On the evaluation of the eigenvalues of the finite differences Laplacian over a hexagon

DOI10.1007/BF02576416zbMath0641.65078OpenAlexW2062248618MaRDI QIDQ1100865

A. Fontani, Dario Andrea Bini

Publication date: 1987

Published in: Calcolo (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02576416

zbMATH Keywords

complexityeigenvalue problemorthogonalizationHelmholtz equationLaplacianshiftinginverse power methodfast direct method7-point finite difference approximationcapacitance matrix techniques

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Direct numerical methods for linear systems and matrix inversion (65F05) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the accuracy of finite difference approximations to the eigenvalues of differential and integral operators
• Eigenvalues of the Laplacian in Two Dimensions
• The Eigenvalues of an Equilateral Triangle
• Cutoff Wavenumbers and Modes of Hexagonal Waveguides
• The Direct Solution of the Discrete Poisson Equation on Irregular Regions
• Bigradients and the Euclid-Sturm Algorithm