A variational principle for the scattered wave

D. E. Freund, R. A. Farrell

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


A Schwinger-type variational principle is presented for the scattered field in the case of scalar wave scattering with an arbitrary field incident on an object of arbitrary shape with homogeneous Dirichlet boundary conditions. The result is variationally invariant at field points ranging from the surface of the scatterer to the farfield and is an important extension of the usual Schwinger variational principle for the scattering amplitude, which is a farfield quantity. Also, a generic procedure, physically motivated by the general principles of boundary conditions and shadowing, is presented for constructing simple trial functions to approximate the fields. The variational principle and the trial function design are tested for the special case of a spherical scatterer and accurate answers are found over the entire frequency range.

Original languageEnglish (US)
Pages (from-to)1847-1860
Number of pages14
JournalJournal of the Acoustical Society of America
Issue number5
StatePublished - May 1990
Externally publishedYes

ASJC Scopus subject areas

  • Arts and Humanities (miscellaneous)
  • Acoustics and Ultrasonics


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