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Computing the Sound of the Sea in a Seashell

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arxiv 2009.02956 v2 pith:2VGO2XJ3 submitted 2020-09-07 math.SP cs.NAmath.NA

Jonathan Ben-Artzi , Marco Marletta , Frank Rösler This is my paper · ORCID
classification math.SPcs.NAmath.NA
keywords chamberresonatoraccessaddressedalgorithmanswerapproximationassume
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abstract

The question of whether there exists an approximation procedure to compute the resonances of any Helmholtz resonator, regardless of its particular shape, is addressed. A positive answer is given, and it is shown that all that one has to assume is that the resonator chamber is bounded and that its boundary is $\mathcal C^2$. The proof is constructive, providing a universal algorithm which only needs to access the values of the characteristic function of the chamber at any requested point.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the computation of geometric features of spectra of linear operators on Hilbert spaces

    math.SP 2019-08 conditional novelty 8.0 of 10

    First algorithms and solvability-complexity classifications for computing Lebesgue measure, capacity, and fractal dimensions of spectra of infinite-dimensional linear operators.

  2. Computing Spectral Measures and Spectral Types

    math.SP 2019-08 conditional novelty 8.0 of 10

    First general algorithms compute spectral measures, point/continuous/singular decompositions, functional calculus, and Radon-Nikodym derivatives for self-adjoint or unitary operators with known column decay, with Solv...

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