Heinrichs, W. Finite element versus finite difference preconditioning for spectral multigrid methods. (English) Zbl 0785.65110 Beauwens, R. (ed.) et al., Iterative methods in linear algebra. Proceedings of the IMACS international symposium, Brussels, Belgium, 2-4 April, 1991. Amsterdam: North-Holland. 203-207 (1992). Summary: Finite element and finite difference preconditioning for spectral multigrid methods are compared. For preconditioning we employ one step of a line-Gauss-Seidel relaxation. Furthermore different multigrid strategies are compared. The computational work of the various methods is estimated. We deduce that the most efficient strategy consists of a Richardson relaxation preconditioned by one \(V\)-cycle of a finite element multigrid method. Numerical results are presented.For the entire collection see [Zbl 0778.00018]. Cited in 1 Document MSC: 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 65N35 Spectral, collocation and related methods for boundary value problems involving PDEs 65F35 Numerical computation of matrix norms, conditioning, scaling 65F10 Iterative numerical methods for linear systems 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation Keywords:collocation; Poisson equation; finite element; finite difference; preconditioning; spectral multigrid methods; line-Gauss Seidel relaxation; Richardson relaxation; numerical results PDFBibTeX XMLCite \textit{W. Heinrichs}, in: Iterative methods in linear algebra. Proceedings of the IMACS international symposium, Brussels, Belgium, 2-4 April, 1991. Amsterdam: North-Holland. 203--207 (1992; Zbl 0785.65110)