Unit Cube Test for Double Surface Integrals in Frequency Domain Integral Equation Formulations

The numerical solution of the frequency domain integral equation based formulations require the solution of various double surface integrals. The evaluation of such integrals depends on the distance between the source and observation points, respectively. Many typical integrals can be solved using a numerical integration or a combination of numerical and analytical approach. The paper is on the unit cube test developed for testing various combinations of double surface integrals. Several combinations of source and observation triangles are considered including the far term and near terms, respectively. The numerical solution of integral is facilitated by Gaussian quadrature utilizing the Dunavant's rules for triangles. The extensive tests are carried out to investigate the solution convergence with respect to the increasing frequency and the various utilized discretization schemes.