A combined method for computing the field of a point source in a surface waveguide.
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Kirpichnikova, N.Ya., Philippov, V.B., Fadeeva, S.Yu. (2005)
Zapiski Nauchnykh Seminarov POMI
Roy Choudhuri, S.K., Chatterjee, Gargi (1990)
International Journal of Mathematics and Mathematical Sciences
George Dassios (1982)
Δελτίο της Ελληνικής Μαθηματικής Εταιρίας
Rawlins, A.D. (2004)
Journal of Applied Mathematics
Alain Bamberger, François Coron, Jean-Michel Ghidaglia (1987)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Valery Yakhno, Ali Sevimlican (2011)
Applications of Mathematics
The time-dependent system of partial differential equations of the second order describing the electric wave propagation in vertically inhomogeneous electrically and magnetically biaxial anisotropic media is considered. A new analytical method for solving an initial value problem for this system is the main object of the paper. This method consists in the following: the initial value problem is written in terms of Fourier images with respect to lateral space variables, then the resulting problem...
Michael S. Vogelius, Darko Volkov (2000)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Michael S. Vogelius, Darko Volkov (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
We consider solutions to the time-harmonic Maxwell's Equations of a TE (transverse electric) nature. For such solutions we provide a rigorous derivation of the leading order boundary perturbations resulting from the presence of a finite number of interior inhomogeneities of small diameter. We expect that these formulas will form the basis for very effective computational identification algorithms, aimed at determining information about the inhomogeneities from electromagnetic boundary measurements. ...
Houssem Haddar, Armin Lechleiter (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
We analyze the accuracy and well-posedness of generalized impedance boundary value problems in the framework of scattering problems from unbounded highly absorbing media. We restrict ourselves in this first work to the scalar problem (E-mode for electromagnetic scattering problems). Compared to earlier works, the unboundedness of the rough absorbing layer introduces severe difficulties in the analysis for the generalized impedance boundary conditions, since classical compactness arguments are no...
A. G. Ramm (2009)
Bulletin of the Polish Academy of Sciences. Mathematics
A class of infinite-dimensional dissipative dynamical systems is defined for which there exists a unique equilibrium point, and the rate of convergence to this point of the trajectories of a dynamical system from the above class is exponential. All the trajectories of the system converge to this point as t → +∞, no matter what the initial conditions are. This class consists of strongly dissipative systems. An example of such systems is provided by passive systems in network theory (see, e.g., MR0601947...
J. M. Combes, P. D. Hislop, A. Tip (1999)
Annales de l'I.H.P. Physique théorique
Kim Dang Phung (2000)
ESAIM: Control, Optimisation and Calculus of Variations
Kim Dang Phung (2010)
ESAIM: Control, Optimisation and Calculus of Variations
We consider the exact controllability and stabilization of Maxwell equation by using results on the propagation of singularities of the electromagnetic field. We will assume geometrical control condition and use techniques of the work of Bardos et al. on the wave equation. The problem of internal stabilization will be treated with more attention because the condition divE=0 is not preserved by the system of Maxwell with Ohm's law.
Loula Fezoui, Stéphane Lanteri, Stéphanie Lohrengel, Serge Piperno (2005)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
A Discontinuous Galerkin method is used for to the numerical solution of the time-domain Maxwell equations on unstructured meshes. The method relies on the choice of local basis functions, a centered mean approximation for the surface integrals and a second-order leap-frog scheme for advancing in time. The method is proved to be stable for cases with either metallic or absorbing boundary conditions, for a large class of basis functions. A discrete analog of the electromagnetic energy is conserved...
Loula Fezoui, Stéphane Lanteri, Stéphanie Lohrengel, Serge Piperno (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
A Discontinuous Galerkin method is used for to the numerical solution of the time-domain Maxwell equations on unstructured meshes. The method relies on the choice of local basis functions, a centered mean approximation for the surface integrals and a second-order leap-frog scheme for advancing in time. The method is proved to be stable for cases with either metallic or absorbing boundary conditions, for a large class of basis functions. A discrete analog of the electromagnetic energy is conserved...
Małgorzata Kopisz (1988)
Applicationes Mathematicae
B. Ducomet (1992)
Annales de l'I.H.P. Physique théorique
Li, Ping, Stagnitti, Frank (2004)
Mathematical Problems in Engineering
Li, Ying, Luo, Jianshu, Ni, Guyan, Shi, Jiyuan (2010)
Mathematical Problems in Engineering
Charles A. Stuart, Huan-Song Zhou (2001)
Annales de l'I.H.P. Analyse non linéaire
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