On Modified Green's Functions in Exterior Problems for the Helmholtz Equation.
Abstract
Recently, Jones has presented a method for overcoming the non uniqueness problem arising in boundary integral equation formulation of the Dirichlet and Neumann problems for the Helmholtz equation. The major portion of Jones' analysis concerned the exterior Neumann problem in two dimensions although he indicated how the results generalized to three dimensions and suggested that the exterior Dirichlet problem could be similarly treated. Ursell simplified the proof of a key theorem, but confined his remarks to the exterior Neumann problem in two dimensions. The authors presented a systematic exposition of boundary integral equation formulations of both Dirichlet and Neumann problems and presented a number of useful properties of the boundary integral operators arising in both layer theoretic and Green's function approaches. In particular, it was shown that uniqueness of the boundary integral equation formulations of exterior problems could be retained even at eigenvalues of the corresponding adjoint interior problems by treating a pair of coupled equations. That treatment dealt with three dimensional problems although the results remain intact when the fundamental solution of the Helmhotz equation in n dimensions is used.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1981
- Accession Number
- ADA111089
Entities
People
- G. F. Roach
- R. E. Kleinman
Organizations
- University of Delaware