On the Stability of Time-Domain Magnetic Field Integral Equation Using Laguerre Functions

Ming Da Zhu, Tapan Kumar Sarkar, Heng Chen, Yizhi Wu

Research output: Contribution to journalArticle

Abstract

The marching-on-in-degree (MOD) method has been proposed for solving time-domain integral equations (TDIEs), and it uses the associated Laguerre functions as temporal basis and testing functions. Although the MOD scheme is assumed to be stable and accurate, there exists little investigation into the accuracy of the integral operations involving the associated Laguerre functions of high degree. It is shown in this paper that the numerical quadrature for integrating the highly oscillatory Laguerre functions may not be accurate and this may result in instability for the MOD solvers. In this paper, the highly oscillatory nature of the high-degree associated Laguerre functions is investigated first. Based on that, the numerical procedures are described which result in the inaccuracy of the numerical quadrature associated with the highly oscillatory nature for the higher order Laguerre functions. This can produce instability for the MOD solvers when a solution requires a high degree of the Laguerre functions. Hence, a novel Filon-type quadrature method and a stabilized MOD technique for time-domain magnetic field integral equations (TD-MFIE-SMOD) are presented in this paper. Some numerical results are presented to illustrate the validity of the proposed Filon-type quadrature rule resulting in stable solution of the TD-MFIE for transient scattering problems.

Original languageEnglish (US)
Article number8641309
Pages (from-to)3939-3947
Number of pages9
JournalIEEE Transactions on Antennas and Propagation
Volume67
Issue number6
DOIs
StatePublished - Jun 1 2019

Fingerprint

Integral equations
Magnetic fields
Scattering
Testing

Keywords

  • Associated Laguerre functions
  • highly oscillatory quadrature
  • magnetic field integral equation
  • marching-on-in-degree (MOD)
  • stability
  • time-domain integral equation

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

On the Stability of Time-Domain Magnetic Field Integral Equation Using Laguerre Functions. / Zhu, Ming Da; Sarkar, Tapan Kumar; Chen, Heng; Wu, Yizhi.

In: IEEE Transactions on Antennas and Propagation, Vol. 67, No. 6, 8641309, 01.06.2019, p. 3939-3947.

Research output: Contribution to journalArticle

Zhu, Ming Da ; Sarkar, Tapan Kumar ; Chen, Heng ; Wu, Yizhi. / On the Stability of Time-Domain Magnetic Field Integral Equation Using Laguerre Functions. In: IEEE Transactions on Antennas and Propagation. 2019 ; Vol. 67, No. 6. pp. 3939-3947.
@article{c7cf52d6c3dd4cb794b5725d3cfed8d4,
title = "On the Stability of Time-Domain Magnetic Field Integral Equation Using Laguerre Functions",
abstract = "The marching-on-in-degree (MOD) method has been proposed for solving time-domain integral equations (TDIEs), and it uses the associated Laguerre functions as temporal basis and testing functions. Although the MOD scheme is assumed to be stable and accurate, there exists little investigation into the accuracy of the integral operations involving the associated Laguerre functions of high degree. It is shown in this paper that the numerical quadrature for integrating the highly oscillatory Laguerre functions may not be accurate and this may result in instability for the MOD solvers. In this paper, the highly oscillatory nature of the high-degree associated Laguerre functions is investigated first. Based on that, the numerical procedures are described which result in the inaccuracy of the numerical quadrature associated with the highly oscillatory nature for the higher order Laguerre functions. This can produce instability for the MOD solvers when a solution requires a high degree of the Laguerre functions. Hence, a novel Filon-type quadrature method and a stabilized MOD technique for time-domain magnetic field integral equations (TD-MFIE-SMOD) are presented in this paper. Some numerical results are presented to illustrate the validity of the proposed Filon-type quadrature rule resulting in stable solution of the TD-MFIE for transient scattering problems.",
keywords = "Associated Laguerre functions, highly oscillatory quadrature, magnetic field integral equation, marching-on-in-degree (MOD), stability, time-domain integral equation",
author = "Zhu, {Ming Da} and Sarkar, {Tapan Kumar} and Heng Chen and Yizhi Wu",
year = "2019",
month = "6",
day = "1",
doi = "10.1109/TAP.2019.2899018",
language = "English (US)",
volume = "67",
pages = "3939--3947",
journal = "IEEE Transactions on Antennas and Propagation",
issn = "0018-926X",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "6",

}

TY - JOUR

T1 - On the Stability of Time-Domain Magnetic Field Integral Equation Using Laguerre Functions

AU - Zhu, Ming Da

AU - Sarkar, Tapan Kumar

AU - Chen, Heng

AU - Wu, Yizhi

PY - 2019/6/1

Y1 - 2019/6/1

N2 - The marching-on-in-degree (MOD) method has been proposed for solving time-domain integral equations (TDIEs), and it uses the associated Laguerre functions as temporal basis and testing functions. Although the MOD scheme is assumed to be stable and accurate, there exists little investigation into the accuracy of the integral operations involving the associated Laguerre functions of high degree. It is shown in this paper that the numerical quadrature for integrating the highly oscillatory Laguerre functions may not be accurate and this may result in instability for the MOD solvers. In this paper, the highly oscillatory nature of the high-degree associated Laguerre functions is investigated first. Based on that, the numerical procedures are described which result in the inaccuracy of the numerical quadrature associated with the highly oscillatory nature for the higher order Laguerre functions. This can produce instability for the MOD solvers when a solution requires a high degree of the Laguerre functions. Hence, a novel Filon-type quadrature method and a stabilized MOD technique for time-domain magnetic field integral equations (TD-MFIE-SMOD) are presented in this paper. Some numerical results are presented to illustrate the validity of the proposed Filon-type quadrature rule resulting in stable solution of the TD-MFIE for transient scattering problems.

AB - The marching-on-in-degree (MOD) method has been proposed for solving time-domain integral equations (TDIEs), and it uses the associated Laguerre functions as temporal basis and testing functions. Although the MOD scheme is assumed to be stable and accurate, there exists little investigation into the accuracy of the integral operations involving the associated Laguerre functions of high degree. It is shown in this paper that the numerical quadrature for integrating the highly oscillatory Laguerre functions may not be accurate and this may result in instability for the MOD solvers. In this paper, the highly oscillatory nature of the high-degree associated Laguerre functions is investigated first. Based on that, the numerical procedures are described which result in the inaccuracy of the numerical quadrature associated with the highly oscillatory nature for the higher order Laguerre functions. This can produce instability for the MOD solvers when a solution requires a high degree of the Laguerre functions. Hence, a novel Filon-type quadrature method and a stabilized MOD technique for time-domain magnetic field integral equations (TD-MFIE-SMOD) are presented in this paper. Some numerical results are presented to illustrate the validity of the proposed Filon-type quadrature rule resulting in stable solution of the TD-MFIE for transient scattering problems.

KW - Associated Laguerre functions

KW - highly oscillatory quadrature

KW - magnetic field integral equation

KW - marching-on-in-degree (MOD)

KW - stability

KW - time-domain integral equation

UR - http://www.scopus.com/inward/record.url?scp=85067054480&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85067054480&partnerID=8YFLogxK

U2 - 10.1109/TAP.2019.2899018

DO - 10.1109/TAP.2019.2899018

M3 - Article

VL - 67

SP - 3939

EP - 3947

JO - IEEE Transactions on Antennas and Propagation

JF - IEEE Transactions on Antennas and Propagation

SN - 0018-926X

IS - 6

M1 - 8641309

ER -