STRONG AND WEAK FORMS OF THE METHOD OF MOMENTS AND THE COUPLED DIPOLE METHOD FOR SCATTERING OF TIME-HARMONIC ELECTROMAGNETIC FIELDS

1992 ◽  
Vol 03 (03) ◽  
pp. 583-603 ◽  
Author(s):  
AKHLESH LAKHTAKIA
Keyword(s):  
Electromagnetic Fields ◽  
Method Of Moments ◽  
Electromagnetic Scattering ◽  
Final Section ◽  
The Other ◽  
Numerical Techniques ◽  
Scattering Problems ◽  
Time Harmonic

Algorithms based on the method of moments (MOM) and the coupled dipole method (CDM) are commonly used to solve electromagnetic scattering problems. In this paper, the strong and the weak forms of both numerical techniques are derived for bianisotropic scatterers. The two techniques are shown to be fully equivalent to each other, thereby defusing claims of superiority often made for the charms of one technique over the other. In the final section, reductions of the algorithms for isotropic dielectric scatterers are explicitly given.

scholarly journals Application of Two-Dimensional Compressive Sensing to Wavelet Method of Moments for Fast Analysis of Wide-Angle Electromagnetic Scattering Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Yi Liu ◽  
Qi Qi ◽  
Xinyuan Cao ◽  
Mingsheng Chen ◽  
Guoqing Deng ◽  
...  
Keyword(s):  
Compressive Sensing ◽  
Method Of Moments ◽  
Electromagnetic Scattering ◽  
Wide Angle ◽  
Two Dimensional ◽  
Induced Current ◽  
Linear Superposition ◽  
Scattering Problems ◽  
Wavelet Method ◽  
Right Hand

To efficiently solve the electromagnetic scattering problems over a wide incident angle, a novel scheme by introducing the two-dimensional compressive sensing theory into the wavelet method of moments is proposed. In this scheme, a linear system of equations with multiple right-hand sides in wavelet domain is formed firstly, and one side of the bilateral sparse transform to the induced current matrix is simultaneously accomplished and then the bilateral measurement of the induced current matrix is operated by the linear superposition of the right-hand side vectors a few times and the extraction of rows from the impedance matrix. Finally, after completing the other side of the bilateral sparse transform, the wide-angle problems can be solved rapidly by two times of recovery algorithm with prior knowledge. The basic principle is elaborated in detail, and the effectiveness is demonstrated by numerical experiments.

scholarly journals Three-Dimensional Time-Harmonic Electromagnetic Scattering Problems from Bianisotropic Materials and Metamaterials: Reference Solutions Provided by Converging Finite Element Approximations

Electronics ◽  
2020 ◽  
Vol 9 (7) ◽  
pp. 1065
Author(s):  
Praveen Kalarickel Ramakrishnan ◽  
Mirco Raffetto
Keyword(s):  
Finite Element ◽  
Electromagnetic Scattering ◽  
Three Dimensional ◽  
Well Posedness ◽  
Scattering Problems ◽  
Finite Element Approximations ◽  
Time Harmonic ◽  
The Media ◽  
Constitutive Parameters ◽  
Numerical Approaches

A recently developed theory is applied to deduce the well posedness and the finite element approximability of time-harmonic electromagnetic scattering problems involving bianisotropic media in free-space or inside waveguides. In particular, three example problems are considered of which one deals with scattering from plasmonic gratings that exhibit bianisotropy while the other two deal with bianisotropic obstacles inside waveguides. The hypotheses that guarantee the reliability of the numerical results are verified, and the ranges of the constitutive parameters of the media involved for which the finite element solutions are guaranteed to be reliable are deduced. It is shown that, within these ranges, there can be significant bianisotropic effects for the practical media considered as examples. The ensured reliability of the obtained results can make them useful as benchmarks for other numerical approaches. To the best of our knowledge, no other tool can guarantee reliable solutions.

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