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Perturbative Analysis of the Method of Particular Solutions for Improved Inclusion of High-Lying Dirichlet Eigenvalues
2009
SIAM Journal on Numerical Analysis
The Dirichlet eigenvalue or "drum" problem in a domain Ω ⊂ R 2 becomes numerically challenging at high eigenvalue (frequency) E. In this regime the method of particular solutions (MPS) gives spectral accuracy for many domain shapes. It requires a number of degrees of freedom scaling as √ E, the number of wavelengths on the boundary, in contrast to direct discretization for which this scaling is E. Our main result is an inclusion bound on eigenvalues that is a factor O( √ E) tighter than the
doi:10.1137/080724022
fatcat:3jnpdqbv6veqdp3mml5r3nb22u