The Laplacian eigenvalues of a polygon

DOI10.1016/j.camwa.2004.10.010zbMath1069.65121OpenAlexW1978433134MaRDI QIDQ1770681

Gilbert Strang, Pavel Grinfeld

Publication date: 7 April 2005

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2004.10.010

zbMATH Keywords

Finite elementsNumerical examplesLaplace eigenvaluesShape optimizationPolygonsBoundary perturbationsMoving boundary derivative

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (10)

Notes on the nonlinear dependence of a multiscale coupled system with respect to the interface ⋮ Shape Optimization and Electron Bubbles ⋮ Shape recognition using eigenvalues of the Dirichlet Laplacian ⋮ Domain dependence of eigenvalues of elliptic type operators ⋮ Hadamard's formula inside and out ⋮ Computing ultra-precise eigenvalues of the Laplacian within polygons ⋮ Eigenvalue Characterization and Computation for the Laplacian on General 2-D Domains ⋮ Laplace eigenvalues on regular polygons: a series in \(1/N\) ⋮ A reverse quantitative isoperimetric type inequality for the Dirichlet Laplacian ⋮ Spectroscopy of drums and quantum billiards: Perturbative and nonperturbative results

Uses Software

• DistMesh

Cites Work

• A Simple Mesh Generator in MATLAB
• Reviving the Method of Particular Solutions
• Approximations and Bounds for Eigenvalues of Elliptic Operators
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