Translation of transient acoustic fields

Michael J. Carley

Translation of transient acoustic fields

Computational Physics 2026-07-16 v1

Authors: Michael J. Carley

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 computational effort scales approximately as $N^{2}$ where $N$ is the order of spherical harmonic expansion for the field data.

Keywords

acoustic field translation spherical harmonic expansion point and shoot Kirchhoff-Helmholtz integral Fast Multipole Method time-domain

Cite

@article{arxiv.2607.15138,
  title  = {Translation of transient acoustic fields},
  author = {Michael J. Carley},
  journal= {arXiv preprint arXiv:2607.15138},
  year   = {2026}
}