TY - JOUR
T1 - An unconditionally stable scheme for the finite-difference time-domain method
AU - Chung, Young Seek
AU - Sarkar, Tapan K.
AU - Jung, Baek Ho
AU - Salazar-Palma, Magdalena
N1 - Copyright:
Copyright 2004 Elsevier Science B.V., Amsterdam. All rights reserved.
PY - 2003/3
Y1 - 2003/3
N2 - In this work, we propose a numerical method to obtain an unconditionally stable solution for the finite-difference time-domain (FDTD) method for the TEz case. This new method does not utilize the customary explicit leapfrog time scheme of the conventional FDTD method. Instead we solve the time-domain Maxwell's equations by expressing the transient behaviors in terms of weighted Laguerre polynomials. By using these orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically, which results in an implicit relation. In this way, the time variable is eliminated from the computations. By introducing the Galerkin temporal testing procedure, the marching-on in time method is replaced by a recursive relation between the different orders of the weighted Laguerre polynomials if the input waveform is of arbitrary shape. Since the weighted Laguerre polynomials converge to zero as time progresses, the electric and magnetic fields when expanded in a series of weighted Laguerre polynomials also converge to zero. The other novelty of this approach is that, through the use of the entire domain-weighted Laguerre polynomials for the expansion of the temporal variation of the fields, the spatial and the temporal variables can be separated. To verify the accuracy and the efficiency of the proposed method, we compare the results of the conventional FDTD method with the proposed method.
AB - In this work, we propose a numerical method to obtain an unconditionally stable solution for the finite-difference time-domain (FDTD) method for the TEz case. This new method does not utilize the customary explicit leapfrog time scheme of the conventional FDTD method. Instead we solve the time-domain Maxwell's equations by expressing the transient behaviors in terms of weighted Laguerre polynomials. By using these orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically, which results in an implicit relation. In this way, the time variable is eliminated from the computations. By introducing the Galerkin temporal testing procedure, the marching-on in time method is replaced by a recursive relation between the different orders of the weighted Laguerre polynomials if the input waveform is of arbitrary shape. Since the weighted Laguerre polynomials converge to zero as time progresses, the electric and magnetic fields when expanded in a series of weighted Laguerre polynomials also converge to zero. The other novelty of this approach is that, through the use of the entire domain-weighted Laguerre polynomials for the expansion of the temporal variation of the fields, the spatial and the temporal variables can be separated. To verify the accuracy and the efficiency of the proposed method, we compare the results of the conventional FDTD method with the proposed method.
KW - Finite difference time domain (FDTD)
KW - Laguerre polynomials
KW - Unconditionally stable scheme
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U2 - 10.1109/TMTT.2003.808732
DO - 10.1109/TMTT.2003.808732
M3 - Article
AN - SCOPUS:0037360108
VL - 51
SP - 697
EP - 704
JO - IEEE Transactions on Microwave Theory and Techniques
JF - IEEE Transactions on Microwave Theory and Techniques
SN - 0018-9480
IS - 3
ER -