Accuracy aspects for diffraction-based computation of scattering

Abstract

Edge-diffraction based modeling, in the form of the Edge Source Integral Equation (ESIE), [J. Acoust. Soc. Am. 133, pp. 3681-3691, 2013], has proven efficient and accurate for radiation problems such as modeling loudspeakers in convex-shaped rigid enclosures. Some singularity issues have been identified for certain source/receiver positions, and the problem as regards receiver positions can be avoided through a recently suggested hybrid technique [Proc. Meet. of Acoustics. 26, 015001, 2016]. The hybrid technique uses the edge-diffraction formulation to find the sound pressure at the surface of the scatterer, and employs the Kirchhoff-Helmholtz Integral Equation to propagate the surface sound pressure to external receiver points. For these techniques mentioned above, computed results are assumed to converge towards a correct result, and one usually has to use the finest mesh that is computable with the available resources. Such a single computation does, however, not directly indicate the accuracy of the result, but by employing computations for several mesh sizes, a Taylor expansion model of the computation error can offer the possibility for a Richardson extrapolation as a convergence acceleration technique. This technique is well-known for some computation techniques but possibly not so widely known. Here, this technique will be demonstrated for some particularly challenging cases of computing far-field backscattering at low frequencies from compact scatterers with the ESIE method, as well as some other challenging geometries. Pronounced cancellation effects between first- and higher-order diffraction components lead to very high accuracy requirements for the computations, and convergence acceleration turns out to be highly effective. [Portions of this material are based upon work supported by the Office of Naval Research under Contract No. N68335- 17-C-0336; the Research Council of Norway, project no. 240278; and the ERCIM Alain Bensoussan Fellowship Programme].