Accuracy improvement of the second-kind integral equations for generally shaped objects

Su Yan, Jian Ming Jin, Zaiping Nie

Research output: Contribution to journalArticle

Abstract

In computational electromagnetics, second-kind integral equations are usually considered less accurate than their first-kind counterparts. The loss of the numerical accuracy is mainly due to the discretization error of the identity operators involved in second-kind IEs. In the previous studies, it was shown that by using the Buffa-Christiansen (BC) functions as testing functions, such a discretization error can be suppressed significantly, and the numerical accuracy of the second-kind IEs in the far-field calculation for spherical objects can be improved dramatically. In this paper, this technique is generalized for generally shaped objects in both perfect electric conductor and dielectric cases by using the BC functions as the testing functions, and by handling the near-singularities in the evaluation of the system matrix elements carefully. The extinction theorem is applied for accurate evaluation of the numerical errors in the calculation of scattering problems for generally shaped objects. Several examples are given to demonstrate the performance of this technique, and several important conclusive remarks are drawn.

Original languageEnglish (US)
Article number6330998
Pages (from-to)788-797
Number of pages10
JournalIEEE Transactions on Antennas and Propagation
Volume61
Issue number2
DOIs
StatePublished - Jan 1 2013

Fingerprint

Integral equations
integral equations
computational electromagnetics
Electric conductors
Computational electromagnetics
electric conductors
evaluation
Testing
far fields
extinction
theorems
Scattering
operators
matrices
scattering

Keywords

  • Buffa-Christiansen functions
  • extinction theorem
  • first-kind integral equations
  • near-singularity extraction
  • numerical accuracy
  • second-kind integral equations
  • testing scheme

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

Accuracy improvement of the second-kind integral equations for generally shaped objects. / Yan, Su; Jin, Jian Ming; Nie, Zaiping.

In: IEEE Transactions on Antennas and Propagation, Vol. 61, No. 2, 6330998, 01.01.2013, p. 788-797.

Research output: Contribution to journalArticle

@article{b8f2049ea97446b8bbecff5ba9971083,
title = "Accuracy improvement of the second-kind integral equations for generally shaped objects",
abstract = "In computational electromagnetics, second-kind integral equations are usually considered less accurate than their first-kind counterparts. The loss of the numerical accuracy is mainly due to the discretization error of the identity operators involved in second-kind IEs. In the previous studies, it was shown that by using the Buffa-Christiansen (BC) functions as testing functions, such a discretization error can be suppressed significantly, and the numerical accuracy of the second-kind IEs in the far-field calculation for spherical objects can be improved dramatically. In this paper, this technique is generalized for generally shaped objects in both perfect electric conductor and dielectric cases by using the BC functions as the testing functions, and by handling the near-singularities in the evaluation of the system matrix elements carefully. The extinction theorem is applied for accurate evaluation of the numerical errors in the calculation of scattering problems for generally shaped objects. Several examples are given to demonstrate the performance of this technique, and several important conclusive remarks are drawn.",
keywords = "Buffa-Christiansen functions, extinction theorem, first-kind integral equations, near-singularity extraction, numerical accuracy, second-kind integral equations, testing scheme",
author = "Su Yan and Jin, {Jian Ming} and Zaiping Nie",
year = "2013",
month = "1",
day = "1",
doi = "10.1109/TAP.2012.2224835",
language = "English (US)",
volume = "61",
pages = "788--797",
journal = "IEEE Transactions on Antennas and Propagation",
issn = "0018-926X",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "2",

}

TY - JOUR

T1 - Accuracy improvement of the second-kind integral equations for generally shaped objects

AU - Yan, Su

AU - Jin, Jian Ming

AU - Nie, Zaiping

PY - 2013/1/1

Y1 - 2013/1/1

N2 - In computational electromagnetics, second-kind integral equations are usually considered less accurate than their first-kind counterparts. The loss of the numerical accuracy is mainly due to the discretization error of the identity operators involved in second-kind IEs. In the previous studies, it was shown that by using the Buffa-Christiansen (BC) functions as testing functions, such a discretization error can be suppressed significantly, and the numerical accuracy of the second-kind IEs in the far-field calculation for spherical objects can be improved dramatically. In this paper, this technique is generalized for generally shaped objects in both perfect electric conductor and dielectric cases by using the BC functions as the testing functions, and by handling the near-singularities in the evaluation of the system matrix elements carefully. The extinction theorem is applied for accurate evaluation of the numerical errors in the calculation of scattering problems for generally shaped objects. Several examples are given to demonstrate the performance of this technique, and several important conclusive remarks are drawn.

AB - In computational electromagnetics, second-kind integral equations are usually considered less accurate than their first-kind counterparts. The loss of the numerical accuracy is mainly due to the discretization error of the identity operators involved in second-kind IEs. In the previous studies, it was shown that by using the Buffa-Christiansen (BC) functions as testing functions, such a discretization error can be suppressed significantly, and the numerical accuracy of the second-kind IEs in the far-field calculation for spherical objects can be improved dramatically. In this paper, this technique is generalized for generally shaped objects in both perfect electric conductor and dielectric cases by using the BC functions as the testing functions, and by handling the near-singularities in the evaluation of the system matrix elements carefully. The extinction theorem is applied for accurate evaluation of the numerical errors in the calculation of scattering problems for generally shaped objects. Several examples are given to demonstrate the performance of this technique, and several important conclusive remarks are drawn.

KW - Buffa-Christiansen functions

KW - extinction theorem

KW - first-kind integral equations

KW - near-singularity extraction

KW - numerical accuracy

KW - second-kind integral equations

KW - testing scheme

UR - http://www.scopus.com/inward/record.url?scp=84873372004&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84873372004&partnerID=8YFLogxK

U2 - 10.1109/TAP.2012.2224835

DO - 10.1109/TAP.2012.2224835

M3 - Article

AN - SCOPUS:84873372004

VL - 61

SP - 788

EP - 797

JO - IEEE Transactions on Antennas and Propagation

JF - IEEE Transactions on Antennas and Propagation

SN - 0018-926X

IS - 2

M1 - 6330998

ER -