Multiple-scattering frequency-time hybrid solver for the wave equation in interior domains
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- by Oscar P. Bruno and Tao Yin
- Math. Comp. 93 (2024), 551-587
- DOI: https://doi.org/10.1090/mcom/3872
- Published electronically: July 24, 2023
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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.References
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Bibliographic Information
- Oscar P. Bruno
- Affiliation: Department of Computing & Mathematical Sciences, California Institute of Technology, 1200 East California Blvd., Pasadena, California 91125
- MR Author ID: 42560
- ORCID: 0000-0001-8369-3014
- Email: obruno@caltech.edu
- Tao Yin
- Affiliation: LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
- MR Author ID: 1046452
- Email: yintao@lsec.cc.ac.cn
- Received by editor(s): June 2, 2022
- Received by editor(s) in revised form: February 4, 2023, and May 7, 2023
- Published electronically: July 24, 2023
- Additional Notes: The first author was supported by NSF, DARPA and AFOSR through contracts DMS-2109831, HR00111720035, FA9550-19-1-0173 and FA9550-21-1-0373, and by the NSSEFF Vannevar Bush Fellowship under contract number N00014-16-1-2808. The second author was supported by NSFC through Grants No. 12171465 and 12288201.
- © Copyright 2023 American Mathematical Society
- Journal: Math. Comp. 93 (2024), 551-587
- MSC (2020): Primary 35L05, 65M80, 65T99, 65R20
- DOI: https://doi.org/10.1090/mcom/3872
- MathSciNet review: 4678577