A 3D spectral multigrid method

摘要

We consider a 3D spectral multigrid method for 3D elliptic problems with arbitrary anisotropies. The smoothing method is a preconditioned Richardson iteration, where a pseudospectral discretization is used on the right-hand side, and a finite-difference discretization on the left-hand side. In each step of this iteration, a finite-difference problem is solved approximately, by plane-relaxation sweeps. The plane relaxation requires the solution of 2D finite-difference problems. These problems are solved approximately using 2D multigrid cycles.