Low-Frequency Surface Integral Equation Solution by Multilevel Green's Function Interpolation With Fast Fourier Transform Acceleration

Abstract

A fast low-frequency solver for surface integral equations is presented. Multilevel Lagrange interpolation of the pertinent homogenous space Green's functions is employed for the factorization of the integral operators. For high computational efficiency, the resulting multilevel convolution/translation operators are diagonalized by fast Fourier transform. A fast adaptive multilevel scheme of the interpolation procedure makes the approach also suitable for broadband applications. The method is investigated for the solution of electric field and combined field integral equations. For the electric field integral equation, the dyadic and mixed-potential integral equation formulations are considered and discussed. Furthermore, the impact of extrapolation errors on the approximation accuracy of the respective Green's functions is analyzed. In several numerical examples, excellent efficiency with respect to computation time and memory requirements as well as good accuracy of the obtained results is demonstrated.