A fast combined field volume integral equation solution to EM scattering by 3-d dielectric objects of arbitrary permittivity and permeability

A fast solution to the combined field volume integral equation (CFVIE) for electromagnetic scattering by large three-dimensional dielectric bodies of arbitrary permittivity and permeability is presented. The CFVIE is formulated in the region of the scatterers by expressing the total fields as the sum of the incident wave and the radiated wave due to both the electric and magnetic polarization currents. The resultant integral equation is solved using the method of moments (MoM). Then the precorrected fast Fourier transform (P-FFT) method is applied to reduce the memory requirement and accelerate the matrix-vector multiplication in the MoM solution. In the implementation of the P-FFT method, two sets of projection operators are constructed respectively for the projections of the electric sources and magnetic sources. In addition, two sets of interpolation operators are also applied respectively for the computation of the vector/scalar potentials and the curl of the vector potentials in the support of the testing functions. The resultant method has a memory requirement of O (N) and a computational complexity of O (N log N) respectively, where N denotes the number of unknowns.