Maxwell equations is the nitedi erence timedomain method fdtd. Spacetime discontinuous galerkin method for maxwells equations. Sep 24, 2018 in this paper, we develop a totally new direct finite difference solver for solving the maxwells equations in kerrtype nonlinear media. Timedomain finitedifference and finiteelement methods. Pdf finite element approximation of maxwells equations with.
The permittivity and permeability of the cloak model are described by the drude dispersion model. Timedomain finite element methods for maxwells equations in metamaterials jichun li, yunqing huang auth. Finite difference time domain fdtd methods for solution. Since it is a timedomain method, fdtd solutions can cover a wide. Finite element timedomain bodyofrevolution maxwell. Finitedifference timedomain or yees method named after the chinese american applied mathematician kane s. Request pdf timedomain finite element methods for maxwells equations in metamaterials the purpose of this book is to provide an uptodate. Nov 28, 2015 in this paper, we propose a new timedomain finite element method for solving the time dependent maxwells equations coupled with the lorentz metamaterial model. Analysis of a finite element method for maxwells equations.
An explicit time domain finite element algorithm is presented for the maxwells equations in 30, for complex media in 28 only numerical result. A new fdtd scheme for maxwells equations in kerrtype. The most widespread timedomain method for the numerical simulation of the maxwell equations is the nitedi erence timedomain method fdtd. Analysis of stability and dispersion in a finite element. Abstract pdf 246 kb 2001 a vector finite element timedomain method for solving maxwells equations on unstructured hexahedral grids. Energyconserved splitting finitedifference timedomain. The fdtd method is secondorder accurate and very e cient for simple geometries. Solving metamaterial maxwells equations via a vector wave integro. Jichun li and yunqing huang, perfectly matched layers, timedomain finite element methods for maxwells equations in metamaterials, 10. Siam journal on scientific computing society for industrial. The book finishes with some interesting simulations such as backward wave propagation and timedomain cloaking with metamaterials. Time domain finite element method for maxwells equations. Solving metamaterial maxwells equations via a vector wave.
In this paper, we discuss the time domain metamaterial maxwells equations. Timedomain finite element methods for metamaterials. Spacetime discontinuous galerkin method for maxwells. Timedomain finite element methods for maxwells equations. The lorentz metamaterial maxwells equations are much more complicated than the standard maxwells equations in free space. Springer series in computational mathematics, vol 43. Huang, timedomain finite element methods for maxwells equations in metamaterials, springer series in computational mathematics, vol. Modeling and analysis of the optical black hole in. Very little work is devoted to dispersive media using finite element method fem, though there is some work in finite difference timedomain fdtd modeling of dispersive media started since 1990 23, chapter 9. In this paper we propose a timedomain finite element method for modeling of electromagnetic cloaks. A fullydiscrete finite element method is proposed in the paper, and numerical results supporting the analysis are presented. Development of discontinuous galerkin methods for maxwells. Hence developing efficient finite element timedomain fetd methods plays a very important role in simulating wave propagation in general media and metamaterials.
Developing a timedomain finiteelement method for modeling. Jul 26, 2006 time domain finite element methods for maxwell s equations in metamaterials, 241283. Developing a timedomain finite element method for the. An implicit discontinuous galerkin method is introduced to solve the timedomain maxwells equations in metamaterials. This discovery makes solving metamaterial maxwells equations more efficient than those techniques previously investigated,,, where two or four unknowns each is a 2d or 3d vector have to be solved. Though there exist many excellent works on finite element methods for solving maxwells equations in various. A polynomial chaos method for dispersive electromagnetics. An adaptive finite element method with perfectly matched. Finite difference time domain fdtd methods for solution of maxwells equations case study in simulation sciences dr. Implicit dg method for time domain maxwells equations. Finally, we construct a finite element method for maxwells equations in a lorentz. Developing a timedomain finite element method for the lorentz metamaterial model and applications. Journal of mathematical analysis and applications 397. The most widespread time domain method for the numerical simulation of the maxwell equations is the nitedi erence time domain method fdtd.
Yee, born 1934 is a numerical analysis technique used for modeling computational electrodynamics finding approximate solutions to the associated system of differential equations. We explore to principles to map the original threedimensional 3d bor problem to an. On the other hand, though there are many excellent work on finite element methods fems for solving maxwells equations in free space e. Pdf recent advances in timedomain maxwells equations. Distinguished from the rungekutta discontinuous galerkin method rkdg and the finite element time domain method fetd, in our scheme, discontinuous galerkin methods are used to discretize not only the spatial domain but also the temporal domain.
The maxwells equations in metamaterials are represented by integraldifferential equations. The finitedifference timedomain method artech house, norwood, ma, 2005, 3rd ed. Shen, analysis of the scattering by an unbounded rough surface, math. Siam journal on scientific computing siam society for. In this paper, we propose a new timedomain finite element method for solving the time dependent maxwells equations coupled with the lorentz metamaterial model. Electromagnetic scattering for timedomain maxwells.
Finite difference time domain or yee s method named after the chinese american applied mathematician kane s. Finite element methods for maxwells equations request pdf. Developing a time domain finite element method for the lorentz metamaterial model and applications. Timedomain finitedifference and finiteelement methods for. Sorry, we are unable to provide the full text but you may find it at the following locations. In this paper, timedomain finite element methods for the full system of maxwells equations with cubic nonlinearities in 3d are presented, including a selection of computational experiments. The first method is based on integraldifferential equations transformed from the governing equations.
In this paper we propose a time domain finite element method for modeling of electromagnetic cloaks. In this paper, we present a mixed fe bor solver for timedomain maxwells curl equations based on transformation optics to,,, and discretization principles based on the discrete exterior calculus dec of differential forms. Pdf discontinuous galerkin methods for metamaterials. Finite element timedomain bodyofrevolution maxwell solver. Examples include the convergence effect happened in the concave lenses formed by the negative refraction index metamatrials, and total re.
A fully discrete discontinuous galerkin method is introduced for solving timedependent maxwells equations. Since the first successful construction of a metamaterial with both negative permittivity and permeability in 2000, the study of metamaterials. Recent advances in timedomain maxwells equations in. It has been widely used for electromagnetic simulation, for instance in radar cross section computations and electromagnetic compatibility investigations. Recent advances in timedomain maxwells equations in metamaterials 55 3. Quick finite elements for electromagnetic waves download. Development of discontinuous galerkin methods for maxwell. In this paper, we present three secondorder finite element methods solving maxwells equations when metamaterials are involved. Developing finite element methods for simulating transformation optics devices with metamaterials wei yang1, jichun li2. In recent years, we have made some initial effort,, in developing and analyzing some finite element methods fem for timedomain maxwells equations involving metamaterials, but all our previous work were based on standard finite element methods. Timedomain finite element methods for maxwells equations in meta. Developing finite element methods for maxwells equations in a colecole dispersive medium. Pdf recent advances in timedomain maxwells equations in. Developing finite element methods for maxwells equations in.
Keywords maxwells equations finite element method lorentz metamaterial model. Numerical methods for maxwells equations summer semester. Jichun li and yunqing huang, discontinuous galerkin methods for metamaterials, time domain finite element methods for maxwell s equations in metamaterials, 10. Analysis of a timedomain finite element method for 3d. Engineered metamaterials have shown great promise as building blocks for. Request pdf timedomain finite element methods for maxwells equations in metamaterials the purpose of this book is to provide an uptodate introduction to the timedomain finite element. Although the first mixed finite element error analysis for the debye problem was given.
Our scheme is based on discontinuous galerkin method in spatial domain and cranknicolson method in temporal domain. This is accomplished by assuming we are in a homogeneous medium. Developing finite element methods for maxwells equations. An explicit time domain finite element algorithm is presented for the maxwell s equations in 30, for complex media in 28 only numerical result. Leapfrog method inspiring from the classic fdtd scheme, we can formulate a leap. Finite element and finite difference methods for maxwells. In this paper, time domain finite element methods for the full system of maxwell s equations with cubic nonlinearities in 3d are presented, including a selection of computational experiments. Download pdf finiteelementmethodsformaxwellsequations. Discontinuous galerkin methods for maxwells equations in drude. Since the first successful construction of a metamaterial with both negative permittivity and permeability in 2000, the study of metamaterials has attracted significant. Energyconserved splitting finite difference timedomain methods for maxwell s equations in three dimensions. Mathematical analysis and finite element time domain simulation of. The direct we also prove the continuous stability for the kerr model and the discrete stability for the proposed scheme.
Since the first successful construction of a metamaterial with both negative permittivity and permeability in 2000, the study of metamaterials has attracted significant attention from. In section 3, we present a fully discrete finite element method for solving the vector wave integrodifferential equation. Energy evolution of multisymplectic methods for maxwell equations with perfectly matched layer boundary. In this paper, timedomain finite element methods for the full system of maxwell s equations with cubic nonlinearities in 3d are presented, including a selection of computational experiments. This book is a selfcontained, programmingoriented and learnercentered book on finite element method fem, with special emphasis given to developing matlab programs for numerical modeling of electromagnetic boundary. Numerical methods for metamaterial design download ebook. Request pdf time domain finite element method for maxwells equations in this paper, we discuss a time domain finite element method for. Pdf maxwells equations in a bounded debye medium are formulated in terms of the. In this paper, we present a mixed fe bor solver for time domain maxwell s curl equations based on transformation optics to,,, and discretization principles based on the discrete exterior calculus dec of differential forms. In section 3, we discuss the finite difference time domain or yee. Here, faradays law and the amperemaxwell equation are used to construct lossy wave equations for both \\mathbfe\ and \\mathbfh\, respectively. Time domain finite element methods for maxwell s equations in metamaterials.
Request pdf timedomain finite element methods for maxwell s equations in metamaterials the purpose of this book is to provide an uptodate introduction to the timedomain finite element. Finitedifference timedomain simulation of spacetime cloak. The development and practical implementation of edge finite element methods for metamaterial maxwells equations are the main focus of the book. Superconvergence of mixed finite element approximations to 3. The model to be solved is quite challenging in that we have to solve a coupled problem with different partial differential equations given in. Jichun li and yunqing huang, a matlab edge element code for metamaterials, timedomain finite element methods for maxwells equations in metamaterials, 10. Timedomain finite element methods for maxwells equations in. Timedomain finite element methods for maxwell s equations in metamaterials jichun li, yunqing huang auth. The applications of timedomain finite element method tdfem for the dispersive media were seen only very recently. The purpose of this book is to provide an uptodate introduction to the timedomain finite element methods for maxwells equations involving metamaterials. Numerical solution of initial boundary value problems involving maxwells equations in isotropic media.
Since the first successful construction of a metamaterial with both negative. Various components of the resulting 2nd order differential equations in time are. Timedomain finite element methods for maxwells equations in metamaterials, 241283. Timedomain finite element methods for maxwells equations in metamaterials, volume 43. The colecole model contains a fractional time derivative term, which couples with the standard maxwells equations in free space and creates some challenges in developing and analyzing timedomain finite element methods for solving this model as mentioned in our earlier work j.
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