scholarly journals On the Well-posedness of the Damped Time-harmonic Galbrun Equation and the Equations of Stellar Oscillations

2021 ◽  
Vol 53 (4) ◽  
pp. 4068-4095
Author(s):  
Martin Halla ◽  
Thorsten Hohage
Keyword(s):  
Well Posedness ◽  
Stellar Oscillations ◽  
Time Harmonic

scholarly journals On well-posedness of time-harmonic problems in an unbounded strip for a thin plate model

2019 ◽  
Vol 17 (6) ◽  
pp. 1487-1529 ◽  
Author(s):  
Laurent Bourgeois ◽  
Lucas Chesnel ◽  
Sonia Fliss
Keyword(s):  
Thin Plate ◽  
Well Posedness ◽  
Plate Model ◽  
Time Harmonic

Well Posedness

2012 ◽  
Author(s):  
G. F. Roach ◽  
I. G. Stratis ◽  
A. N. Yannacopoulos
Keyword(s):  
Variational Formulation ◽  
Eigenvalue Problems ◽  
Dimensional Space ◽  
Well Posedness ◽  
Finite Dimensional Space ◽  
Chiral Media ◽  
Exterior Problems ◽  
Finite Dimensional ◽  
Time Harmonic ◽  
Interior Domain

This chapter presents rigorous mathematical results concerning the solvability and well posedness of time-harmonic problems for complex electromagnetic media, with a special emphasis on chiral media. It also presents some results concerning eigenvalue problems in cavities filled with complex electromagnetic materials. The chapter also studies the behaviour of the interior domain problem for a chiral medium in the limit of low chirality. Next, it presents some comments related to the well posedness and solvability of exterior problems. Finally, using an appropriate finite-dimensional space and the variational formulation of the discretised version of the original boundary value problem, this chapter obtains numerical methods for the solution of the Maxwell equations for chiral media.

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.

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 Uniqueness in Inverse Electromagnetic Conductive Scattering by Penetrable and Inhomogeneous Obstacles with a Lipschitz Boundary

2012 ◽  
Vol 2012 ◽  
pp. 1-21
Author(s):  
Fenglong Qu
Keyword(s):  
Electromagnetic Waves ◽  
Direct Problem ◽  
Field Data ◽  
Near Field ◽  
Uniqueness Result ◽  
Well Posedness ◽  
Surface Parameter ◽  
Large Sphere ◽  
Time Harmonic ◽  
Electric Dipoles

This paper is concerned with the problem of scattering of time-harmonic electromagnetic waves by a penetrable, inhomogeneous, Lipschitz obstacle covered with a thin layer of high conductivity. The well posedness of the direct problem is established by the variational method. The inverse problem is also considered in this paper. Under certain assumptions, a uniqueness result is obtained for determining the shape and location of the obstacle and the corresponding surface parameterλ(x)from the knowledge of the near field data, assuming that the incident fields are electric dipoles located on a large sphere with polarizationp∈ℝ3. Our results extend those in the paper by F. Hettlich (1996) to the case of inhomogeneous Lipschitz obstacles.

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 Μερικές διαφορικές εξισώσεις και προβλήματα της επιστήμης των υλικών

2014 ◽  
Author(s):  
Ευτυχία Αργυροπούλου
Keyword(s):  
Hilbert Space ◽  
Main Part ◽  
Semigroup Theory ◽  
Divergence Form ◽  
Elliptic Type ◽  
Well Posedness ◽  
Initial Value ◽  
Time Harmonic ◽  
Periodic Unfolding Method ◽  
Unfolding Method

The main objective of this thesis is the homogenization of partial dierentialequations (mainly Maxwell'As equations) describing electromagneticphenomena in complex media. In particular, we study the homogenization ofMaxwell'As equations focusing on the periodic unfolding method in complexmedia under Drude-Born-Fedorov type, local in time, constitutive relations.Firstly, we formulate Maxwell'A s problem as an evolution initial value(Cauchy) problem in a Hilbert space supplemented with the constitutiverelations of a bianisotropic medium (the most general linear medium in electromagnetics).Further, we analyze the notion of homogenization and weapply it as examples to equations of elliptic type in divergence form and toMaxwell'As system in bianisotropic media.We present also the method of periodic unfolding in the case of an ellipticpartial dierential equation and in the main part of this work we considerthe problem of the well-posedness of the time-dependent Maxwell'As equationsin a Drude-Born-Fedorov type environment considering the elds to beelements of an appropriate Hilbert space. In order to prove the existence anduniqueness we apply the Faedo-Galerkin method and for the continuous dependencefrom the initial data we use semigroup theory for operators. Therest of the main part of the thesis deals with the homogenization of theconsidered problem, using the periodic unfolding method.In the last chapter, we examine the time-harmonic Maxwell problem ina bianisotropic cavity, which we study by transforming it to an eigenvalueproblem.

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