article
The application of integral equation methods to the numerical solution of some exterior boundary-value problems
Proceedings of the Royal Society of London A Mathematical and Physical Sciences · 1971 · Vol. 323(1553) · pp. 201–210
A.J. Burton✉(National Physical Laboratory)G. F. Miller(National Physical Laboratory)
Abstract
Abstract The application of integral equation methods to exterior boundary-value problems for Laplace’s equation and for the Helmholtz (or reduced wave) equation is discussed. In the latter case the straightforward formulation in terms of a single integral equation may give rise to difficulties of non-uniqueness; it is shown that uniqueness can be restored by deriving a second integral equation and suitably combining it with the first. Finally, an outline is given of methods for transforming the integral operators with strongly singular kernels which occur in the second equation.
Electromagnetic Scattering and AnalysisElectromagnetic Simulation and Numerical MethodsNumerical methods in engineeringIntegral equationMathematicsElectric-field integral equationHelmholtz equationSummation equationLaplace's equationMathematical analysisIntegro-differential equationUniquenessBoundary value problem
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1,185
FWCI
1.97
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11
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References
Improved Integral Formulation for Acoustic Radiation Problems
The Journal of the Acoustical Society of America · 1968 · 1,025 citations
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The application of integral equation methods to the numerical solution of some exterior boundary-value problems
Proceedings of the Royal Society of London A Mathematical and Physical Sciences · 1971 · 1,185 citations
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