A multi-resolution 4-D FFT approach to parametric boundary Integral Equations for helical structures

This paper gives a report of an ongoing research to develop parametric boundary integral equations for helical structures and their application in the computation of induced currents and losses in three-phase power cables. The proposed technique is formulated in terms of the Electric Field Integral Equation (EFIE) or the Magnetic Field Integral Equation (MFIE) for a penetrable object together with the appropriate periodic Green's functions and a suitable parameterization of the helical structure. A simple and efficient numerical scheme is proposed for the computation of the impedance matrix in the Method of Moments (MoM) which is based on a multi-resolution 4-D FFT computation followed by polynomial extrapolation. Numerical examples are included demonstrating that the singular integrals have almost linear convergence and hence that linear or quadratic extrapolation can be used to yield accurate results.