On modified Green functions in exterior problems for the Helmholtz equation
- 8 October 1982
- journal article
- Published by The Royal Society in Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- Vol. 383 (1785) , 313-332
- https://doi.org/10.1098/rspa.1982.0133
Abstract
The question of non-uniqueness in boundary integral equation formulations of exterior problems for the Helmholtz equation has recently been resolved with the use of additional radiating multipoles in the definition of the Green function. The present note shows how this modification may be included in a rigorous formalism and presents an explicit choice of coefficients of the added terms that is optimal in the sense of minimizing the least-squares difference between the modified and exact Green functions.Keywords
This publication has 5 references indexed in Scilit:
- Boundary integral equations for the Helmholtz equation: The third boundary value problemMathematical Methods in the Applied Sciences, 1982
- Integral Operators in Potential TheoryLecture Notes in Mathematics, 1980
- Boundary Integral Equations for the Three-Dimensional Helmholtz EquationSIAM Review, 1974
- Approximate Green's functions and the solution of related integral equationsArchive for Rational Mechanics and Analysis, 1970
- On the approximate solution of elliptic, self adjoint boundary value problemsArchive for Rational Mechanics and Analysis, 1967