On the spectrum of the iteration operator associated to the finite element preconditioning of Chebyshev collocation calculations

DOI10.1016/0045-7825(90)90033-IzbMath0727.65089OpenAlexW2073761720MaRDI QIDQ803743

P. Francken, Ernest Mund, Michel O. Deville

Publication date: 1990

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0045-7825(90)90033-i

zbMATH Keywords

eigenvaluesspectrumiteration operatorChebyshev collocation schemesDirichlet model problemfinite element preconditioning

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Boundary value problems for second-order elliptic equations (35J25) Inequalities involving eigenvalues and eigenvectors (15A42) Iterative numerical methods for linear systems (65F10)

Related Items (6)

On the condition number of some spectral collocation operators and their finite element preconditioning ⋮ Preconditioned Chebyshev collocation methods and triangular finite elements ⋮ Low-Order Preconditioning of High-Order Triangular Finite Elements ⋮ An explicit spectral collocation method using nonpolynomial basis functions for the time‐dependent Schrödinger equation ⋮ Chebyshev collocation solutions of flow problems ⋮ The piecewise-linear finite volume scheme: The best known lowest-order preconditioner for the \(\frac{d^2}{dx^2}\) Chebyshev spectral operator

Cites Work

• Chebyshev 3-D spectral and 2-D pseudospectral solvers for the Helmholtz equation
• Chebyshev pseudospectral solution of second-order elliptic equations with finite element preconditioning
• Spectral methods for problems in complex geometries
• Preconditioned minimal residual methods for Chebyshev spectral calculations
• Finite-Element Preconditioning for Pseudospectral Solutions of Elliptic Problems
• Spectral Calculations of One-Dimensional Inviscid Compressible Flows
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