The locally corrected Nyström method applied to 3D scalar SIE in acoustic cavities using curvilinear coordinates

In this work we make a comparison of the results obtained by the Locally Corrected Nyström method and a parametric method previously proposed by the authors to solve the scalar surface integral equation in order to determine the resonant modes in 3D acoustic cavities. Both methods are set up in basis of a parametric representation in curvilinear orthogonal coordinates. So, any geometry that involves quadrics or higher order surfaces can be considered. Different cavities whose modes can be analytically determined for the purpose of comparison of results are considered. It is found that for a spherical cavity it gives the proper results locating the modes as predicted analytically while for the cubical cavity, the Locally Corrected Nyström method gives some imprecision in the calculation of the modes despite using high order numerical quadrature, probably due to the presence of edges where derivatives of the basis vectors are not defined.