Multigrid methods for combined finite difference and Fourier problems (Q1110998)

Considered are combinations of finite difference and pseudo-spectral approximations for 2D and 3D elliptic problems with periodic and first or second kind boundary conditions. This is of interest since the usual combination of Fourier with Chebyshev approximation not only has a condition number greater by two orders but also may result (for not appropriately chosen smoothing iterations) into loss of convergence. The paper contains a description of several details of multigrid methods to solve the discretized equations, lists parameters (being optimal in case of constant coefficients) for the weighted residual relaxation of \textit{A. Brandt} [Lect. Notes Math. 960, 220-312 (1982; Zbl 0505.65037)], and shows much numerical results.