scholarly journals Mosco convergence for $H$ (curl) spaces, higher integrability for Maxwell's equations, and stability in direct and inverse EM scattering problems

2019 ◽  
Vol 21 (10) ◽  
pp. 2945-2993 ◽  
Author(s):  
Hongyu Liu ◽  
Luca Rondi ◽  
Jingni Xiao
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Mosco Convergence ◽  
Em Scattering ◽  
Scattering Problems ◽  
Higher Integrability

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.

Sumudu Applications to Maxwell's Equations

PIERS Online ◽  
2009 ◽  
Vol 5 (4) ◽  
pp. 355-360 ◽  
Author(s):  
Fethi Bin Muhammad Belgacem
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations

Maxwell’s Equations versus Newton’s Third Law

2018 ◽  
Author(s):  
Glyn Kennell ◽  
Richard Evitts
Keyword(s):  
Electric Fields ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Simulated Data ◽  
Numerical Data ◽  
Transport Equations ◽  
Concentration Gradients ◽  
Third Law

The presented simulated data compares concentration gradients and electric fields with experimental and numerical data of others. This data is simulated for cases involving liquid junctions and electrolytic transport. The objective of presenting this data is to support a model and theory. This theory demonstrates the incompatibility between conventional electrostatics inherent in Maxwell's equations with conventional transport equations. <br>

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