A mixed-order stabilized bi-conjugate gradient FFT method for magnetodielectric objects

Magnetodielectric materials have many emerging applications, but their scattering problems are challenging for volume integral equation solvers. In this paper, a mixed-order stabilized bi-conjugate gradient FFT (mixed-order BCGS-FFT) method for solving the scattering problem of magnetodielectric objects is presented. This method uses the volumetric roof-top basis functions as testing functions for the coupled field volume integral equation (CFVIE) and basis functions for the electric and magnetic flux densities (D,B). However, unlike the conventional weak form BCGS-FFT methods for dielectric objects, the mixed-order BCGS-FFT method uses the second-order curl conforming basis functions for the electric and magnetic vector potentials (F,A). The curl conforming basis functions preserve the continuity of the tangential components for F and A, while the use of second-order basis functions avoids the zero terms caused by the divergence operations on the vector potentials. Numerical examples show excellent performance of the mixed-order BCGS-FFT method over the currently available BCGS-FFT method as well as high accuracy of the mixed-order BCGS-FFT method on large contrast magnetodielectric scatterers.