Proceedings of the Royal Society of London A Mathematical and Physical Sciences · 1971 · 1.2K citations · 5 references
Natural SciencesMathematicsComputational MechanicsDifferential EquationsFluid DynamicsBoundary ConditionsBoundary-value ProblemsIntegral Equation FormulationsIntegral EquationsNumerical Methods For Differential EquationsPartial Differential EquationsBoundary Integral EquationsExterior Boundary Value ProblemsHelmholtz EquationIntegral Equation KernelsOperatorsSingular Integral EquationsSingular Integral Operators
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.
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