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PreprintCC BY 4.0arXiv

Translation of transient acoustic fields

  • Michael J. Carley
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Abstract

A method is presented for the translation of acoustic field data from a source to a target region. Field data are represented as spherical harmonic expansions on spheres surrounding the source and target regions respectively and expansions are translated using a ``point and shoot'' method using the Kirchhoff--Helmholtz integral to carry out an axial translation from one sphere to the other. The principal motivation for the method is its use in a time-domain Fast Multipole Method, and test cases reflective of this application are presented. The method converges to six digits for appropriate values of parameters and for the values of N considered here computational effort scales approximately as N2 where N is the order of spherical harmonic expansion for the field data. The method is causal and thus avoids artifacts generated in methods which are not based on intrinsically causal formulations.

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Cite

BibTeXRIS
BibTeX
@misc{carley2026translation,
  title = {{Translation of transient acoustic fields}},
  author = {Michael J. Carley},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.15138},
  eprint = {2607.15138},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.15138},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Translation of transient acoustic fields
AU  - Michael J. Carley
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2607.15138
UR  - https://arxiv.org/abs/2607.15138
AB  - A method is presented for the translation of acoustic field data from a source to a target region. Field data are represented as spherical harmonic expansions on spheres surrounding the source and target regions respectively and expansions are translated using a ``point and shoot'' method using the Kirchhoff--Helmholtz integral to carry out an axial translation from one sphere to the other. The principal motivation for the method is its use in a time-domain Fast Multipole Method, and test cases reflective of this application are presented. The method converges to six digits for appropriate values of parameters and for the values of N considered here computational effort scales approximately as N^2 where N is the order of spherical harmonic expansion for the field data. The method is causal and thus avoids artifacts generated in methods which are not based on intrinsically causal formulations.
ER  -