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BIT Numerical Mathematics

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01.03.2015

A spectrally accurate direct solution technique for frequency-domain scattering problems with variable media

verfasst von: Adrianna Gillman, Alex H. Barnett, Per-Gunnar Martinsson

Erschienen in: BIT Numerical Mathematics | Ausgabe 1/2015

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Abstract

This paper presents a direct solution technique for the scattering of time-harmonic waves from a bounded region of the plane in which the wavenumber varies smoothly in space. The method constructs the interior Dirichlet-to-Neumann (DtN) map for the bounded region via bottom-up recursive merges of (discretization of) certain boundary operators on a quadtree of boxes. These operators take the form of impedance-to-impedance (ItI) maps. Since ItI maps are unitary, this formulation is inherently numerically stable, and is immune to problems of artificial internal resonances. The ItI maps on the smallest (leaf) boxes are built by spectral collocation on tensor-product grids of Chebyshev nodes. At the top level the DtN map is recovered from the ItI map and coupled to a boundary integral formulation of the free space exterior problem, to give a provably second kind equation. Numerical results indicate that the scheme can solve challenging problems 70 wavelengths on a side to 9-digit accuracy with 4 million unknowns, in under 5 min on a desktop workstation. Each additional solve corresponding to a different incident wave (right-hand side) then requires only 0.04 s.

Vorheriger Artikel An efficient algorithm for computing acoustic wave interactions in large -obstacle three dimensional configurations

Nächster Artikel When is the error in the -BEM for solving the Helmholtz equation bounded independently of ?

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The choice of bump height and width needs to be made carefully to ensure that a usable bandgap exists; this was done by creating a separate spectral solver for the band structure of the periodic problem.

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Titel: A spectrally accurate direct solution technique for frequency-domain scattering problems with variable media
verfasst von: Adrianna Gillman
Alex H. Barnett
Per-Gunnar Martinsson
Publikationsdatum: 01.03.2015
Verlag: Springer Netherlands
Erschienen in: BIT Numerical Mathematics / Ausgabe 1/2015
Print ISSN: 0006-3835
Elektronische ISSN: 1572-9125
DOI: https://doi.org/10.1007/s10543-014-0499-8

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