Computing elliptic membrane high frequencies by Mathieu and Galerkin methods

DOI10.1007/s10665-006-9070-1zbMath1107.74021OpenAlexW2037670508MaRDI QIDQ873171

Robert W. Scharstein, Howard B. Wilson

Publication date: 28 March 2007

Published in: Journal of Engineering Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10665-006-9070-1

zbMATH Keywords

convergenceeigenvalue solver

Mathematics Subject Classification ID

Vibrations in dynamical problems in solid mechanics (74H45) Finite element methods applied to problems in solid mechanics (74S05) Numerical approximation of solutions of dynamical problems in solid mechanics (74H15) Membranes (74K15)

Related Items

Exact solution for vibration analysis of an eccentric elliptical membrane, Tensor solutions in irregular domains: eigenvalue problems, Spectral collocation solutions to multiparameter Mathieu's system, Applying GMRES to the Helmholtz equation with strong trapping: how does the number of iterations depend on the frequency?, A Sylvester–Arnoldi type method for the generalized eigenvalue problem with two‐by‐two operator determinants, Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation, Quasi-analytical solution of two-dimensional Helmholtz equation, High-accuracy calculation of eigenvalues of the Laplacian in an ellipse (with Neumann boundary condition), High-frequency estimates on boundary integral operators for the Helmholtz exterior Neumann problem

Uses Software

• Matlab
• Algorithm 804

Cites Work

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• Asymptotic solution of eigenvalue problems
• Computing eigenmodes of elliptic operators using radial basis functions
• Numerical solution of Mathieu's equation
• Whispering-gallery modes and resonances of an elliptic cavity
• Eigenfrequencies of an Elliptic Membrane
• Visualization of Special Eigenmode Shapes of a Vibrating Elliptical Membrane
• Eigenmodes of Isospectral Drums
• Algebraic methods to compute Mathieu functions
• The discretized harmonic oscillator: Mathieu functions and a new class of generalized Hermite polynomials
• A Complete Method for the Computations of Mathieu Characteristic Numbers of Integer Orders
• Approximations and Bounds for Eigenvalues of Elliptic Operators