Characterization and integration of the singular test integrals in the method‐of‐moments implementation of the electric‐field integral equation

Abstract

The method-of-moments implementation of the electric-field integral equation yields many code-verification challenges due to the different sources of numerical error and their possible interactions. Matters are further complicated by singular integrals, which arise from the presence of a Green's function. In this paper, we provide approaches to separately assess the numerical errors arising from the use of basis functions to approximate the solution and the use of quadrature to approximate the integration. Through these approaches, we are able to verify the code and compare the error from different quadrature options.

Code-Verification Techniques for the Method-of-Moments Implementation of the Combined-Field Integral Equation

“…The CFIE linearly combines the EFIE (13) and MFIE (15) to yield the variational problem find J ∈ V, such that:…”

“…These integrals contain a Green's function, which yields singularities when the test and source elements share one or more edges or vertices, and near-singularities when they are otherwise close. The accurate evaluation of these integrals is an active research topic, with many approaches being developed to address the (near-)singularity for the inner, sourceelement integral [1][2][3][4][5][6][7][8][9][10], as well as for the outer, test-element integral [11][12][13][14][15].…”

“…Given the computational expense of computing accurate reference solutions, assessing these integral evaluations is best accomplished through extensive unit testing as complementary code verification. Examples for the EFIE are included in [15,49]. This paper is organized as follows.…”

Code-verification techniques for the method-of-moments implementation of the electric-field integral equation

“…However, the presence of a Green's function in these equations yields singularities when the test and source elements share one or more edges or vertices, and near-singularities when they are otherwise close. Many approaches have been developed to address the singularity and near-singularity for the inner, source-element integral [1][2][3][4][5][6][7][8][9][10], as well as for the outer, test-element integral [11][12][13][14][15].…”

Accurate and Efficient Evaluation of the Scattering of Bodies of Revolution Based on Magnetic Field Integral Equation

“…The analysis of scattering by perfectly electrically conducting (PEC) objects is an important problem in electromagnetics. One branch of solution methods to characterize the electromagnetic scattering is based on the electric field integral equation (EFIE) [1,2]. In this method, the equivalence principle is employed to obtain an integral representation for the electric fields inside or outside the object.…”