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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]

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]

Electromagnetic scattering by super-thin conducting objects is formulated by integral equation approach. It could be difficult to obtain accurate solutions for such a problem because the current density changes dramatically near the edges of such objects and many low-quality meshes exist on the side faces of objects when discretized. Traditionally, the electric field integral equation is used to describe the problem and the three-dimensional (3-D) objects are approximated as a two-dimensional (2-D) open structure with a summation of the current density at two opposite sides. In this communication, the magnetic field integral equation (MFIE) is employed to govern the problem and the super-thin objects are strictly treated as 3-D objects. The MFIE is a second-kind integral equation resulting in a better conditioning and can also release the low-frequency breakdown problem, but it has not been applied to very thin structures. In the method of moments solution, a robust near-singularity treatment for its kernel is developed based on the Green’s lemma. The derived formulations are friendly and very suitable for low-quality triangular meshes. Numerical examples are presented to demonstrate the scheme and good results have been obtained. [ABSTRACT FROM PUBLISHER]