A Simple Transformation for Near-Singular Integrals on Curvilinear Elements

Author

Haobo Yuan ; Zhijun Wang ; Xiaojie Dang ; Nan Wang

Author_Institution

North Univ. of China, Taiyuan, China

Volume

63

Issue

6

fYear

2015

fDate

Jun-15

Firstpage

2827

Lastpage

2833

Abstract

It is difficult to evaluate the near-singular four-dimensional integrals in the Galerkin magnetic-field integral equations (MFIE), especially for the curvilinear elements. This communication presents a hyperbolic transformation to cancel the near singularities in the 1/R² kernel on curved quadrilateral elements, which is addressed theoretically and numerically. This method has a much simpler formula than the so-called DIRECTFN method, and its convergence rate may be much faster than the latter. This is demonstrated by evaluating the near-singular integral of a sharp-edged structure composed of two curvilinear quadrilaterals.

Keywords

Galerkin method; convergence of numerical methods; hyperbolic equations; magnetic field integral equations; transforms; DIRECTFN method; Galerkin magnetic-field integral equations; convergence rate; curved quadrilateral elements; curvilinear elements; curvilinear quadrilaterals; hyperbolic transformation; near-singular 4D integrals; sharp-edged structure; Impedance; Integral equations; Kernel; Method of moments; Periodic structures; Surface impedance; Vectors; Curvilinear quadrilateral; curvilinear quadrilateral; magnetic-field integral equation; magnetic-field integral equation (MFIE); near singularity; transformation;

fLanguage

English

Journal_Title

Antennas and Propagation, IEEE Transactions on

Publisher

ieee

ISSN

0018-926X

Type

jour

DOI

10.1109/TAP.2015.2417897

Filename

7072459