The method of moments (MoM) solution of combined field integral equation (CFIE) for electromagnetic scattering problems requires calculation of singular double surface integrals. When Galerkin's method with triangular vector basis functions, Rao-Wilton-Glisson functions, and the CFIE are applied to solve electromagnetic scattering by a dielectric object, both RWG and n/spl times/RWG functions (n is normal unit vector) should be considered as testing functions. Robust and accurate methods based on the singularity extraction technique are presented to evaluate the impedance matrix elements of the CFIE with these basis and test functions. In computing the impedance matrix elements, including the gradient of the Green's function, we can avoid the logarithmic singularity on the outer testing integral by modifying the integrand. In the developed method, all singularities are extracted and calculated in closed form and numerical integration is applied only for regular functions. In addition, we present compact iterative formulas for computing the extracted terms in closed form. By these formulas, we can extract any number of terms from the singular kernels of CFIE formulations with RWG and n/spl times/RWG functions.

Calculation of CFIE impedance matrix elements with RWG and n/spl times/RWG functions

Among the most popular approaches used for simulating plasmonic systems, the discrete dipole approximation suffers from poorly scaling volume discretization and limited near-field accuracy. We demonstrate that transformation to a surface integral formulation improves scalability and convergence and provides a flexible geometric approximation allowing, e.g., to investigate the influence of fabrication accuracy. The occurring integrals can be solved quasi-analytically, permitting even rapidly changing fields to be determined arbitrarily close to a scatterer. This insight into the extreme near-field behavior is useful for modeling closely packed particle ensembles and to study "hot spots" in plasmonic nanostructures used for plasmon-enhanced Raman scattering.

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Surface integral formulation for 3D simulations of plasmonic and high permittivity nanostructures

Combined field integral equation (CFIE) is applied for computing electromagnetic scattering by arbitrarily shaped three dimensional dielectric and composite objects. The objectives of this paper are as follows. First, to present a CFIE formulation which can be used in the analysis of piecewise dielectric and composite metallic and dielectric objects with junctions. Second, to show that properly choosing the coupling coefficients of the equations the conditioning of the discretized matrix equation can be essentially improved and rapidly converging iterative solutions can be obtained even without preconditioning.

Application of combined field Integral equation for electromagnetic scattering by dielectric and composite objects

Extensions of finite-difference time-domain (FDTD) and finite-element time-domain (FETD) algorithms are reviewed for solving transient Maxwell equations in complex media. Also provided are a few representative examples to illustrate the modeling capabilities of FDTD and FETD for complex media. The term complex media refers here to media with dispersive, (bi)anisotropic, inhomogeneous, and/or nonlinear properties present in the constitutive tensors.

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Time-Domain Finite-Difference and Finite-Element Methods for Maxwell Equations in Complex Media

Numerical solution of electromagnetic scattering by homogeneous dielectric objects with the method of moments (MoM) and Rao-Wilton-Glisson (RWG) basis functions is discussed. It is shown that the low-frequency breakdown associated to the MoM solution of scattering by dielectric objects can be avoided by the classical Muller formulation without the loop-tree or loop-star basis functions. Two variations of the Muller formulation, T-Mu/spl uml/ller and N-Muller, are considered. It is demonstrated that only the N-Muller formulation with the Galerkin method and RWG functions gives stable solution. Discretization of the N-Muller formulation leads to a well-conditioned matrix equation and rapidly converging iterative solutions on a wide frequency range from very low frequencies to microwave frequencies. At zero frequency, the N-Muller formulation decouples into the electrostatic and magnetostatic integral equations.

Well-conditioned Muller formulation for electromagnetic scattering by dielectric objects

We present an accurate method of moments (MoM) solution of the combined field integral equation (CFIE) using the multilevel fast multipole algorithm (MLFMA) for scattering by large, three-dimensional (3-D), arbitrarily shaped, homogeneous objects. We first investigate several different MoM formulations of the CFIE and propose a new formulation, which is both accurate and free of interior resonances. We then employ the MLFMA to significantly reduce the memory requirement and computational complexity of the MoM solution. Numerical results are presented to demonstrate the accuracy and capability of the proposed method. The method can be extended in a straightforward manner to scatterers composed of different homogeneous dielectric and conducting objects.

Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies

Experimental Results of the Y-junction microstrip circulator with a ferrite sphere have been reported in the literature. In this paper, the finite difference time domain (FDTD) method is used to analyze this kind of circulator. Comparisons between the experimental results and our numerical results confirm the validity of our program. The profiles of the power-density flow inside the ferrite sphere are given and the effects of circulator parameters on circulation characteristics are investigated to further understand the performance of the circulator with a ferrite sphere.

Fdtd analysis of y-junction microstrip circulator with a ferrite sphere

A simple finite difference time domain (FDTD) scheme for chiral media is developed for modeling the chiral discontinuities in the waveguide with the aid of the second-order backward finite difference. The accuracy of the FDTD scheme is demonstrated by the comparison between our calculated results and those in the literature for achiral and chiral media. Comparisons of characteristics between chiral and achiral discontinuities in the waveguide are presented at last.

Three-Dimensional FDTD Analysis of Chiral Discontinuities in the Waveguide

An approach is developed for 3D microstrip discontinuities using the finite element method (FEM) and the perfectly matched layers (PML). It is shown that iterative solvers are not suitable for this problem since the matrix equations from the PML-used FEM modeling are rather ill-conditioned and lead to a very slow or nonconvergent result. A newly developed package SuperLU of the sparse LU decomposition solver is incorporated into our developed approach running on a PC-based parallel platform. Various implementation techniques are detailed. Numerical experiments clearly show that the developed approach is reliable, efficient, and suitable for modeling 3D microstrip discontinuities. © 2001 John Wiley & Sons, Inc. Int J RF and Microwave CAE 11: 38–47, 2001

Parallel electromagnetic modeling of 3D microstrip discontinuities using FEM and PML

A new approach is proposed to reduce the reflection error () of a perfectly matched layer PML in the frequency-domain finite- element solution of electromagnetics problems. The approach is based on the complementary nature of a PML backed by a perfect electric conduc- () ( ) tor PEC and one backed by a perfect magnetic conductor PMC . By aeraging the solutions obtained by PEC- and PMC-backed PML, the << error is reduced by 20 log R dB, where R is the reflection coefficient of the PEC- or PMC-backed PML. Numerical results are presented to demonstrate the accuracy of the complementary PMLs. Q 1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett 14: 284)287, 1997.

X. Q. Sheng

Papers

Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies

Fdtd analysis of y-junction microstrip circulator with a ferrite sphere

Three-Dimensional FDTD Analysis of Chiral Discontinuities in the Waveguide

Parallel electromagnetic modeling of 3D microstrip discontinuities using FEM and PML

Complementary perfectly matched layers to reduce reflection errors