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Multiple-scattering frequency-time hybrid solver for the wave equation in interior domains.
- Source :
-
Mathematics of Computation . Mar2024, Vol. 93 Issue 346, p551-587. 37p. - Publication Year :
- 2024
-
Abstract
- This paper proposes a frequency-time hybrid solver for the time-dependent wave equation in two-dimensional interior spatial domains. The approach relies on four main elements, namely, (1) A multiple scattering strategy that decomposes a given interior time-domain problem into a sequence of limited-duration time-domain problems of scattering by overlapping open arcs, each one of which is reduced (by means of the Fourier transform) to a sequence of Helmholtz 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 evolution for 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00255718
- Volume :
- 93
- Issue :
- 346
- Database :
- Academic Search Index
- Journal :
- Mathematics of Computation
- Publication Type :
- Academic Journal
- Accession number :
- 174272859
- Full Text :
- https://doi.org/10.1090/mcom/3872