimensional partial differential equations (PDEs). As a model problem we have chosen the anisotropic diffusion equation, on a unit hypercube. We present some techniques for building the general...