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Electromagnetic diffraction modelling and recent numerical simulation approaches, on the canonical 2D non-penetrable wedge scattering problem, are reviewed in this introduction paper.

The Error Cross-Section (ECS) is introduced to quantify the error associated with the numerical solution of electromagnetic scattering problems. The ECS accounts for different approximations and inaccuracies in the object discretization and numerical computations. The ECS definition is based on the power conservation principle and is visualized by comparing it to the radar cross-section of a thin wire for twodimensional (2-D) problems or a small sphere for three-dimensional (3-D) problems. The proposed ECS method is independent of the adopted numerical technique and therefore can be used to give confidence in the obtained solution using several methods, such as the Method of Moments (MoM) and the Finite-Difference FrequencyDomain (FDFD) method. Application of the ECS to the optimization of certain parameters for some numerical formulations, such as the CombinedField Integral Equation (CFIE) is also presented.

Two finite difference time-domain (FDTD) scattered-field formulations for chiral objects are developed and presented in this paper. The first formulation provides single frequency results, while the second formulation provides multi frequency results from one FDTD simulation. Both formulations are developed for three dimensional electromagnetic applications. Numerical results from the single frequency formulation is presented for the scattering from a chiral sphere. In the multi-frequency formulation, the evaluation of both the electric and magnetic field values at every half-time step, unlike the conventional leap-frog algorithm, is needed to minimize the memory size required to store past values of the field components. Results of this formulation are presented for the co-polarization and cross-polarization of the reflected and transmitted waves from a chiral slab due to normal incidence of a plane wave and for the scattered field from a chiral sphere. Validation is performed by comparing the results with those based on the exact solution.

As an alternative to the finitedifference time-domain (FDTD), the finiteelement method (FEM), and the method of moments (MoM) based on the surface integral equation (SIE), a volume-integral equation (VIE) approach using the method of moments and conjugate-gradient methods is presented to address a wide variety of complex problems in computational electromagnetics. A formulation of the volume integral method is presented to efficiently address inhomogeneous regions in multi-layered media. Since volume element discretization is limited to local inhomogeneous regions, numerical solutions for many complex problems can be achieved more efficiently than FDTD, FEM, and MoM/SIE. This is the first of a series of papers dealing with volume-integral equations; in subsequent papers of this series we will apply volume-integrals to problems in the field on nondestructive evaluation.

A novel three-dimensional hybrid Finite Element Method (FEM) and Physical Optics (PO) technique for the efficient analysis of scattering problems is presented. It makes use of FEM for the regions with small and complex features and PO for the analysis of the electrically large objects of the structure taking into account mutual interactions between the FEM domains and the objects analyzed with PO. The hybrid method proposed makes use of an iterative FEM for open region problems that allows the FEM domain to be truncated with a minimum number of unknowns while retaining the original sparse and banded structure of the FEM matrices, and also an easy hybridization with other numerical techniques (as PO in this paper). Several numerical results are given showing some of the features of the method.

A review of the past 25 years of progress and future challenges in the higher order computational electromagnetics (CEM) is presented. Higher order CEM techniques use current/field basis functions of higher orders defined on large (e.g., on the order of a wavelength in each dimension) curvilinear geometrical elements, which greatly reduces the number of unknowns for a given problem. The paper reviews and discusses generalized curved parametric quadrilateral, triangular, hexahedral, and tetrahedral elements and various types of higher order hierarchical and interpolatory vector basis functions, in both divergence- and curl-conforming arrangements, within the available and emerging higher order CEM methods and codes.

In this paper, we present the analysis of electromagnetic scattering from arbitrarily shaped three-dimensional (3-D) conducting objects coated with dielectric materials. The integral equation treated here is the combined field integral equation (CFIE). The objectives of this paper is to illustrate that only the CFIE formulation is a valid methodology in removing defects, which occur at a frequency corresponding to an internal resonance of the structure. Numerical results of radar cross sections (RCS) for coated conducting structures are presented and compared with other available solutions.