Handling impedance surfaces in diffraction modeling

An edge-diffraction based method for computing the scattering from rigid convex 3D polyhedra, the "Edge Source Integral Equation" (ESIE), has previously been shown to give very accurate results and to be an efficient calculation method, in comparison with the boundary element method. Here, the ESIE method is used in a secondary source approach, referred to as "ESIE+SS", to compute the scattering from rigid convex objects with impedance boundary conditions at part of the surface. Secondary piston sources are introduced at the impedance surface and made to fulfill the boundary conditions. Expressions are presented for handling 2D scattering problems with the 3D ESIE method. The ESIE+SS method is evaluated by computing the 2D scattering from a 3 m by 0.2 m rigid box where a 0.3 m wide patch has a locally reacting impedance boundary condition that represents a 20 cm thick porous absorber. For a nearfield 2D point source and a circle of receivers, across the frequency range 50 Hz-2.5 kHz, the ESIE+SS computed the pressure within [ - 0.30,+0.32] dB of the reference FEM results for 90% of all the data points. Large errors were observed for some receiver positions, for the same reason as has been previously found for the ESIE method: a slow convergence for the higher-order diffraction computations. It was found that for the transfer functions that represent the interaction between the secondary sources, diffraction can typically be left out, which reduces the computational load.