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Title: Multiple-scattering frequency-time hybrid solver for the wave equation in interior domains
This paper proposes a frequency-time hybrid solver for the time-dependent wave equation in two-dimensionalinterior spatial domains. The approach relies on four main elements, namely, (1) A multiple scattering strategy that decomposes a giveninteriortime-domain problem into a sequence oflimited-durationtime-domain problems of scattering by overlapping open arcs, each one of which is reduced (by means of the Fourier transform) to a sequence ofHelmholtz frequency-domain problems; (2) Boundary integral equations on overlapping boundary patches for the solution of the frequency-domain problems in point (1); (3) A smooth“Time-windowing and recentering”methodology that enables both treatment of incident signals of long duration and long time simulation; and, (4) A Fourier transform algorithm that delivers numerically dispersionless,spectrally-accurate time evolutionfor given incident fields. By recasting the interior time-domain problem in terms of a sequence of open-arc multiple scattering events, the proposed approach regularizes the full interior frequency domain problem—which, if obtained by either Fourier or Laplace transformation of the corresponding interior time-domain problem, must encapsulate infinitely many scattering events, giving rise to non-uniqueness and eigenfunctions in the Fourier case, and ill conditioning in the Laplace case. Numerical examples are included which demonstrate the accuracy and efficiency of the proposed methodology.  more » « less
Award ID(s):
2109831
PAR ID:
10516799
Author(s) / Creator(s):
;
Corporate Creator(s):
Editor(s):
Brenner, Susan
Publisher / Repository:
Mathematics of Computation
Date Published:
Journal Name:
Mathematics of Computation
Edition / Version:
1
Volume:
93
Issue:
346
ISSN:
0025-5718
Page Range / eLocation ID:
551 to 587
Subject(s) / Keyword(s):
MULTIPLE-SCATTERING wave equation
Format(s):
Medium: X Size: 41MB Other: pdf
Size(s):
41MB
Sponsoring Org:
National Science Foundation
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