Galerkin-Legendre spectral method for the 3D Helmholtz equation

DOI10.1006/jcph.2000.6504zbMath0959.65130OpenAlexW2023271554MaRDI QIDQ1578080

F. Auteri, Luigi Quartapelle

Publication date: 9 January 2001

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jcph.2000.6504

zbMATH Keywords

algorithmHelmholtz equationsseparation of variablesdiagonalization algorithmGalerkin-Legendre spectral methodfast elliptic spectral solver3D Poisson equationnonhomogeneous Dirichlet condition

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Direct numerical methods for linear systems and matrix inversion (65F05)

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Cites Work

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• Chebyshev 3-D spectral and 2-D pseudospectral solvers for the Helmholtz equation
• Spectral approximation for elliptic boundary value problems
• The accurate solution of Poisson's equation by expansion in Chebyshev polynomials
• Galerkin spectral method for the vorticity and stream function equations
• Direct solution of partial difference equations by tensor product methods
• Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials
• Efficient Spectral-Galerkin Method II. Direct Solvers of Second- and Fourth-Order Equations Using Chebyshev Polynomials