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Time domain electromagnetic scattering using finite elements and perfectly matched layers. (English) Zbl 1067.78013

Summary: We consider a model for the interrogation of a planar Debye medium by a non-harmonic microwave pulse from an antenna source in free space, and we compute the reflected solution using finite elements in the spatial variables and finite differences in the time variable. Perfectly matched layers (PMLs) and an absorbing boundary condition are used to damp waves interacting with artificial boundaries imposed to allow finite computational domains. We present simulation results showing that numerical reflections from interfaces at PML boundaries can be controlled.

MSC:

78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
78A45 Diffraction, scattering
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
78M25 Numerical methods in optics (MSC2010)
Full Text: DOI

References:

[1] Albanese, R.; Penn, J.; Medina, R., Short-rise-time microwave pulse propagation through dispersive biological media, J. Opt. Soc. Am. A, 6, 9, 1441-1446 (1989)
[2] Balanis, C. A., Advanced Engineering Electromagnetics (1989), John Wiley and Sons: John Wiley and Sons New York
[3] Banks, H. T.; Buksas, M. W.; Lin, T., Electromagnetic Material Interrogation Using Conductive Interfaces and Acoustic Wavefronts (2000), SIAM: SIAM Philadelphia · Zbl 1008.78500
[4] Banks, H. T.; Kepler, G. M., Reduced order computational methods for electromagnetic material interrogation using pulsed signals and conductive reflecting interfaces, J. Inverse Ill-posed Problems, 11, 4, 10-20 (2003) · Zbl 1048.35130
[5] Berenger, J.-P., A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 114, 2, 185-200 (1994) · Zbl 0814.65129
[6] Blaschak, J. G.; Franzen, J., Precursor propagation in dispersive media from short-rise-time pulses at oblique incidence, J. Opt. Soc. Am. A, 12, 1501-1512 (1995)
[7] V.A. Bokil, M.W. Buksas. A 2D mixed finite element formulation of the uniaxial perfectly matched layer, J. Comput. Phys. (submitted); V.A. Bokil, M.W. Buksas. A 2D mixed finite element formulation of the uniaxial perfectly matched layer, J. Comput. Phys. (submitted)
[8] Brillouin, L., Wave Propagation and Group Velocity (1960), Academic Press: Academic Press New York · Zbl 0094.41601
[9] Buksas, M. W., Implementing the perfectly matched layer absorbing boundary condition with mimetic differencing schemes, (Teixeira, F. L., Geometric Methods for Computational Electromagnetics. Geometric Methods for Computational Electromagnetics, Progress in Electromagnetic Research Series, vol. 32 (2001), EMW Publishing: EMW Publishing Cambridge, MA), 383-411
[10] Engquist, B.; Majda, A., Absorbing boundary conditions for the numerical simulation of waves, Math. Computat., 31, 139, 629-651 (1977) · Zbl 0367.65051
[11] Friedlander, F. G., Introduction to the Theory of Distributions (1982), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0499.46020
[12] Petropoulos, P. G., On the termination of the perfectly matched layer with local absorbing boundary conditions, J. Comput. Phys., 143, 665-673 (1998) · Zbl 0920.65077
[13] Sacks, Z. S.; Kingsland, D. M.; Lee, R.; Lee, J.-F., A perfectly matched anisotropic absorber for use as an absorbing boundary condition, IEEE Trans. Antennas Propagat., 43, 12, 1460-1463 (1995)
[14] Turkel, E.; Yefet, A., Absorbing PML boundary layers for wave-like equations, Appl. Numer. Math., 27, 533-557 (1998) · Zbl 0933.35188
[15] Ziolkowski, R. W., Time-derivative Lorentz material model-based absorbing boundary condition, IEEE Trans. Antennas Propagat., 45, 1530-1535 (1997)
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