scholarly journals Convergence of the uniaxial PML method for time-domain electromagnetic scattering problems

2021 ◽  
Author(s):  
Changkun Wei ◽  
Jiaqing Yang ◽  
Bo Zhang
Keyword(s):  
Time Domain ◽  
Electromagnetic Scattering ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Scattering Problems ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Time Domain Electromagnetic ◽  
Numer Anal ◽  
The Time Domain

In this paper, we propose and study the uniaxial perfectly matched layer (PML) method for three-dimensional time-domain electromagnetic scattering problems, which has a great advantage over the spherical one in dealing with problems involving anisotropic scatterers. The truncated uniaxial PML problem is proved to be well-posed and stable, based on the Laplace transform technique and the energy method. Moreover, the $L^2$-norm and $L^{\infty}$-norm error estimates in time are given between the solutions of the original scattering problem and the truncated PML problem, leading to the exponential convergence of the time-domain uniaxial PML method in terms of the thickness and absorbing parameters of the PML layer. The proof depends on the error analysis between the EtM operators for the original scattering problem and the truncated PML problem, which is different from our previous work (SIAM J. Numer. Anal. 58(3) (2020), 1918-1940).

Exponential convergence of Cartesian PML method for Maxwell’s equations in a two-layer medium

2020 ◽  
Vol 54 (3) ◽  
pp. 929-956
Author(s):  
Xiaoqi Duan ◽  
Xue Jiang ◽  
Weiying Zheng
Keyword(s):  
Electromagnetic Scattering ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Numerical Solutions ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Layered Media ◽  
Theoretical Work ◽  
Scattering Problems ◽  
Layer Medium

The perfectly matched layer (PML) method is extensively studied for scattering problems in homogeneous background media. However, rigorous studies on the PML method in layered media are very rare in the literature, particularly, for three-dimensional electromagnetic scattering problems. Cartesian PML method is favorable in numerical solutions since it is apt to deal with anisotropic scatterers and to construct finite element meshes. Its theories are more difficult than circular PML method due to anisotropic wave-absorbing materials. This paper presents a systematic study on the Cartesian PML method for three-dimensional electromagnetic scattering problem in a two-layer medium. We prove the well-posedness of the PML truncated problem and that the PML solution converges exponentially to the exact solution as either the material parameter or the thickness of PML increases. To the best of the authors’ knowledge, this is the first theoretical work on Cartesian PML method for Maxwell’s equations in layered media.

Hydrogeophysical exploration of three-dimensional salinity anomalies with the time-domain electromagnetic method (TDEM)

2010 ◽  
Vol 380 (3-4) ◽  
pp. 318-329 ◽  
Author(s):  
Peter Bauer-Gottwein ◽  
Bibi N. Gondwe ◽  
Lars Christiansen ◽  
Daan Herckenrath ◽  
Lesego Kgotlhang ◽  
...  
Keyword(s):  
Time Domain ◽  
Three Dimensional ◽  
Electromagnetic Method ◽  
Time Domain Electromagnetic ◽  
The Time Domain

scholarly journals Electromagnetic scattering for time-domain Maxwell’s equations in an unbounded structure

2017 ◽  
Vol 27 (10) ◽  
pp. 1843-1870 ◽  
Author(s):  
Yixian Gao ◽  
Peijun Li
Keyword(s):  
Time Domain ◽  
Electromagnetic Scattering ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Scattering Problem ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
The Time Domain

The goal of this work is to study the electromagnetic scattering problem of time-domain Maxwell’s equations in an unbounded structure. An exact transparent boundary condition is developed to reformulate the scattering problem into an initial-boundary value problem in an infinite rectangular slab. The well-posedness and stability are established for the reduced problem. Our proof is based on the method of energy, the Lax–Milgram lemma, and the inversion theorem of the Laplace transform. Moreover, a priori estimates with explicit dependence on the time are achieved for the electric field by directly studying the time-domain Maxwell equations.

On: “Induced‐polarization effects in time‐domain electromagnetic measurements” by M. F. Flis, G. A. Newman, and G. W. Hohmann (GEOPHYSICS, 54, 514–523, April 1989).

Geophysics ◽  
1989 ◽  
Vol 54 (12) ◽  
pp. 1655-1656 ◽  
Author(s):  
Richard Smith
Keyword(s):  
Time Domain ◽  
Three Dimensional ◽  
Polarization Current ◽  
Electromagnetic Measurements ◽  
Charging Current ◽  
Time Domain Electromagnetic ◽  
Time Domain Response ◽  
The Time Domain ◽  
Theoretical Results ◽  
Insight Into

Flis et al. provide useful insight into the time‐domain response of three‐dimensional polarizable bodies; however, their inference that negative transients are caused by a polarization current which reverses direction disagrees with the previously published theoretical results of Smith et al. (1988) and Smith and West (1988), who found that the polarization current is always negative (provided that the chargeability m and charging current are positive).

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