共查询到20条相似文献，搜索用时 15 毫秒
1.
In this article, we consider the time‐dependent Maxwell's equations in a bounded domain when dispersive media are involved. The Crank‐Nicolson scheme is developed to approximate the electric field equation by Nedelec edge elements and is proved to be optimal convergent in energy norm. The analysis is carried out for Debye medium, but the same results hold true for other dispersive media such as plasma and Lorentz medium. Furthermore, our analysis extends straightforward to cases when a dispersive medium and a simple medium (such as air) are coupled. Mathematics Subject Classification (2000): 65N30, 35L15, 78‐08. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 相似文献
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In this paper, we study a numerical scheme to solve coupled Maxwell's equations with a nonlinear conductivity. This model plays an important role in the study of type‐II superconductors. The approximation scheme is based on backward Euler discretization in time and mixed conforming finite elements in space. We will prove convergence of this scheme to the unique weak solution of the problem and develop the corresponding error estimates. As a next step, we study the stability of the scheme in the quasi‐static limit ? → 0 and present the corresponding convergence rate. Finally, we support the theory by several numerical experiments. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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The main purpose of the present article is to prove the discrete compactness property for Arnold‐Boffi‐Falk spaces of any order. Results of numerical experiments confirming the theory are also reported. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005 相似文献
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The energy‐conserved splitting finite‐difference time‐domain (EC‐S‐FDTD) method has recently been proposed to solve the Maxwell equations with second order accuracy while numerically keep the L2 energy conservation laws of the equations. In this paper, the EC‐S‐FDTD scheme for the 3D Maxwell equations is proved to be energy‐conserved and unconditionally stable in the discrete H1 norm. The EC‐S‐FDTD scheme is of second‐order accuracy both in time step and spatial steps, which suggests the super‐convergence of this scheme in the discrete H1 norm. And the divergence of the electric field of the EC‐S‐FDTD scheme in the discrete L2 norm is second‐order accurate. Numerical experiments confirm our theoretical analysis. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
5.
Yunqing Huang Jichun Li Qun Lin 《Numerical Methods for Partial Differential Equations》2012,28(6):1794-1816
In this article, we consider the time‐dependent Maxwell's equations modeling wave propagation in metamaterials. One‐order higher global superclose results in the L2 norm are proved for several semidiscrete and fully discrete schemes developed for solving this model using nonuniform cubic and rectangular edge elements. Furthermore, L∞ superconvergence at element centers is proved for the lowest order rectangular edge element. To our best knowledge, such pointwise superconvergence result and its proof are original, and we are unaware of any other publications on this issue. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential 2011 相似文献
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This paper studies the scattering of electromagnetic waves from a (local) perturbation of a fixed surface, the boundary of a given obstacle in ?3. The goal is to produce an algorithm for solving boundary value problems in the exterior of the perturbed domain solely based on the knowledge of the Green function for the original surface. This is done by solving a boundary integral equation which only involves the perturbed portion of the boundary. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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Juan E. Santos 《Numerical Methods for Partial Differential Equations》1998,14(4):407-437
A collection of global and domain decomposition mixed finite element schemes for the approximate solution of the harmonic Maxwell's equations on a bounded domain with absorbing boundary conditions at the artificial boundaries are presented. The numerical procedures allow us to solve efficiently the direct problem in magnetotellurics consisting of determining the electromagnetic scattered field in a two–dimensional earth model of arbitrary conductivity properties. Convergence results for the numerical procedures are derived. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 407–437, 1998 相似文献
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A stable iterative solver for the simulation of optical waves in metals using finite difference frequency domain (FDFD) method is presented. The corresponding discretization of Maxwell's equations enables simulating electromagnetic waves in structures when materials with negative permittivity are involved. Convergence of the iterative solver is proved for positive and negative permittivities. Numerical results are presented for a thin‐film silicon solar cell structure containing silver back contact. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
10.
Yunqing Huang;Jichun Li;Xin Liu; 《Numerical Methods for Partial Differential Equations》2024,40(2):e23069
In this paper, we develop a local discontinuous Galerkin (LDG) method to simulate the wave propagation in an electromagnetic concentrator. The concentrator model consists of a coupled system of four partial differential equations and one ordinary differential equation. Discrete stability and error estimate are proved for both semi-discrete and full-discrete LDG schemes. Numerical results are presented to justify the theoretical analysis and demonstrate the interesting wave concentration property by the electromagnetic concentrator. 相似文献
11.
This paper presents an algebraic multigrid method for the efficient solution of the linear system arising from a finite element discretization of variational problems in H0(curl,Ω). The finite element spaces are generated by Nédélec's edge elements. A coarsening technique is presented, which allows the construction of suitable coarse finite element spaces, corresponding transfer operators and appropriate smoothers. The prolongation operator is designed such that coarse grid kernel functions of the curl‐operator are mapped to fine grid kernel functions. Furthermore, coarse grid kernel functions are ‘discrete’ gradients. The smoothers proposed by Hiptmair and Arnold, Falk and Winther are directly used in the algebraic framework. Numerical studies are presented for 3D problems to show the high efficiency of the proposed technique. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
12.
F. Assous P. Ciarlet P.‐A. Raviart E. Sonnendrücker 《Mathematical Methods in the Applied Sciences》1999,22(6):485-499
The solution of Maxwell's equations in a non‐convex polyhedral domain is less regular than in a smooth or convex polyhedral domain. In this paper we show that this solution can be decomposed into the orthogonal sum of a singular part and a regular part, and we give a characterization of the singular part. We also prove that the decomposition is linked to the one associated to the scalar Laplacian. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
13.
The electromagnetic interior transmission problem is a boundary value problem, which is neither elliptic nor self-adjoint. The associated transmission eigenvalue problem has important applications in the inverse electromagnetic scattering theory for inhomogeneous media. In this paper, we show that, in general, there do not exist purely imaginary electromagnetic transmission eigenvalues. For constant index of refraction, we prove that it is uniquely determined by the smallest (real) transmission eigenvalue. Finally, we show that complex transmission eigenvalues must lie in a certain region in the complex plane. The result is verified by examples. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
14.
This paper is concerned with the discontinuous Galerkin approximation of the Maxwell eigenproblem. After reviewing the theory developed in [A. Buffa, I. Perugia, Discontinuous Galerkin approximation of the Maxwell eigenproblem, Technical Report 24-PV, IMATI-CNR, Pavia, Italy, 2005 〈http://www.imati.cnr.it/∼annalisa/PS/maxwell.pdf〉], we present a set of numerical experiments which both validate the theory, and provide further insight regarding the practical performance of discontinuous Galerkin methods, particularly in the case when non-conforming meshes, characterized by the presence of hanging nodes, are employed. 相似文献
15.
In this paper, we consider the solutions of magnetic field in the Darwin model to the Maxwell's equations in 2D unbounded domain. We first deduce the variational formulation and prove the well‐posedness of the weak solution, and then prove the existence and uniqueness of the infinite element solution. Error estimate and the numerical examples are provided. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 相似文献
16.
In this note, we present some blowup results of solutions to the one-dimensional compressible Navier–Stokes equations with Maxwell's law. First, we improve the blowup result of Hu and Wang [Math. Nachr. 92 (2019), 826–840] with initial density away from vacuum by removing two restrictions. Next, we give a blowup result for the solutions with decay at far fields. Finally, we construct some special analytical solutions to exhibit the blowup or non-blowup phenomena for the relaxed system. 相似文献
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Timothy Meagher Bin Jiang Peng Jiang 《Numerical Methods for Partial Differential Equations》2020,36(5):1129-1144
An enhanced finite-difference time-domain (FDTD) algorithm is built to solve the transverse electric two-dimensional Maxwell's equations with inhomogeneous dielectric media where the electric fields are discontinuous across the dielectric interface. The new algorithm is derived based upon the integral version of the Maxwell's equations as well as the relationship between the electric fields across the interface. To resolve the instability issue of Yee's scheme (staircasing) caused by discontinuous permittivity across the interface, our algorithm revises the permittivities and makes some corrections to the scheme for the cells around the interface. It is also an improvement over the contour-path effective permittivity algorithm by including some extra terms in the formulas. The scheme is validated in solving the scattering of a dielectric cylinder with exact solution from Mie theory and is then compared with the above contour-path method, the usual staircasing and the volume-average method. The numerical results demonstrate that the new algorithm has achieved significant improvement in accuracy over other methods. Furthermore, the algorithm has a simple structure and can be merged into current FDTD software packages easily. The C++ source code for this paper is provided as supporting information for public access. 相似文献
19.
In this paper, Newmark time‐stepping scheme and edge elements are used to numerically solve the time‐dependent scattering problem in a three‐dimensional polyhedral cavity. Finite element methods based on the variational formulation derived in Van and Wood (Adv. Comput. Math., to appear) are considered. Existence and uniqueness of the discrete problem is proved by using Babuska–Brezzi theory. Finite element error estimate and stability of the Newmark scheme are also established. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
20.
In this paper, we analyze the energy‐conserved splitting finite‐difference time‐domain (FDTD) scheme for variable coefficient Maxwell's equations in two‐dimensional disk domains. The approach is energy‐conserved, unconditionally stable, and effective. We strictly prove that the EC‐S‐FDTD scheme for the variable coefficient Maxwell's equations in disk domains is of second order accuracy both in time and space. It is also strictly proved that the scheme is energy‐conserved, and the discrete divergence‐free is of second order convergence. Numerical experiments confirm the theoretical results, and practical test is simulated as well to demonstrate the efficiency of the proposed EC‐S‐FDTD scheme. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献