TY - JOUR
T1 - On the Stability of Time-Domain Magnetic Field Integral Equation Using Laguerre Functions
AU - Zhu, Ming Da
AU - Sarkar, Tapan K.
AU - Chen, Heng
AU - Wu, Yizhi
N1 - Funding Information:
Manuscript received February 10, 2018; revised September 16, 2018; accepted October 19, 2018. Date of publication February 13, 2019; date of current version May 31, 2019. This work was supported in part by the National Natural Science Foundation of China under Grant 61301029, in part by the Science and Technology Commission of Shanghai under Grant 14510711600, and in part by the Fundamental Research Funds for Central Universities under Grant 17D110417. (Corresponding author: Ming-Da Zhu.) M.-D. Zhu is with the School of Electronic Engineering, Xidian University, Xi’an 710071, China, and also with the Department of Electrical Engineering and Computer Science, Syracuse University, Syracuse, NY 13244 USA (e-mail: mingda.zhu@live.com).
Publisher Copyright:
© 1963-2012 IEEE.
PY - 2019/6
Y1 - 2019/6
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
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U2 - 10.1109/TAP.2019.2899018
DO - 10.1109/TAP.2019.2899018
M3 - Article
AN - SCOPUS:85067054480
SN - 0018-926X
VL - 67
SP - 3939
EP - 3947
JO - IEEE Transactions on Antennas and Propagation
JF - IEEE Transactions on Antennas and Propagation
IS - 6
M1 - 8641309
ER -