Sign in
Author

Conference

Journal

Organization

Year

DOI
Look for results that meet for the following criteria:
since
equal to
before
between
and
Search in all fields of study
Limit my searches in the following fields of study
Agriculture Science
Arts & Humanities
Biology
Chemistry
Computer Science
Economics & Business
Engineering
Environmental Sciences
Geosciences
Material Science
Mathematics
Medicine
Physics
Social Science
Multidisciplinary
Keywords
(12)
fdtd method
Finite Difference Time Domain
Finite Difference Time Domain Method
laguerre polynomial
Numerical Method
Recursion Relation
Temporal Variability
Temporal Variation
Transient Behavior
Electric and Magnetic Fields
Marching On In Time
Time Domain
Subscribe
Academic
Publications
An unconditionally stable scheme for the finitedifference timedomain method
An unconditionally stable scheme for the finitedifference timedomain method,10.1109/TMTT.2003.808732,IEEE Transactions on Microwave Theory and Techn
Edit
An unconditionally stable scheme for the finitedifference timedomain method
(
Citations: 59
)
BibTex

RIS

RefWorks
Download
YoungSeek Chung
,
Tapan K. Sarkar
,
Baek Ho Jung
,
Magdalena SalazarPalma
In this work, we propose a
numerical method
to obtain an unconditionally stable solution for the finitedifference timedomain (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 timedomain 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 marchingon 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 domainweighted Laguerre polynomials for the expansion of the
temporal variation
of the fields, the spatial and the temporal variables can be separated.
Journal:
IEEE Transactions on Microwave Theory and Techniques  IEEE TRANS MICROWAVE THEORY
, vol. 51, no. 3, pp. 697704, 2003
DOI:
10.1109/TMTT.2003.808732
Cumulative
Annual
View Publication
The following links allow you to view full publications. These links are maintained by other sources not affiliated with Microsoft Academic Search.
(
ieeexplore.ieee.org
)
(
www.cis.syr.edu
)
(
ieeexplore.ieee.org
)
(
ieeexplore.ieee.org
)
More »
Citation Context
(41)
...Recently, a new unconditionally stable FDTD method with weighted Laguerre polynomials (WLPFDTD) [
7
]‐[9] was introduced...
...It can eliminate the restriction of the CFL condition, without the special treatment for the additional terms, and only a limited number of iterations are needed to achieve a satisfactory accuracy [
7
]...
...A set of orthogonal basis functions can be constructed using Laguerre Polynomials [
7
], given by...
...According to the derivational procedure in [
7
], (1)‐(3) can be written as...
...Meanwhile, only a limited number of iterations are needed to achieve a satisfactory accuracy [
7
]...
...The upper limit of infinity can be replaced by a finite time interval [
7
]...
ZhaoYang Cai
,
et al.
The WLPFDTD Method for Periodic Structures With Oblique Incident Wave
...On the other hand, another unconditionally stable scheme were intelligently developed [
5
], [6] for the conventional gridbased finitedifference timedomain (FDTD) method; there the weighted decaying Laguerre polynomials are used as temporal basis and testing functions to expand unknown field quantities and to minimize residual errors in the time domain; then a procedure of the Method of Moments or Method of Weighted Residuals as described ...
...The method has been shown to be efficient due to the fact that its solutions can be computed in a recursive marchinorder manner [
5
]...
...Therefore, an orthogonal set of basis functions can be formed as [
5
]:...
...Scaling factor is used to increase or decrease the support provided by the above expansion as described in [
5
]...
...For any expanded field component function (with being , and ), its firstorder temporal derivative with respect to time is [
5
]:...
...Upper limit is chosen in such a way that the waveform of source has practically decayed to zero after [
5
]...
...The value of can be determined by [
5
], [8], where is the temporal duration to be simulated and is the bandwidth of the signal of interest...
...Then it can be stored for the subsequent computations as described in [
5
]...
...In both examples, the modulated Gaussian pulse below is chosen as an exciting electric current source, the same as the one used in [
5
]:...
Xiaojie Chen
,
et al.
An Unconditionally Stable Radial Point Interpolation Meshless Method W...
...The time span is chosen in such a way that the waveformsofinteresthavepracticallydecayedtozero[
8
].Forconvenience,wedefine asetof auxiliary matricesas(19)‐(24), shown at the bottom of the following page...
YanTao Duan
,
et al.
Efficient Implementation for 3D LaguerreBased FiniteDifference Time...
...In order to eliminate the stability condition constraint, a new unconditionally stable FDTD method with weighted Laguerre polynomials (WLPs) can be used [
2
]...
...The weighted Laguerre functions are given as [
2
]...
...where . Insert (6) and (7) into (1)–(4), According to the derivational procedure in [
2
], (1)–(4) can be written as...
...The update equations of the magnetic field components can be derived from (10) and (11) according to the procedure described in [
2
]...
...In an actual simulation, the expansion coefficients of the electric field components must be updated as following sequence: , and . Then, one can reconstruct the field components in the time domain according to the method in [
2
]...
...The agreement between FDTD, conventional WLPFDTD [
2
], and efficient WLPFDTD is very good...
YanTao Duan
,
et al.
PML Absorbing Boundary Condition for Efficient 2D WLPFDTD Method
...To over come this difficulty, an unconditionally stable FDTD with weighted Laguerre polynomials (WLP–FDTD) was proposed [
4
]...
...With reference to Chung et al.[
4
], using the basis weighted...
Yin Qin
,
et al.
An unconditionally stable FDTD with weighted Laguerre polynomials in c...
References
(9)
Toward the development of a threedimensional unconditionally stable finitedifference timedomain method
(
Citations: 209
)
Fenghua Zhen
,
Zhizhang Chen
,
Jiazong Zhang
Journal:
IEEE Transactions on Microwave Theory and Techniques  IEEE TRANS MICROWAVE THEORY
, vol. 48, no. 9, pp. 15501558, 2000
A dispersive boundary condition for microstrip component analysis using the FDTD method
(
Citations: 58
)
Zhiqiang Bi
,
Keli Wu
,
Chen Wu
,
John Litva
Journal:
IEEE Transactions on Microwave Theory and Techniques  IEEE TRANS MICROWAVE THEORY
, vol. 40, no. 4, pp. 774777, 1992
The transforms and applications handbook
(
Citations: 143
)
A. D. Poularikas
Published in 1996.
3D ADIFDTD methodunconditionally stable timedomain algorithm for solving full vector Maxwell's equations
(
Citations: 119
)
Takefumi Namiki
Journal:
IEEE Transactions on Microwave Theory and Techniques  IEEE TRANS MICROWAVE THEORY
, vol. 48, no. 10, pp. 17431748, 2000
Numerical simulation of microstrip resonators and filters using the ADIFDTD method
(
Citations: 10
)
Takefumi Namiki
,
Koichi Ito
Journal:
IEEE Transactions on Microwave Theory and Techniques  IEEE TRANS MICROWAVE THEORY
, vol. 49, no. 4, pp. 665670, 2001
Sort by:
Citations
(59)
The WLPFDTD Method for Periodic Structures With Oblique Incident Wave
(
Citations: 1
)
ZhaoYang Cai
,
Bin Chen
,
Qin Yin
,
Run Xiong
Journal:
IEEE Transactions on Antennas and Propagation  IEEE TRANS ANTENNAS PROPAGAT
, vol. 59, no. 10, pp. 37803785, 2011
An Unconditionally Stable Radial Point Interpolation Meshless Method With Laguerre Polynomials
Xiaojie Chen
,
Yiqiang Yu
,
Donglin Su
Journal:
IEEE Transactions on Antennas and Propagation  IEEE TRANS ANTENNAS PROPAGAT
, vol. 59, no. 10, pp. 37563763, 2011
Efficient Implementation for 3D LaguerreBased FiniteDifference TimeDomain Method
YanTao Duan
,
Bin Chen
,
DaGang Fang
,
BiHua Zhou
Journal:
IEEE Transactions on Microwave Theory and Techniques  IEEE TRANS MICROWAVE THEORY
, vol. 59, no. 1, pp. 5664, 2011
PML Absorbing Boundary Condition for Efficient 2D WLPFDTD Method
YanTao Duan
,
Bin Chen
,
HaiLin Chen
,
DaGang Fang
Journal:
IEEE Antennas and Wireless Propagation Letters  IEEE ANTENN WIREL PROPAG LETT
, vol. 10, pp. 846849, 2011
An unconditionally stable FDTD with weighted Laguerre polynomials in cylindrical coordinates
Yin Qin
,
Chen Bin
,
Xiong Run
,
Cai Zhaoyang
Conference:
IEEE International Conference on Microwave Technology & Computational Electromagnetics  ICMTCE
, 2011