Perfect Electric Conductor Objects Research Articles

An MLFMA-Based Eigenmode Theory for Electromagnetic Scattering Analysis From Electrically Large and Complex Conducting Objects

The eigenmode theory, which uses the modal currents solved from surface differential equations (SDEs) as the basis functions of the method of moment (MoM), has been applied to the analysis of electromagnetic scattering and radiation problems of electrically small and simple perfect electrically conducting (PEC) objects. In this article, a multilevel fast multipole algorithm (MLFMA)-based eigenmode theory is presented for analyzing electromagnetic scattering from electrically large and complex PEC objects. The method applies the MLFMA to accelerate the matrix-vector multiplications involved in filling the dense impedance matrix and therefore is much more efficient than the conventional eigenmode theory, especially for electrically large objects. Meanwhile, the way to determine a priori the number of the required modal currents for arbitrarily shaped objects is presented, which makes the MLFMA-based eigenmode theory applicable to the scattering analysis from complex objects. Numerical results verify the accuracy and efficiency of the proposed method.

Characteristic Mode Formulations of Composite PEC and Lossy Dielectric Objects

Lossy dielectric substrate affects the performance of a nearby perfect electric conductor (PEC) antenna. This letter presents a set of formulae for characteristic mode analysis (CMA) of composite PEC and lossy dielectric objects. It is based on the volume-surface integral equation and substructure treatment that separates the radiation and dissipation powers of the composite structure. A narrow PEC plate (that represents a dipole antenna) is placed in proximity of a thick, lossy dielectric material, and CMA of this structure is presented as an example. The separation gap between the PEC and dielectric objects affects the resonance and radiation efficiency of the antenna, and it is shown that CMA accurately captures those effects. The influence of dielectric loss on the modal orthogonality is discussed. Since the PEC item dominates over the coupling one in the substructure operator, the computed modes maintain good orthogonality with low-loss dielectrics. Owing to the physical insights of CMA, it has many potential applications associated with lossy materials.

On the Use of Hybrid CFIE–EFIE for Objects Containing Closed–Open Surface Junctions

To effectively solve the electromagnetic scattering or radiation properties from the perfect electric conductor objects containing closed-open surface junctions, how to establish the hybrid combined field integral equation-electric field integral equation (CFIE-EFIE) is studied, which is different from the existing scheme for the objects, where the closed and open parts are separate. Furthermore, it is found that when the integral equation is solved using the method of moments, if the widely used RWG basis functions are employed to expand the induced surface current, the CFIE-EFIE may give inaccurate numerical results for the objects containing fine structures. The numerical accuracy can be improved by introducing the linear-linear (LL) basis functions. Moreover, to pursue a high computational efficiency, the LL and RWG basis functions are simultaneously used to expand the current on the fine structures and other relatively smooth surfaces, respectively, whose validity is verified by the numerical results.

A well‐conditioned integral equation for electromagnetic scattering from composite inhomogeneous bi‐anisotropic material and closed perfect electric conductor objects

A well-conditioned volume-surface integral equation, called the volume integral equation-combined field integral equation, is applied to analyse electromagnetic (EM) scattering from arbitrarily shaped three-dimensional composite objects comprising both inhomogeneous bi-anisotropic material and closed perfect electric conductors (PECs). The equivalent surface and volume currents are respectively expanded using the commonly used RWG and SWG basis functions, while a matrix equation is derived by the method of moments. Because the magnetic field integral equation is involved in modelling the surface electric current, and the constitutive parameters are all tensors, some new kinds of singularities are encountered and properly handled in the filling process of the impedance matrix. Several numerical results of EM scattering from composite bi-anisotropy and closed PEC objects are shown to illustrate the accuracy and efficiency of the proposed scheme. The validity of the continuity condition of electric flux enforced on the bi-anisotropy-PEC interfaces, which can be used to eliminate the volumetric electric unknowns, is also verified.

Accelerated Sherman–Morrison–Woodbury Formula-Based Preconditioner With Characteristic Basis Function Method

Based on the Sherman–Morrison–Woodbury (SMW) formula and the characteristic basis function method (CBFM) in the iterative solution of the electric field integral equation, a fast preconditioner algorithm is proposed in this letter. The SMW preconditioner is an improved version of the conventional block diagonal preconditioner and can be constructed as a sparse approximate inverse matrix of the impedance matrix to reduce the number of iterations. The CBFM is applied to reduce the storage costs of the compressed impedance and the preconditioner. The reduced preconditioner can efficiently accelerate the matrix-vector product. For validation, the numerical results of several perfect electric conductor objects are obtained to demonstrate the performance of the iterative solution time and the memory requirement of the preconditioner.

A novel approach for electromagnetic inverse scattering of a two‐dimensional perfect electric conductor object

A two-dimensional shape determination technique for a perfect electric conductor target using electromagnetic inverse scattering is presented. The proposed algorithm uses the scattered field pattern and an inverse scattering technique derived from Green's function to retrieve the geometry of an unknown target. This method uses the scattering field data over a band of observation points, which is synthesized using frequency domain “method of moment” computational technique. We have verified this algorithm with four different types of numerical examples.

On the Volume-Surface Integral Equation for Scattering From Arbitrary Shaped Composite PEC and Inhomogeneous Bi-Isotropic Objects

A new generalized volume-surface integral equation, volume integral equation-combined field integral equation (VIE-CFIE), is proposed to analyze the electromagnetic (EM) scattering from composite objects comprised of both perfect electric conductor (PEC) and inhomogeneous bi-isotropic material. By discretizing the objects using triangular and tetrahedral cells on which the commonly used Rao-Wilton-Glisson (RWG) and Schaubert-Wilton-Glisson (SWG) basis functions are respectively defined, the matrix equation is derived using the method of moments (MoM) and the Galerkin’s testing. Furthermore, the continuity condition (CC) of electric flux is explicitly enforced on the PEC and bi-isotropy interfaces. In this way, the number of volumetric unknowns is reduced based on the same set of meshes, particularly for the thin coated PEC objects. A convenient way to embed the CC into the context of MoM solution is provided in detail. Several numerical results of EM scattering from coated PEC objects are shown to illustrate the accuracy and efficiency of the proposed method.

Discontinuous Galerkin Method Using Laguerre Polynomials for Solving a Time-Domain Electric Field Integral Equation

A discontinuous Galerkin time-domain electric field integral equation method based on a marching-on-in-degree (MOD) scheme for simulating transient responses of perfect electric conductor objects is proposed in this letter. With the help of half-Rao–Wilton–Glisson spatial basis functions, we can simulate transient scattering responses of three-dimensional structures with either conformal or nonconformal meshes. The weighted Laguerre polynomials are chosen as temporal basis functions and implemented for the MOD scheme. Under such circumstances, the developed algorithm eliminates late-time instabilities and the limitation of Courant–Friedrichs–Lewy criteria. In addition, we adopt a fast-Fourier-transform-based blocking scheme to accelerate the temporal convolution of the MOD procedure. Some numerical examples are given to validate its stability and accuracy.

A Nonconformal Surface Integral Equation for Electromagnetic Scattering by Multiscale Conducting Objects

We present a nonconformal surface integral equation method for the analysis of time-harmonic electromagnetic scattering by multiscale perfect electrically conducting (PEC) objects. To alleviate the burden of geometrical processing, a mixed triangle/quadrilateral mesh with arbitrary nonconformity is adopted in this method. A vectorial piecewise constant basis function is defined over the unstructured mesh as the trial and test functions. The recently developed reverse operation self-consistent evaluation approach is employed to evaluate the hypersingular integrals. Due to the utilization of this locally defined basis function, the function space is enlarged from the commonly used div-conforming space to the square-integrable counterpart. Therefore, it will be possible to apply different polygonal elements or basis functions with different orders according to the local characteristics of the geometry. Several numerical results are presented to validate the accuracy and demonstrate the versatility of the proposed method for modeling multiscale and electrically large PEC objects.

A novel implementation of IEDG-based DDM for solving electromagnetic scattering from large and complex PEC objects

ABSTRACTA novel implementation of the integral equation discontinuous Galerkin (IEDG)-based domain decomposition method (DDM), named as the IEDG-DDM, is developed for the efficient analysis of electromagnetic scattering from large and complex perfect electrically conducting (PEC) objects. Due to the nature of the IEDG scheme, the proposed DDM is nonconformal and nonoverlapping. Therefore, each sub-domain can be meshed independently according to the local geometrical feature, leading to a flexible discretization and a minimum number of unknowns. Different from the IEDG formulation in the skew-symmetric interior penalty DDM, the current continuity at the sub-domain boundaries is enforced through a properly defined interior penalty term, where the error energy from the electric potential is minimized. Consequently, the troublesome implementation of the stabilization term, which requires complex geometrical operations to find the intersection of edges in a nonconformal mesh, can be totally avoided. The proposed DDM results in an effective nonoverlapping domain decomposition preconditioner and a fast convergence of Krylov sub-space iterative solvers can be achieved. This method can be easily applied to curved sub-domain boundaries or curvilinear discretizations. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method.

An efficient high order plane wave time domain algorithm for transient electromagnetic scattering analysis

An efficient high order plane wave time domain algorithm is presented for analyzing the transient scattering from three dimensional electrically large conducting objects. This method uses a set of hierarchical divergence-conforming vector basis functions to accurately represent the current distribution on the perfect electrically conducting (PEC) surface. The higher order functions can significantly reduce the number of unknowns without compromise on the accuracy. The time domain combined field integral equation (TD-CFIE) is then discretized using the hierarchical divergence-conforming vector basis functions and shifted Lagrange polynomial functions in spatial and time domain, respectively. The final matrix equation can be accelerated using the plane wave time domain (PWTD) algorithm. Finally, a parallel algorithm that can execute on a distributed-memory parallel cluster is developed, which provides an appealing avenue for analyzing the transient scattering from three-dimensional electrically large complex PEC objects. Numerical examples are given to demonstrate the accuracy and efficiency of the method.

Scattering from an object behind multi-layer periodic gratings of cylindrical shapes

The problem of electromagnetic scattering from a perfect electric conductor (PEC) object of arbitrary cross-section behind multilayer of periodic gratings of circular cylinders is solved by a hybrid method combining the Method of Moments (MoM), decomposition, and the Physical Optics methods. The periodic grating’s periodic cell consists of multiple layers of lossy-dielectric scattering elements situated in free space. The PEC object under the periodic gratings assumed to be electrically large. A set of electric-field integral equations (EFIEs) for the perturbation currents both on the portion of the PEC object and the periodic gratings most strongly interacting with each other obtained using the surface equivalence principle and a decomposition method. Then, MoM is used to solve the EFIEs in the frequency domain to obtain the scattered electric field.

An Efficient Hybrid Method of Iterative MoM-PO and Equivalent Dipole-Moment for Scattering From Electrically Large Objects

A new efficient hybrid method is proposed for calculating the electromagnetic scattering and radiation from electrically large, three-dimensional, perfect electric conductor objects. The method consists of efficient iterative method of moments-physical optics (EI-MoM-PO) and equivalent dipole moment (EDM). The EDM is adopted to fill the MoM impedance matrix and accelerate the evaluation of the coupling between MoM and PO regions, which promotes the computing efficiency. Furthermore, combined with EI-MoM-PO method, the proposed hybrid method is easier to implement and the formulations are more refined compared to the traditional MoM-PO method. Numerical results indicate that the proposed method has high accuracy and good robustness and can greatly reduce the computational time.

Fast Fourier Transform Accelerated Finite-Difference Delay Modeling Method

ABSTRACTThis article presents the fast Fourier transform scheme to accelerate the solution of finite-difference delay modeling method. The proposed fast Fourier transform–finite-difference delay modeling method projects the primary source onto a uniform auxiliary grid that enclosed the scatterer. The auxiliary sources can reproduce the equivalent transient fields of the primary source when source and observation points are far away from each other. After the projection, the impedance matrices have the spatial and temporal translational invariance property. The fast Fourier transform–finite-difference delay modeling method takes advantage of the translational invariance property to reduce the memory requirement and computational complexity of the original finite-difference delay modeling method. Numerical results about the electromagnetic scattering from perfect electric conductor objects are given to demonstrate the validity and efficiency of the proposed method.

A Discontinuous Galerkin Time-Domain Integral Equation Method for Electromagnetic Scattering From PEC Objects

A discontinuous Galerkin time-domain integral equation (DG-TDIE) method based on the marching-on-in-time (MOT) scheme is presented to analyze the transient scattering from arbitrarily shaped perfect electrically conducting (PEC) objects. In this paper, the mono-polar Rao–Wilton–Glisson (RWG) functions are chosen as the trial and the test spatial functions, while the triangular basis functions are for the temporal expansion. Therefore, it is flexible and convenient to analyze objects with nonconformal discretization or targets containing more than three surfaces in contact with each other. Numerical results are presented to demonstrate the accuracy and the efficiency of the DG-TDIE method.

Electromagnetic scattering analysis using nonconformal meshes and monopolar curl-conforming basis functions

A scheme for electromagnetic scattering analysis of perfect electric conducting (PEC) objects using nonconformal meshes is developed in this paper. The difference of the integral operators for the electric field integral equation (EFIE) and the magnetic field integral equation (MFIE) are analyzed in detail. It is shown theoretically that basis functions used to expand the surface currents for the MFIE may not necessarily be divergence-conforming. The nonconformal meshes and monopolar n×RWG basis functions are used together to solve the MFIE. Details for the implementation of the proposed method are presented. The method is verified through the numerical results for electromagnetic scattering analysis from several PEC objects. It is shown that this method is a suitable choice for using nonconformal meshes when solving electromagnetic scattering problems with the MFIE.

A nonconformal scheme for scattering analysis from PEC objects

A novel nonconformal scheme for electromagnetic scattering analysis from perfect electric conducting (PEC) objects is presented in this paper. In this nonconformal scheme, the constant vector basis functions defined on a single triangle element are used as basis functions to solve the magnetic field integral equation (MFIE). Several commonly used basis functions for the MFIE are discussed and it is shown that the use of the new basis functions for the MFIE is reasonable. The construction of constant vector basis function as well as details for the calculation of the admittance matrix elements resulted from the use of method of moments (MoM) to the MFIE are given. It is shown that the use of the constant vector basis functions to the MFIE results in an efficient nonconformal scheme. Numerical results further validate the effectivity and efficiency of the proposed nonconformal scheme.

Shape Reconstruction of Mixed Boundary Objects by Linear Sampling Method

Geometric reconstruction of dielectric objects in the presence of a perfect electric conducting (PEC) object is investigated with the application of linear sampling method (LSM). The scattered fields from the cylindrical objects of circular cross sections are represented as a multipole expansion, and a numerical analysis is carried out to explore the behavior and limitations of LSM. By considering various numerical examples, the imaging capabilities of LSM for mixed cases (both dielectric and PEC objects) are studied in terms of frequency of operation and permittivity of dielectric objects. To overcome the drawbacks of standard LSM indicator, a modified LSM indicator based on a multifrequency approach is introduced. Apart from the synthetic data, the analysis is also validated by the experimental data provided by the Fresnel Institute.

A Higher Order Nyström Scheme for a Marching-on-in-Time Solution of Time-Domain Integral Equation

A marching-on-in-time (MOT) solution of the time-domain integral equation (TDIE) using the higher order Nystrom scheme is developed to analyze the transient electromagnetic scattering from arbitrarily shaped perfect electrically conducting (PEC) objects. In this scheme, the curvilinear triangular patches are utilized to discretize the PEC objects for their great ability to model geometric configuration. Moreover, we use the Lagrange interpolation polynomials to stand for the spatial basis functions, and the triangle functions to represent the temporal basis functions. Furthermore, the spatial and temporal point-matching is applied. Numerical examples demonstrate that the proposed scheme is stable, accurate, and efficient.

Acceleration of the Impedance Matrix Filling for Marching-on-in-Degree Method by Equivalent Dipole Moment

In this article, the equivalent dipole moment method is employed to accelerate the marching-on-in-degree method for the time-domain combined field integral equation. Each element can be viewed as a dipole model when the distance between the source and the testing basis functions is beyond a threshold distance. In this way, the impedance matrix elements of each order can be easily computed by a simple procedure, and the computational time is reduced significantly for transient electromagnetic scattering. Numerical results are presented to demonstrate the efficiency of the proposed method for electromagnetic scattering from perfect electric conductor objects.