Boundary Integral Equations for the Helmholtz Equation: The Third Boundary Value Problem.

Abstract

The third boundary value problem, or Robin problem, for the Helmholtz equation in an exterior domain in R3 may be cast with Green's theorem, as a boundary integral equation. This equation is not equivalent to the original problem because it has eigenvalues at wave numbers for which the exterior problem is soluble. However, a second boundary equation is derived and it is shown that the pair is equivalent to the original boundary value problem.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1980
Accession Number
ADA089921

Entities

People

  • R. E. Kleinman
  • T. S. Angell

Organizations

  • University of Delaware

Tags

Communities of Interest

  • C4I
  • Counter WMD

DTIC Thesaurus Topics

  • Applied Mathematics
  • Boundaries
  • Boundary Value Problems
  • Cartesian Coordinates
  • Classification
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Helmholtz Equations
  • Inequalities
  • Integral Equations
  • Integrals
  • Mathematics
  • Security
  • Three Dimensional
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)