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.

scholarly journals Well Posedness and Finite Element Approximability of Three-Dimensional Time-Harmonic Electromagnetic Problems Involving Rotating Axisymmetric Objects

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 218 ◽  
Author(s):  
Praveen Kalarickel Ramakrishnan ◽  
Mirco Raffetto
Keyword(s):  
Finite Element ◽  
Boundary Value Problems ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Well Posedness ◽  
Electromagnetic Problems ◽  
Time Harmonic ◽  
First Time

A set of sufficient conditions for the well posedness and the convergence of the finite element approximation of three-dimensional time-harmonic electromagnetic boundary value problems involving non-conducting rotating objects with stationary boundaries or bianisotropic media is provided for the first time to the best of authors’ knowledge. It is shown that it is not difficult to check the validity of these conditions and that they hold true for broad classes of practically important problems which involve rotating or bianisotropic materials. All details of the applications of the theory are provided for electromagnetic problems involving rotating axisymmetric objects.

Transient and Time-Harmonic Infinite Elements for Near-Surface Computations of Three-Dimensional Structures Submerged in a Half-Space

1995 ◽  
Author(s):  
Loukas F. Kallivokas ◽  
Jacobo Bielak
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Half Space ◽  
Three Dimensional ◽  
Scattering Problems ◽  
Near Surface ◽  
Infinite Element ◽  
Infinite Elements ◽  
Time Harmonic ◽  
Element Method

Abstract This paper is concerned with the numerical solution by the finite element method of transient and time-harmonic three-dimensional acoustic scattering problems in infinite and semi-infinite domains. Its main objective is to illustrate how a local second-order surface-only infinite element — either transient or time-harmonic — developed recently for the three-dimensional wave equation in a full-space can be applied readily to scattering problems with penetrable objects near a planar free surface. Taking a problem in structural acoustics as a prototype, the combined infinite element-finite element method is used here to determine the total and scattered pressure patterns generated when a traveling plane wave impinges upon a structure of general geometry submerged in an acoustic fluid in half-space. One key feature of this methodology is that the ordinary differential equations that result from the spatial discretization maintain the symmetry and sparsity associated with problems defined only over interior domains; the resulting equations can then be solved by standard step-by-step time integration techniques. Thus, the combination of low bandwidth matrices with the ease of use of the infinite elements places the method in an ideal position to meet the large computational demands typically associated with large-scale underwater acoustics problems.

WELL-POSEDNESS AND FINITE ELEMENT APPROXIMABILITY OF TIME-HARMONIC ELECTROMAGNETIC BOUNDARY VALUE PROBLEMS INVOLVING BIANISOTROPIC MATERIALS AND METAMATERIALS

2009 ◽  
Vol 19 (12) ◽  
pp. 2299-2335 ◽  
Author(s):  
PAOLO FERNANDES ◽  
MIRCO RAFFETTO
Keyword(s):  
Finite Element ◽  
Original Problem ◽  
Boundary Value ◽  
Well Posedness ◽  
Problem Domain ◽  
Scattering Problems ◽  
Lipschitz Continuous ◽  
Time Harmonic ◽  
Microwave Components ◽  
Well Posed

A boundary value problem for the time harmonic Maxwell system is investigated through a variational formulation which is shown to be equivalent to it and well-posed if and only if the original problem is. Different bianisotropic materials and metamaterials filling subregions of the problem domain with Lipschitz continuous boundaries are allowed. Well-posedness and finite element approximability of the variational problem are proved by Lax–Milgram and Strang lemmas for a class of material configurations involving bianisotropic materials and metamaterials. Belonging to this class is not necessary, yet, for well-posedness and finite element approximability. Nevertheless, the material configurations of many radiation or scattering problems and many models of microwave components involving bianisotropic materials or metamaterials belong to the above class. Moreover, none of the other available tools commonly used to prove well-posedness seems to be able to cope with the material configurations left out by our treatment.

scholarly journals 3D Unsteady Diffusion and Reaction-Diffusion with Singularities by GFEM with 27-Node Hexahedrons

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Estaner Claro Romão
Keyword(s):  
Finite Element ◽  
Variable Temperature ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Third Order ◽  
Order Of Accuracy ◽  
Finite Element Approximations ◽  
Temperature Solution ◽  
The One ◽  
Primary Variable

The Galerkin Finite Element Method (GFEM) with 8- and 27-node hexahedrons elements is used for solving diffusion and transient three-dimensional reaction-diffusion with singularities. Besides analyzing the results from the primary variable (temperature), the finite element approximations were used to find the derivative of the temperature in all three directions. This technique does not provide an order of accuracy compatible with the one found in the temperature solution; thereto, a calculation from the third order finite differences is proposed here, which provide the best results, as demonstrated by the first two applications proposed in this paper. Lastly, the presentation and the discussion of a real application with two cases of boundary conditions with singularities are proposed.

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 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).

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