Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods

Abstract

[1] In this paper, formulation of the surface integral equations for solving electromagnetic scattering by dielectric and composite metallic and dielectric objects with iterative methods is studied. Four types of formulations are considered: T formulations, N formulations, the combined field integral equation formulation, and the Müller formulation. By studying properties of the integral equations and their testing in the Galerkin method, ''optimal'' forms for each formulation type are derived. Numerical examples demonstrate that the developed new formulations lead to clear improvements in the convergence rates when the matrix equations are solved iteratively with the generalized minimal residual method. Both the Rao-Wilton-Glisson and Trintinalia-Ling (TL) basis functions are used in expanding the unknown electric and magnetic surface current densities. In particular, the first-order TL basis functions are required in the N formulations to maintain the solution accuracy when the surfaces include sharp edges.Citation: Ylä-Oijala, P., M. Taskinen, and S. Järvenpää (2005), Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods, Radio Sci., 40, RS6002,

SQUEEZING MAXWELL'S EQUATIONS INTO THE NANOSCALE (Invited Paper)

“…Among the infinitely many possibilities, we fulfill the procedure of [42], which has proven to render a set of stable and well-conditioned equations. Let us denote with S ij (or S ji ) the interface between two homogeneous regions R i and R j .…”

Analysis of photonic-crystal problems with MLFMA and approximate Schur preconditioners

“…Among many choices, CTF and JMCFIE are usually most suitable formulations in terms of accuracy and efficiency [7]. CTF is a modified and more stable version of the well-known Poggio-MillerChang-Harrington-Wu-Tsai (PMCHWT) formulation [3]. This formulation is practically a first-kind integral equation, and it produces ill-conditioned matrix equations without preconditioning.…”

“…1. Problems are formulated with the combined tangential formulation (CTF) [3] and the electric and magnetic current combined-field integral equation (JM-CFIE) [4], discretized with the Rao-Wilton-Glisson (RWG) functions [5]. Matrix equations are solved iteratively using the multilevel fast multipole algorithm (MLFMA) [6], and iterative solutions are accelerated via novel approximate Schur preconditioners (ASPs).…”

Numerical Analysis of Combined Field Integral Equation Formulations for Electromagnetic Scattering by Dielectric and Composite Objects

“…These equations are obtained by taking the tangential components of the surface integral representations of the total electric and magnetic fields on the surface S. N-EFIE i , N-EFIE e , N-MFIE i and N-MFIE e are the corresponding surface integral equations obtained by operating with n e × and n i × to the surface integral representations on S. More details on the derivation of these equations is presented in [13].…”

“…The permittivity of the object, a parameter that does not appear in the PEC case, has a significant effect on the properties of the formulations [12][13][14][15][16][17]. In many cases the JM-CFIE formulation has been found to be the most robust one, i.e., its properties are less dependent on the material contrast, frequency and other parameters, in particular, as the complexity or the size of the problem increases [13,18].…”