Computation of electromagnetic fields inside strongly inhomogeneous objects by the weak-conjugate-gradient fast-Fourier-transform method

Abstract

The computation of the electromagnetic field inside a strongly inhomogeneous dielectric object is formulated in terms of a domain-integral equation over the object. We discuss a weak form of the integral equation in which the spatial derivatives are integrated analytically. Doing so, we obtain an equation that is solved efficiently with the advantageous combination of a conjugate-gradient iterative method and a fast-Fourier-transform technique. Numerical computations are performed for a strongly inhomogeneous lossy sphere. For this case we compare the accuracy and the efficiency of the present method with the analytic solution based on the Mie series and the finite-difference time-domain approach. To show that the method is also capable of computing more-complex scattering problems, we assume the incident field to be generated by a (1/2)λ thin-wire dipole. In this case the absorbed power density is presented. All these test cases demonstrate that the weak form of the conjugate-gradient fast-Fourier-transform method can be considered as a comparatively simple and efficient tool for solving realistic electromagnetic wave-field problems.