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

Brian A. Freno; William A. Johnson; Brian F. Zinser; Donald R. Wilton; Francesca Vipiana; Salvatore Campione

doi:10.1016/j.enganabound.2020.12.015

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

Brian A. Freno
, William A. Johnson
, Brian F. Zinser
, Donald R. Wilton
, Francesca Vipiana
, Salvatore Campione

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

In this paper, we characterize the logarithmic singularities arising in the method of moments from the Green's function in integrals over the test domain, and we use two approaches for designing geometrically symmetric quadrature rules to integrate these singular integrands. These rules exhibit better convergence properties than quadrature rules for polynomials and, in general, lead to better accuracy with a lower number of quadrature points. We demonstrate their effectiveness for several examples encountered in both the scalar and vector potentials of the electric-field integral equation (singular, near-singular, and far interactions) as compared to the commonly employed polynomial scheme and the double Ma–Rokhlin–Wandzura (DMRW) rules, whose sample points are located asymmetrically within triangles.

Original language	English
Pages (from-to)	185-193
Number of pages	9
Journal	Engineering Analysis with Boundary Elements
Volume	124
DOIs	https://doi.org/10.1016/j.enganabound.2020.12.015
State	Published - Mar 1 2021
Externally published	Yes

Funding

This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525.

Keywords

Geometrically symmetric quadrature rules
Method of moments
Singular integrals

Access to Document

10.1016/j.enganabound.2020.12.015

Cite this

@article{ae82dd2ccaf04f049d5ceb7fd93d7a6c,

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

abstract = "In this paper, we characterize the logarithmic singularities arising in the method of moments from the Green's function in integrals over the test domain, and we use two approaches for designing geometrically symmetric quadrature rules to integrate these singular integrands. These rules exhibit better convergence properties than quadrature rules for polynomials and, in general, lead to better accuracy with a lower number of quadrature points. We demonstrate their effectiveness for several examples encountered in both the scalar and vector potentials of the electric-field integral equation (singular, near-singular, and far interactions) as compared to the commonly employed polynomial scheme and the double Ma–Rokhlin–Wandzura (DMRW) rules, whose sample points are located asymmetrically within triangles.",

keywords = "Geometrically symmetric quadrature rules, Method of moments, Singular integrals",

author = "Freno, \{Brian A.\} and Johnson, \{William A.\} and Zinser, \{Brian F.\} and Wilton, \{Donald R.\} and Francesca Vipiana and Salvatore Campione",

note = "Publisher Copyright: {\textcopyright} 2020",

year = "2021",

month = mar,

day = "1",

doi = "10.1016/j.enganabound.2020.12.015",

language = "English",

volume = "124",

pages = "185--193",

journal = "Engineering Analysis with Boundary Elements",

issn = "0955-7997",

publisher = "Elsevier",

}

TY - JOUR

T1 - Characterization and integration of the singular test integrals in the method‐of‐moments implementation of the electric‐field integral equation

AU - Freno, Brian A.

AU - Johnson, William A.

AU - Zinser, Brian F.

AU - Wilton, Donald R.

AU - Vipiana, Francesca

AU - Campione, Salvatore

PY - 2021/3/1

Y1 - 2021/3/1

N2 - In this paper, we characterize the logarithmic singularities arising in the method of moments from the Green's function in integrals over the test domain, and we use two approaches for designing geometrically symmetric quadrature rules to integrate these singular integrands. These rules exhibit better convergence properties than quadrature rules for polynomials and, in general, lead to better accuracy with a lower number of quadrature points. We demonstrate their effectiveness for several examples encountered in both the scalar and vector potentials of the electric-field integral equation (singular, near-singular, and far interactions) as compared to the commonly employed polynomial scheme and the double Ma–Rokhlin–Wandzura (DMRW) rules, whose sample points are located asymmetrically within triangles.

AB - In this paper, we characterize the logarithmic singularities arising in the method of moments from the Green's function in integrals over the test domain, and we use two approaches for designing geometrically symmetric quadrature rules to integrate these singular integrands. These rules exhibit better convergence properties than quadrature rules for polynomials and, in general, lead to better accuracy with a lower number of quadrature points. We demonstrate their effectiveness for several examples encountered in both the scalar and vector potentials of the electric-field integral equation (singular, near-singular, and far interactions) as compared to the commonly employed polynomial scheme and the double Ma–Rokhlin–Wandzura (DMRW) rules, whose sample points are located asymmetrically within triangles.

KW - Geometrically symmetric quadrature rules

KW - Method of moments

KW - Singular integrals

UR - https://www.scopus.com/pages/publications/85098472971

U2 - 10.1016/j.enganabound.2020.12.015

DO - 10.1016/j.enganabound.2020.12.015

M3 - Article

AN - SCOPUS:85098472971

SN - 0955-7997

VL - 124

SP - 185

EP - 193

JO - Engineering Analysis with Boundary Elements

JF - Engineering Analysis with Boundary Elements

ER -

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

Abstract

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this