Abstract
We present a Lagrangian approach for increasing the accuracy of the Finite-Difference Time-Domain method in modeling electromagnetic wave interactions in geometries involving curved boundaries. The methodology provides for a mapping of the physical computational domain onto a reference domain with all its boundaries parallel to a Cartesian coordinate system. The Lagrangian formulation offers a convenient way to define a modified set of Maxwell’s equations on the reference domain. This modified set of equations is then discretized using the staggered Cartesian grids of the Yee’s lattice. The attributes of the method are demonstrated through its application to the calculation of the eigenfrequencies of a two-dimensional metallic resonator and the transmission properties of a two-dimensional periodic structure.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
MEFiSTo (Multi-purpose Electromagnetic Field Simulation Tool). Faustus Scientific Corporation, Victoria, B.C., Canada, 2007. http://www.faustcorp.com.
A. C. Cangellaris, C.-C. Lin, and K. K. Mei. Point-matched time domain finite element methods for electromagnetic radiation and scattering. IEEE Trans. Antenn. Propag., 35:1160–1173, 1987.
A. C. Cangellaris and D. B. Wright. Analysis of the numerical error caused by the stair-stepped approximation of a conducting boundary in FDTD simulations of electromagnetic phenomena. IEEE Trans. Antenn. Propag., 39:1518–1525, Oct. 1991.
D. S. Chandrasekharaiah, and L. Debnath. Continuum Mechanics. Academic Press, San Diego, 1994.
R. E. Collin. Foundations for Microwave Engineering. McGraw-Hill, New York, 1966.
R. D. Cook, D. S. Malkus, M. E. Plesha, and R. J. Witt. Concepts and Applications of Finite Element Analysis. John Wiley, New York, 2001.
C. Fumeaux, D. Baumann, and R. Vahldieck. Finite-volume time-domain analysis of a cavity-backed archimedean spiral antenna. IEEE Trans. Antenn. Propag., 54:844–851, Mar. 2006.
R. F. Harrington. Time Harmonic Electromagnetic Fields. John Wiley, New York, 2001.
W. J. R. Hoefer. The transmission line matrix method – theory and applications. IEEE Trans. Microw. Theory Tech., 33:882–893, 1985.
R. Holland. Finite difference solutions of Maxwell’s equations in generalized nonorthogonal coordinates. IEEE Trans. Nucl. Sci., 30:4589–4591, 1983.
G. Li and N. R. Aluru. A Lagrangian approach for electrostatic analysis of deformable conductors. J. Microelectromech. Syst., 11:245–254, 2002.
R. M. Mäkinen, H. De Gersem, T. Weiland, and M. A. Kivikoski. Modeling of lossy curved surfaces in 3-D FIT/FDTD techniques. IEEE Trans. Antenn. Propag., 54:3490–3498, Nov. 2006.
K. K. Mei, A. Cangellaris, and D. J. Angelakos. Conformal time domain finite difference method. Radio Sci., 19:1145–1147, 1984.
J. A. Russer, P. S. Sumant, and A. C. Cangellaris. A Lagrangian approach for the handling of curved boundaries in the finite-difference time-domain method. IEEE MMT-S International Microwave Symposium, pages 717–720, June 2007.
A. Taflove and S. Hagness. Computational Electrodynamics: The Finite-Difference Time-Domain Method. Artech House, Boston, 2005.
K. S. Yee. Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Trans. Antenn. Propag., 14:302–307, May 1966.
W. Yu, Y. Liu, T. Su, N.-T. Huang, and R. Mittra. A robust parallel conformal finite-difference time-domain processing package using the MPI library. IEEE Antenn. Propag. Mag., 47:39–59, June 2005.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Russer, J.A., Sumant, P.S., Cangellaris, A.C. (2008). Modeling of Curved Boundaries in the Finite-Difference Time-Domain Method using a Lagrangian Approach. In: Russer, P., Siart, U. (eds) Time Domain Methods in Electrodynamics. Springer Proceedings in Physics, vol 121. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68768-9_5
Download citation
DOI: https://doi.org/10.1007/978-3-540-68768-9_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-68766-5
Online ISBN: 978-3-540-68768-9
eBook Packages: EngineeringEngineering (R0)