The BCGS-FFT method for electromagnetic scattering from inhomogeneous objects of arbitrary shape embedded in a planarly layered medium

The following novel and unique approaches taken in the stabilized biconjugate fast Fourier transform method (BCGS-FFT) contribute to an accurate and efficient solver in terms of CPU time and RAM requirements.; First, the volume electric field integral equation (EFIE) is chosen to model the physics of electromagnetic scattering from inhomogeneous objects in planarly layered media. The volume EFIE formulation is more suitable to scattering from inhomogeneous objects than the surface EFIE.; Secondly, the "weak-form" discretization procedure is developed to reduce the singularity of the discrete EFIE. Instead of expanding only the unknown in terms of basis functions in MoM and many other numerical methods, a two-level expansion of the unknown and an immediate variable (proportional to the magnetic vector potential) in terms of the basis functions is used to obtain the discrete EFIE.; Thirdly, the BCGS-FFT method, which is a fast Krylov subspace iterative solver---the stabilized bi-conjugate gradient method (Bi-CGSTAB or BCGS for short)---combined with the fast Fourier transform (FFT), is developed to solve the discrete volume EFIE. The Bi-CGSTAB iterative solver is chosen from the Krylov subspace solvers such as the conjugate gradient (CG), biconjugate gradient (BiCG), conjugate gradient square (CGS) and quasi-minimum residual (QMR) for its fastest (compared to CG, BiCG, CGS, QMR) and more smoothly (compared to BiCG, CGS) convergence.; Fourthly, two techniques are used to speed up the computation of the dyadic Green's function for planarly layered media. The dyadic Green's function has a closed-form solution in spectral domain, but not in spatial domain. It can be a bottleneck for numerical methods in layered media. One technique is that the direct term in the Green's function (the same as the Green's function for a homogeneous background) is extracted from the Green's function in the spectral domain by using its spatial form directly. This removes the singularity for the Green's function in spectral domain.; Last but not least, the fast solver is fully validated by comparison to analytical solutions and other independent numerical methods. Applications in near- and far-field applications are explored extensively. The applications show that the BCGS-FFT method is capable of solving large-scale scattering problems from inhomogeneous objects in a planarly layered background. The BCGS-FFT method solved scattering problems with several million unknowns on a single CPU workstation with 1.2 GB memory. With multiple processors, this method is expected to solve even larger problems. (Abstract shortened by UMI.)...