Operator Valued Functions and Boundary Value Problems for the Helmholtz Equation I. Spherical Geometries.

Abstract

The boundary integral operator which arises in a double layer formulation of the Neumann problem for the Helmholtz equation is analyzed as an operator valued function of wave number in the particular case of a spherical boundary. The spectrum of the operator is found and its explicit dependence on wave number is exhibited, both analytically and numerically. In addition, the explicit polar decomposition of the operator is carried out and it is shown that asymptotically the operator becomes selfadjoint for small values of wave numbers and unitary for large values. Advantages of operator factorization are discussed. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1978
Accession Number
ADA062685

Entities

People

  • G. F. Roach
  • R. E. Kleinman

Organizations

  • University of Delaware

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Air Force
  • Applied Mathematics
  • Boundaries
  • Boundary Value Problems
  • Differential Equations
  • Eigenvalues
  • Equations
  • Formulas (Mathematics)
  • Geometry
  • Helmholtz Equations
  • Identities
  • Integral Equations
  • Integrals
  • Mathematics
  • Numbers
  • Partial Differential Equations
  • Spherical Harmonics

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra