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Description
Green’s functions for edge diffraction are often used in analytical modeling of installed jet-noise or trailing edge noise. A new formulation of the exact Green’s function for the problem of diffraction of a point source by a rigid wedge of infinite and finite length is derived. The derivation is based on a variable change in the diffraction integral of the exact Green’s function. The transformation recasts the integral into a Riemann Stieltjes form, with the integration performed over a normalized edge length parameter ranging from 0 to 1 (corresponding to the actual edge length from minus infinity to infinity). For wedges of finite length, the limits of integration match the limits of the finite edge.The new formulation offers two key advantages over existing approaches:i) The singularity of the integrand that exists in all formulations of the exact Green’s function is handled automatically without requiring special techniques such as local analytical approximations or increased number of quadrature points. The new formulation acts as adaptive sampling, focusing on the singular area, which in turn improves computational efficiency. ii) The new Riemann Stieltjes form allows the use of a simple quadrature formula without sacrificing accuracy across all frequencies and source-receiver configurations.When compared to the state-of-the-art exact integral formulation, the new method is substantially faster for all wedge angles, all frequencies and all source-receiver configurations. Compared to an approximate method restricted to high frequencies, the new approach is slower but still computationally competitive.