Multigrid methods for combined finite difference and Fourier problems. (English) Zbl 0657.65118

Heinrichs, Wilhelm

J. Comput. Phys. 78, No. 2, 424-436 (1988).

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 A. Brandt [Lect. Notes Math. 960, 220-312 (1982; Zbl 0505.65037)], and shows much numerical results.

Reviewer: G.Stoyan

MSC:

65N22	Numerical solution of discretized equations for boundary value problems involving PDEs
65N35	Spectral, collocation and related methods for boundary value problems involving PDEs
65F10	Iterative numerical methods for linear systems
35J25	Boundary value problems for second-order elliptic equations

Keywords:

smoothing rates; convergence factors; finite difference method; pseudospectral method; condition number; multigrid methods; weighted residual relaxation

Citations:

Zbl 0505.65037

References:

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