FDTD Method
The Finite Difference Time Domain (FDTD) method is a numerical
(computer-based) approach for analyzing electromagnetic propagation
through and around realistic physical objects.
In this research effort, I am focusing on computationally efficient
methods for incorporating the effects of dielectric relaxation into
the FDTD method.
Recent contributions include:
- Expression of empirical models of complex permittivity
(such as the Cole-Cole, Cole-Davidson, and Havriliak-Negami models)
in terms of a sum of Debye functions ("Debye Sum" methods).
- Application of the particle swarm optimization method and least squares
optimization method to find the Debye sum parameters.
- Determination of the stability conditions for Debye Sum methods.
- Investigation of the accuracy of Debye Sum methods.
My early work in this area constituted the primary portion of my doctoral
research at
The Pennsylvania State University.
Information about my doctoral dissertation is given at the bottom of this
page.
The principal contributions of my doctoral work were:
- Developed the Piecewise Linear Recursive Convolution (PLRC)
algorithm for incorporating dispersive dielectrics characterized
by the Debye and Lorentz permittivity models into the
FDTD method.
- Extended the PLRC algorithm to incorporate non-Debye models of
dielectric relaxation.
- Extended the PLRC algorithm to incorporate the
Van Vleck-Weisskopf model of resonance absorption.
- Developed a methodical approach for the analysis of calculation
errors and stability in FDTD algorithms.
- Developed an algorithm for converting geometrical models based
upon triangular flat facets as used in finite element software
to models based upon rectangular blocks as used in FDTD
software. Applied the conversion algorithm to the analysis of
electromagnetic scattering from aircraft.
Bucknell Student Contributors
- Tim Destan (Presidential Fellow, BSCS '08)
Journal Papers
- David F. Kelley, Timothy J. Destan, and Raymond J. Luebbers,
"Debye Function Expansions of Complex Permittivity Using a
Hybrid Particle Swarm-Least Squares Optimization Approach," IEEE
Transactions on Antennas and Propagation, vol. 55, no. 7,
pp. 1999-2005, July 2007.
- David F. Kelley and Raymond J. Luebbers, "Piecewise Linear
Recursive Convolution for Dispersive Media Using FDTD," IEEE
Transactions on Antennas and Propagation, vol. 44, no. 6,
pp. 792-797, June 1996.
Conference Papers
- David F. Kelley and Raymond J. Luebbers, "Debye Function Expansions of Empirical
Models of Complex Permittivity for Use in FDTD Solutions,"
Proc. IEEE Antennas and Propagation Society International Symposium,
vol. 4, Columbus, OH, June 2003, pp. 372-375.
[References]
- David F. Kelley and Raymond J. Luebbers, "Modification of the PLRC
Algorithm for the Analysis of Propagation through Van Vleck-Weisskopf
Media," Proc. USNC/URSI National Radio Science Meeting,
Salt Lake City, UT, July 2000, p. 85.
- David F. Kelley and Raymond J. Luebbers, "Stability Analysis of the
Piecewise Linear Recursive Convolution Method in One and Three
Dimensions," Proc. USNC/URSI National Radio Science Meeting,
Atlanta, GA, June 1998, p. 30.
- David F. Kelley and Raymond J. Luebbers, "A Scattered Field FDTD
Formulation for Dispersive Media," Proc. IEEE Antennas and Propagation
Society International Symposium, vol. 1, Montreal, Quebec,
Canada, July 1997, pp. 360-363.
- David F. Kelley and Raymond J. Luebbers, "Calculation of Dispersion
Errors for the Piecewise Linear Recursive Convolution Method,"
Proc. IEEE Antennas and Propagation Society International Symposium,
vol. 3, Baltimore, MD, July 1996, pp. 1652-1655.
- David F. Kelley and Raymond J. Luebbers, "Scattered Field Formulation
of the Piecewise Linear Recursive Convolution Method,"
Proc. USNC/URSI National Radio Science Meeting, Baltimore, MD,
July 1996, p. 117.
- David F. Kelley and Raymond J. Luebbers, "The Piecewise Linear Recursive
Convolution Method for Incorporating Dispersive Media into FDTD,"
Proc. 11th Annual Review of Progress in Applied Computational
Electromagnetics, Monterey, CA, March 1995.
- David F. Kelley and Raymond J. Luebbers, "Comparison of Dispersive Media
Modeling Techniques in the Finite Difference Time Domain Method,"
Proc. USNC/URSI National Radio Science Meeting, Seattle, WA,
June 1994.
PhD Dissertation Information
David F. Kelley, Piecewise Linear Recursive Convolution
for the FDTD Analysis of Propagation through Linear Isotropic
Dispersive Dielectrics, PhD thesis, The Pennsylvania State University, 1999.
Abstract:The finite difference time domain (FDTD) method is a widely-used
numerical approach for the analysis of electromagnetic fields. It can be
applied to problems involving materials that exhibit many different
kinds of electromagnetic behavior and geometries that range from the
simple to the complex. The original formulation of the method was based
upon the assumption that the modeled materials have constant
permittivity, permeability, and conductivity; however, most real
materials exhibit some degree of variation in these quantities with
frequency. Recently, several modifications of the FDTD method have
been proposed that permit its application to linear isotropic
dispersive dielectrics with frequency-dependent permittivities modeled
by the Debye and Lorentz equations. These algorithms vary considerably
in their accuracy, computational efficiency, and ease of implementation.
A new approach is presented here that achieves excellent
performance in all three of these areas and that adds the capability of
analyzing propagation through materials characterized by the
Van Vleck-Weisskopf permittivity model. The method is extended to
incorporate into the FDTD solution more complicated models of
permittivity, such as the Cole-Cole and Havriliak-Negami equations, by
approximating the permittivity using a sum of Debye functions. Another
extension is introduced that provides an efficient
approach for incorporating dispersive dielectrics into the solution of
scattering problems by the FDTD method. Finally, several equations are
derived that can be used to assess the stability and
grid dispersion characteristics of the new algorithms.
Table of Contents
| Chapter No. | Chapter Title |
| 1 | Introduction |
| 2 | Fundamentals of the FDTD Method |
| 3 | Permittivity Models for Dispersive Media |
| 4 | The Piecewise Linear Recursive Convolution Method |
| 5 | Incorporation of Empirical Dielectric Relaxation
Models into FDTD |
| 6 | Scattered Field Formulation of the PLRC Method |
| 7 | Stability and Grid Dispersion Analysis |
| 8 | Conclusion |
| Appendix A | Computational Issues Associated with the
Jonscher and Hill Permittivity Models |
| Appendix B | Asymptotic Forms of the Complex Susceptibility
for Fractional Power Law Models |
| Appendix C | Calculation of Lorentz and Van Vleck-Weisskopf
Update Equation Coefficients Using Real Arithmetic |
| Appendix D | Use of the Imaginary Parts of Debye Functions
as Basis Functions |
|