TY - JOUR

T1 - Solution of time domain electric field integral equation using the Laguerre polynomials

AU - Chung, Young Seek

AU - Sarkar, Tapan K.

AU - Jung, Baek Ho

AU - Salazar-Palma, Magdalena

AU - Ji, Zhong

AU - Jang, Seongman

AU - Kim, Kyungjung

N1 - Funding Information:
Manuscript received February 22, 2002; revised August 6, 2003. This work was supported in part by the Ministerio de Ciencia y Tecnología, Spain, under the project TIC2002-02657.

PY - 2004/9

Y1 - 2004/9

N2 - In this paper, we propose a numerical method to obtain a solution for the time domain electric field integral equation (TD-EFIE) for arbitrary shaped conducting structures. This method does not utilize the customary marching-on in time (MOT) solution method often used to solve a hyperbolic partial differential equation. Instead we solve the wave equation by expressing the transient behaviors in terms of Laguerre polynomials. By using these causal orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically. In order to solve the wave equation, we introduce two separate testing procedures, a spatial and temporal testing. By introducing first the Galerkin temporal testing procedure, the MOT procedure is replaced by a recursive relation between the different orders of the weighted Laguerre polynomials. The other novelty of this approach is that through the use of the entire domain Laguerre polynomials for the expansion of the temporal variation of the current, the spatial and the temporal variables can be separated and the temporal variables can be integrated out. For convenience, we use the Hertz vector as the unknown variable instead of the electric current density. To verify our method, we compare the results of a TD-EFIE and inverse Fourier transform of a frequency domain EFIE.

AB - In this paper, we propose a numerical method to obtain a solution for the time domain electric field integral equation (TD-EFIE) for arbitrary shaped conducting structures. This method does not utilize the customary marching-on in time (MOT) solution method often used to solve a hyperbolic partial differential equation. Instead we solve the wave equation by expressing the transient behaviors in terms of Laguerre polynomials. By using these causal orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically. In order to solve the wave equation, we introduce two separate testing procedures, a spatial and temporal testing. By introducing first the Galerkin temporal testing procedure, the MOT procedure is replaced by a recursive relation between the different orders of the weighted Laguerre polynomials. The other novelty of this approach is that through the use of the entire domain Laguerre polynomials for the expansion of the temporal variation of the current, the spatial and the temporal variables can be separated and the temporal variables can be integrated out. For convenience, we use the Hertz vector as the unknown variable instead of the electric current density. To verify our method, we compare the results of a TD-EFIE and inverse Fourier transform of a frequency domain EFIE.

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U2 - 10.1109/TAP.2004.835248

DO - 10.1109/TAP.2004.835248

M3 - Article

AN - SCOPUS:4644363410

VL - 52

SP - 2319

EP - 2328

JO - IEEE Transactions on Antennas and Propagation

JF - IEEE Transactions on Antennas and Propagation

SN - 0018-926X

IS - 9

ER -