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In the solution of frequency- and time-domain integral equations, the singularity cancellation transformations are well-known for the treatments of the singular integrals involving Green’s functions and their gradients. The cancellation transformations for strongly near-singular integrals become inaccurate and inefficient for an extremely deformed triangular patch, and this phenomenon is referred to as shape-dependent problem in this article. As the degree of the singularity increases, the shape-dependent problem of strong near-singularity is more severe than that of the weakly near-singular integrals. Furthermore, if the source triangle is deformed, the accuracy of the cancellation methods decreases when no near singularity exists. In this work, we first investigate the reason for these problems via the theoretical analysis with numerical verification. Second, an updated framework of singularity cancellation methods for strongly near-singular integrals is proposed, which has a fast and consistent convergence rate for both regular and irregular triangles. Third, some numerical experiments are presented to illustrate the effectiveness of the theoretical framework and the proposed transformations. [ABSTRACT FROM AUTHOR]

The singularity cancellation transformations are well-known for calculating weakly singular and near-singular integrals in integral equation solutions. However, some singularity cancellation methods suffer from the shape-dependent problem of inaccuracy and inefficiency for deformed triangles. By the theoretical analysis and numerical verification in this article, the relation between the near-singularity and shape-dependence of the singularity cancellation schemes is discussed. Moreover, a novel framework for devising cancellation transformations of weakly near-singular integrals is presented, which results in fast convergence for both regular and irregular triangular domains. Some numerical results are given to illustrate the validity of the theoretical framework and the efficiency of the proposed transformations. [ABSTRACT FROM AUTHOR]

The combined-field integral equation (CFIE) usually is less accurate than the electric-field integral equation (EFIE), especially for objects with sharp edges and corners. In this work, we propose a simple but accuracy enhanced CFIE (AE-CFIE) strategy for computing scattering from perfect electric conductor (PEC) objects. AE-CFIE directly replaces the original CFIE on the sharp edges with EFIE. Using the dihedral angle of the meshes to describe the sharpness of the geometric structure, the hybrid criterion of EFIE/CFIE has been studied in detail. This strategy can be implemented conveniently under exiting basis functions and only a few lines of code need to be changed. Due to the inclusion of EFIE, AE-CFIE may sacrifice the convergence speed compared with CFIE. Therefore, we also investigate the performance of AE-CFIE with or without the preconditioner. Numerical examples show the performance of AE-CFIE, and a comprehensively study is made to demonstrate its validity, reliability, and stability. [ABSTRACT FROM AUTHOR]

Implementation of max-ortho basis functions is proposed in a method for analysis of axially symmetric metallic antennas based on exact kernel of electric field integral equation in combination with Galerkin testing. High-precision evaluation of matrix elements is enabled by: a) representing them as a linear combination of impedance integrals due to the Legendre polynomials and their first derivatives; b) using the singularity cancelation techniques; and c) evaluating the Legendre polynomials and their first derivatives by well-known recurrent formulas. Applicability of max-ortho bases up to expansion order of $n =128$ is illustrated on a full-wave thick dipole antenna. [ABSTRACT FROM AUTHOR]

Numerical solutions for electromagnetic (EM) integral equations rely on the discretization of integral domains and the use of meshes for geometric description. Meshing geometries is very tedious, especially for complicated structures with many details (tiny parts) and geometric discontinuities (corners or edges), and remeshing could be required in many scenarios. To reduce the costs of generating quality meshes, meshless or mesh-free methods were developed and they have been extensively studied in mechanical engineering though there are less obvious interests in EM community. The meshless methods employ discrete nodes to replace meshes in the description of geometries but the background meshes for integrations are still needed traditionally. In this work, we first address the traditional meshless scheme for solving EM integral equations based on the moving least square (MLS) approximation for unknown currents and the use of background meshes for integrations, and then develop a novel meshless scheme by applying the Green's lemma to the EM surface integral equations with flat domains. The novel scheme transforms a surface integral over a flat domain into a line integral along its boundaries when excluding a singular patch in the domain. Since only the domain boundaries are discretized and no background meshes are needed, the scheme is truly meshless. Numerical examples for EM scattering by flat-surface objects are presented to demonstrate the effectiveness of the novel scheme. [ABSTRACT FROM PUBLISHER]

Using a variational method, we recently determined an electromagnetic “signature” for characterizing a straight wire in free space. The signature consists of the first five resonant frequencies and their widths, more compactly expressed as the first five complex-valued resonant frequencies. Here we apply the variational method to the much more complicated case of determining the same signature for a straight wire or wire pair on a flat interface between a homogeneous earth and air. To calculate the resonances we obtain an integral equation for the current on a wire on the interface between two dielectric media. Complex-valued resonant frequencies are defined as those for which the homogeneous integral equation for the current in an equivalent thin strip on the interface has non-zero solutions. The variational method extracts good approximations to these complex-valued resonant frequencies, without having to solve the integral equation. A table of resonances is given for the case of a relative dielectric constant of the earth equal to 4 and for three values of the ratio of wire radius to wire half-length. [ABSTRACT FROM AUTHOR]

With an interest in finding wires and distinguishing them from other electrically conducting objects, we have looked for an electromagnetic “fingerprint” in terms of resonances of a straight wire of length 2h and radius a. The resonances of the wire are formulated using the theory of the linear antenna, leading to an integral equation for the current on the wire. Complex-valued resonant frequencies are defined as those for which the homogeneous integral equation for the current on the wire has non-zero solutions. By applying a variational technique we obtain approximate numerical solutions for the resonant frequencies and their widths. A table of the first five resonances is given for several ratios of wire half-length h to wire radius a. In a subsequent paper we propose to extend the method described here to deal with wires on an earth-air interface, for example as used to command the detonation of improvised explosive devices. [ABSTRACT FROM AUTHOR]