Finite element preconditioning for spectral multigrid methods
type: Item
instance of: scholarly article
title: Finite element preconditioning for spectral multigrid methods
zbMATH Open document ID: 0795.65078
DOI: 10.1016/S0096-3003(93)90039-H
published in: Applied Mathematics and Computation
publication date: 1994-09-08T00:00:00Z
review text: Second-order linear elliptic equations are considered on a rectangle in the plane. The basic method is collocation by tensor products of Chebyshev polynomials. The method of solution is by a multigrid iteration, where for each iteration the defect is computed from the collocation operator and the new iterate is a line-Gauss-Seidel approximate inverse of a finite element operator. Computed examples indicate that the method is very efficient.
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 519642
zbMATH Keywords: preconditioning
zbMATH Keywords: spectral multigrid methods
zbMATH Keywords: second-order linear elliptic equations
zbMATH Keywords: collocation by tensor products
zbMATH Keywords: Chebyshev polynomials
zbMATH Keywords: multigrid iteration
zbMATH Keywords: finite element
author: Wilhelm Heinrichs
reviewed by: Gerald W. Hedstrom
MaRDI profile type: Publication
cites work: Q4742248
cites work: Improved spectral multigrid methods for periodic elliptic problems
cites work: Boundary Conditions in Chebyshev and Legendre Methods
cites work: Parallelism in spectral methods
cites work: Boundary and interface conditions within a finite element preconditioner for spectral methods
cites work: The fast Fourier transform algorithm: Programming considerations in the calculation of sine, cosine and Laplace transforms
cites work: Black box multigrid
cites work: Chebyshev pseudospectral solution of second-order elliptic equations with finite element preconditioning
cites work: Q3761637
cites work: Line relaxation for spectral multigrid methods
cites work: Multigrid methods for combined finite difference and Fourier problems
cites work: Q4742246
cites work: Direct methods for the solution of the discrete Poisson equation: some comparisons
cites work: Self-sorting mixed-radix fast Fourier transforms
cites work: Spectral multigrid methods for elliptic equations
cites work: Spectral multigrid methods for elliptic equations. II
Recommended article: Preconditioners for the Spectral Multigrid Method
Recommended article: Q3140810
Recommended article: Q3827518
Recommended article: Preconditioners for spectral element methods for elliptic and parabolic problems
Recommended article: Finite-Element Preconditioning for Pseudospectral Solutions of Elliptic Problems
Recommended article: Finite element preconditioning on spectral element discretizations for coupled elliptic equations
Recommended article: Preconditioning spectral element schemes for definite and indefinite problems
Recommended article: Finite-Element Preconditioning of G-NI Spectral Methods
Recommended article: Preconditioning on Element Interfaces for the p-Version Finite Element Method and Spectral Element Method
Recommended article: Q3140846
description: scientific article; zbMATH DE number 519642