Sage Journals: Discover world-class research

Abstract

This paper proposes the complex frequency shifted (CFS) perfectly matched layer (PML) of dispersive media for finite-difference time-domain (FDTD) method combined with weighted Laguerre polynomials (WLP). According to the property of Laguerre basis function, the relative dielectric constant ε _r (ω) of dispersive media and complex frequency shifted (CFS) PML parameters, auxiliary differential equation (ADE) technique is introduced. Based on the ADE technique, the relationship between field components and auxiliary differential variables is derived in Laguerre domain. Using ADE scheme, the relationship between electric flux density D and electric fieldE is derived in Laguerre domain. Substituting auxiliary differential variables into CPML absorbing boundary conditions, using auxiliary differential variables, electric flux density D of order q can be expressed directly by magnetic field H in Laguerre domain. Using the same procedure, magnetic field H of order q can be expressed directly by electric field E in Laguerre domain. Inserting H of order q$ into D , using the relationship between D and E , and using central difference scheme, the formulations for dispersive media are obtained. In order to validate the efficiency of the presented method, two numerical examples are simulated. Numerical results show that, compared with the Berenger PML (BPML) and nearly PML (NPML), the CFS-PML has about more than 24 dB improvement in terms of the maximum relative error and much lower reflection error for the late-time region.

Keywords

Auxiliary differential equation (ADE)dispersive materials finite-difference time-domain (FDTD)

Get full access to this article

View all access options for this article.

References

Xiong

, Chen

, Cai

Z.Y.

and Chen

, A Numerically Efficient Method for the FDTD Analysis of Shielding Effectiveness of Large Shielding Enclosures with Thin-slots, International Journal of Applied Electromagnetics and Mechanics 40 (2012), 251-258.

Mao

Y.F.

, Chen

, Xia

J.-L.

, Chen

and Tang

J.-Z.

, Application of the Leapfrog ADI FDTD Method to Periodic Structures, IEEE Antennas and Wireless Propagation Letters 12 (2013), 599-602.

Pyrialakos

G.G.

, Kantartzis

N.V.

and Tsiboukis

T.D.

, Design of nanocomposite EMC structures via unconditionally-stable nonstandard time-domain schemes and efficient GPU implementation, International Journal of Applied Electromagnetics and Mechanics 46 (2014), 389-399.

Zheng

and Chen

, Numerical dispersion analysis of the unconditionally stable 3-D ADI-FDTD method, IEEE Transactions on Microwave Theory and Techniques 49 (2001), 1006-1009.

Grande

and Pereda

J.A.

, Accuracy limitations of the locally one-dimensional FDTD technique, IEEE Antennas and Wireless Propagation Letters 13 (2014), 1180-1183.

Chung

Y.S.

, Sarkar

T.K.

, Jung

B.H.

and Salazar-Palma

, An unconditionally stable scheme for the finite-difference time-domain method, IEEE Transactions on Microwave Theory and Techniques 51 (2003), 697-704.

and Swaminathan

, A Laguerre-FDTD formulation for frequency-dependent dispersive materials, IEEE Microwave and Wireless Components Letters 21 (2011), 225-227.

Chen

W.J.

, Shao

and Wang

B.Z.

, ADE-Laguerre-FDTD Method for Wave Propagation in General Dispersive Materials, IEEE Microwave and Wireless Components Letters 23 (2013), 228-230.

Berenger

, A Perfectly Matched Layer for the Absorption of Electromagnetic, Journal of Computational Physics 114 (1994), 185-200.

10.

Chen

, Fang

D.G.

and Zhou

B.H.

, Modified Berenger PML Absorbing Boundary Condition for FD-TD Meshes, IEEE Microwave Guided Wave Letters 5 (1995), 399-401.

11.

Cummer

S.A.

, A Simple, Nearly Perfectly Matched Layer for General Electromagnetic Media, IEEE Microwave and Wireless Components Letters 13 (2003), 128-130.

12.

Gedney

S.D.

, An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices, IEEE Transactions on Antennas and Propagation 44 (1996), 1630-1639.

13.

Fang

and Wu

, Generalized perfectly matched layer for the absorption of propagating and evanescent waves in lossless and lossy media, IEEE Transactions on Microwave Theory and Techniques 44 (1996), 2216-2222.

14.

Zhao

and Cangellaris

A.C.

, GT-PML: Generalized theory of perfectly matched layers and its application to the reflectionless truncation of finite-difference time-domain grids, IEEE Transactions on Microwave Theory and Techniques 44 (1996), 2555-2563.

15.

Chen

W.J.

, Shao

, Chen

H.B.

and Wang

B.Z.

, Nearly PML for ADE-WLP-FDTD Modeling in Two-Dimensional Dispersive Media, IEEE Microwave and Wireless Components Letters 24 (2014), 75-77.

16.

Kuzuoglu

and Mittra

, Frequency dependence of the constitutive parameters of causal perfectly matched anisotropic absorbers, IEEE Microwave Guided Wave Letters 6 (1996), 447-449.

17.

Liu

J.F.

, Wan

G.B.

, Zhang

J.S.

and Xi

X.L.

, An Effective CFS-PML Implementation for Cylindrical Coordinate FDTD Method, IEEE Microwave and Wireless Components Letters 22 (2012), 300-302.

18.

Cai

Z.Y.

, Chen

, Liu

, Duan

and Mao

, The CFS-PML for Periodic Laguerre-Based FDTD Method, IEEE Microwave and Wireless Components Letters 22 (2012), 164-166.

19.

Gedney

S.D.

, The perfectly matched layer absorbing medium, in: Advances in Computational Electrodynamics: The Finite Difference Time Domain, A. Taflove, ed., Boston, MA: Artech House, 1998, pp. 263-340.

The CFS-PML for 2-D WLP-FDTD method of dispersive materials

Abstract

Keywords

Get full access to this article

References