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On the derivation of the Green’s function for the Helmholtz equation using generalized functions
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2010
Year
Numerical AnalysisHelmholtz EquationMethod Of Fundamental SolutionBoundary ConditionsGeometric Partial Differential EquationGeneralized FunctionFree Boundary ProblemPotential TheoryGreen ’Free Space SubjectBoundary Element MethodGeneralized FunctionsSommerfeld Radiation ConditionsNumerical Method For Partial Differential Equation
A method for constructing the Green’s function for the Helmholtz equation in free space subject to Sommerfeld radiation conditions is presented. Unlike the methods found in many textbooks, the present technique allows us to obtain all of the possible Green’s functions before selecting the one that satisfies the choice of boundary conditions.