Solving Maxwell’s equations in singular domains with a Nitsche type method

Assous, Franck; Michaeli, Michael

doi:10.1016/j.jcp.2011.03.013

Cited by 7 publications

(6 citation statements)

References 31 publications

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“…We can compare the values of ℎ 1 2 ( 3 , , 0 ), as the values of the integral characteristics of 1 2 , with the values of the integral characteristic is the element of approximate matrix Green's function computed by our method and is the parameter of the approximation corresponding to the number of the terms in each series of the right hand side of (64).…”

Section: Convergence Analysismentioning

confidence: 99%

“…In recent years a lot of attention has been devoted to derivation of the electric and magnetic fields inside bounded domains with perfect conducting boundaries [1][2][3][4]. The study of the distribution of electromagnetic fields inside a real indoor environment (cabinets, desks, etc.)…”

Section: Introductionmentioning

confidence: 99%

“…The theory (existence, uniqueness, and stability estimate theorems) of time-dependent Maxwell's equations in bounded domains with perfect conducting boundary conditions and smooth current and charge densities has been described by Dautray and Lions in [6]. These theoretical results form the background for many computational methods such as finite element method, finitedifference method, finite-difference time domain method, modal expansion method, and Nitsche type method, which have been handled for computation of the electric and magnetic fields in bounded domains with a perfect conducting boundary [1][2][3][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Computing the Electric and Magnetic Matrix Green’s Functions in a Rectangular Parallelepiped with a Perfect Conducting Boundary

Yakhno

Ersoy

2014

Abstract and Applied Analysis

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A method for the approximate computation of frequency-dependent magnetic and electric matrix Green’s functions in a rectangular parallelepiped with a perfect conducting boundary is suggested in the paper. This method is based on approximation (regularization) of the Dirac delta function and its derivatives, which appear in the differential equations for magnetic and electric Green’s functions, and the Fourier series expansion meta-approach for solving the elliptic boundary value problems. The elements of approximate Green’s functions are found explicitly in the form of the Fourier series with a finite number of terms. The convergence analysis for finding the number of the terms is given. The computational experiments have confirmed the robustness of the method.

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Section: Convergence Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Computing the Electric and Magnetic Matrix Green’s Functions in a Rectangular Parallelepiped with a Perfect Conducting Boundary

Yakhno

Ersoy

2014

Abstract and Applied Analysis

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“…ii) The study of the combined effect of Nitsche's symmetrization (cf [21] and [6]) in the spatial scheme for a Galerkin method and a time discretization, for a second order pde obtained through the combined Maxwell's fields.…”

Section: Introductionmentioning

confidence: 99%

On hp-streamline diffusion and Nitsche schemes for the relativistic Vlasov-Maxwell system

Asadzadeh¹,

Kowalczyk²,

Standar³

2019

Kinetic &Amp; Related Models

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We study stability and convergence of hp-streamline diffusion (SD) finite element, and Nitsche's schemes for the three dimensional, relativistic (3 spatial dimension and 3 velocities), time dependent Vlasov-Maxwell system and Maxwell's equations, respectively. For the hp scheme for the Vlasov-Maxwell system, assuming that the exact solution is in the Sobolev space H s+1 (Ω), we derive global a priori error bound of order O(h/p) s+1/2 , where h(= max K h K ) is the mesh parameter and p(= max K p K ) is the spectral order. This estimate is based on the local version with h K = diam K being the diameter of the phase-space-time element K and p K is the spectral order (the degree of approximating finite element polynomial) for K. As for the Nitsche's scheme, by a simple calculus of the field equations, first we convert the Maxwell's system to an elliptic type equation. Then, combining the Nitsche's method for the spatial discretization with a second order time scheme, we obtain optimal convergence of O(h 2 + k 2 ), where h is the spatial mesh size and k is the time step. Here, as in the classical literature, the second order time scheme requires higher order regularity assumptions.Numerical justification of the results, in lower dimensions, is presented and is also the subject of a forthcoming computational work [20].

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“…The classical Nitsche formulation [3] was introduced several years ago to impose weakly essential boundary conditions in the scalar Laplace operator. Then, it has been worked out more generally to several physical fields [2], and particularly to the Maxwell equations [1]. The Nitsche formulation is well adapted to conforming finite element, leading to efficient numerical scheme in the time dependent cases.…”

mentioning

confidence: 99%

Numerical method for stress fields calculation in dissimilar elastic material with initial crack in axially symmetrical geometry

Michaeli¹,

Assous²,

Golubchik³

2013

AIP Conference Proceedings

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This work deals with the crack problem simulation in dissimilar material. We propose a new numerical approach, based on Nitsche's variational formulation, to handle the interface conditions in the Navier-Lame equations between two or more axially symmetrical subdomains, characterized by different material constants. This gives a numerical method easy to implement, that is able to solve problems in axisymmetric domains with cracks, where the stress fields tend to infinity. We present the variational formulation which provides the solution in terms of displacements field in the case of a crack existence for axisymmetrical plate domain Ω made of several different layers characterized by different material properties.

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Solving Maxwell’s equations in singular domains with a Nitsche type method

Cited by 7 publications

References 31 publications

Computing the Electric and Magnetic Matrix Green’s Functions in a Rectangular Parallelepiped with a Perfect Conducting Boundary

Computing the Electric and Magnetic Matrix Green’s Functions in a Rectangular Parallelepiped with a Perfect Conducting Boundary

On hp-streamline diffusion and Nitsche schemes for the relativistic Vlasov-Maxwell system

Numerical method for stress fields calculation in dissimilar elastic material with initial crack in axially symmetrical geometry

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