A mesh-free approach to acoustic scattering from multiple spheres nested inside a large sphere by using diagonal translation operators

Andrew J. Hesford, Jeffrey P. Astheimer, Leslie Greengard, Robert C. Waag

Research output: Contribution to journalArticle


A multiple-scattering approach is presented to compute the solution of the Helmholtz equation when a number of spherical scatterers are nested in the interior of an acoustically large enclosing sphere. The solution is represented in terms of partial-wave expansions, and a linear system of equations is derived to enforce continuity of pressure and normal particle velocity across all material interfaces. This approach yields high-order accuracy and avoids some of the difficulties encountered when using integral equations that apply to surfaces of arbitrary shape. Calculations are accelerated by using diagonal translation operators to compute the interactions between spheres when the operators are numerically stable. Numerical results are presented to demonstrate the accuracy and efficiency of the method.

Original languageEnglish (US)
Pages (from-to)850-861
Number of pages12
JournalJournal of the Acoustical Society of America
Issue number2
Publication statusPublished - 2010


ASJC Scopus subject areas

  • Acoustics and Ultrasonics

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