Accession Number:

ADA088747

Title:

Application of Non-Self-Adjoint Operator Theory to the Singularity Expansion Method (SEM) and the Eigenmode Expansion Method (EEM) in Acoustic and Electromagnetic Problems.

Descriptive Note:

Final rept. 1 Jun 79-31 May 80,

Corporate Author:

MICHIGAN UNIV ANN ARBOR DEPT OF MATHEMATICS

Personal Author(s):

Report Date:

1980-07-01

Pagination or Media Count:

23.0

Abstract:

Eigenfunction expansions for nonselfadjoint operators are important for scalar and electromagnetic wave scattering. Two methods the Singularity Expansion Method SEM, and the Eigenmode Expansion Method EEM which had been developed separately were studied. Criteria for their validity were established moreover, the poles of the Greens function of the SEM are in 1-1 correspondence with the zeros of the eigenvalues of the EEM. A constructive numerical process for determining the poles of the Greens function was developed. Among several other results was the establishment of variational principles for the spectrum of compact nonselfadjoint operators. Another research area was the singularity behavior of eigenfunction expansions of various Greens functions in electromagnetic theory. The principal result shows that in an eigenfunction of a typical Greens function the point singularity of a Greens function is represented by a layer of surface singularity. This characteristic is analogous to the Gibbs phenomenon where the representation of a discontinuous function by an orthogonal expansion creates the spikes which are absent in the original function. Author

Subject Categories:

  • Theoretical Mathematics
  • Acoustics
  • Electricity and Magnetism

Distribution Statement:

APPROVED FOR PUBLIC RELEASE