High-order RKDG Methods for Computational Electromagnetics

Chen, Min-Hung; Cockburn, Bernardo; Reitich, Fernando

doi:10.1007/s10915-004-4152-6

Cited by 79 publications

(63 citation statements)

References 18 publications

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“…It is possible to extend these results to the case of a constant linear operator with a time dependent forcing term [6,30]. This is a case which arises in linear PDEs with time dependent boundary conditions such as Maxwell's equations which arise in computational electromagnetics (see [2]), and can be written as:…”

Section: Optimal Methods For Linear Constant Coefficient Problemsmentioning

confidence: 99%

On high order strong stability preserving runge-kutta and multi step time discretizations

Gottlieb

2005

J Sci Comput

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Strong stability preserving (SSP) high order time discretizations were developed for solution of semi-discrete method of lines approximations of hyperbolic partial differential equations. These high order time discretization methods preserve the strong stability properties-in any norm or seminorm-of the spatial discretization coupled with first order Euler time stepping. This paper describes the development of SSP methods and the recently developed theory which connects the timestep restriction on SSP methods with the theory of monotonicity and contractivity. Optimal explicit SSP Runge-Kutta methods for nonlinear problems and for linear problems as well as implicit Runge-Kutta methods and multi step methods will be collected.

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Section: Optimal Methods For Linear Constant Coefficient Problemsmentioning

confidence: 99%

On high order strong stability preserving runge-kutta and multi step time discretizations

Gottlieb

2005

J Sci Comput

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“…To obtain highly accurate and stable DG methods, suitable numerical fluxes need to be designed over elemental interfaces. The construction of such numerical fluxes can be done in many different ways, related closely to the particular equation at hand, and is particularly powerful when one considers nonlinear conservation laws [7,18,23]. The discontinuous Galerkin method has become very popular in recent years for solving electromagnetic wave propagation problems [18,23].…”

Section: Introductionmentioning

confidence: 99%

“…The DG method is flexible with regards to the choice of the time stepping scheme. One may combine the DG spatial discretization with any global [7,10,18] or local [31,34] explicit time integration scheme, or implicit scheme [6], or even a blending between these two schemes [15,25] provided that the resulting scheme will be stable.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, the behaviour of the DG method with respect to dissipation and dispersion has been well studied by means of theory and numerical experiments [35]. The influence of h-, p-and hp-refinements on the accuracy of the DG method [7,16,23], as well as the discretization error on different kinds of grids [17,18,25,32], were investigated. High-order DG methods in space [10] and in space-time [17] have also been developed.…”

Section: Introductionmentioning

confidence: 99%

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Improving accuracy of high-order discontinuous Galerkin method for time-domain electromagnetics on curvilinear domains

Fahs

2011

International Journal of Computer Mathematics

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The paper discusses high-order geometrical mapping for handling curvilinear geometries in high accuracy discontinuous Galerkin simulations for time-domain Maxwell problems. The proposed geometrical mapping is based on a quadratic representation of the curved boundary and on the adaptation of the nodal points inside each curved element. With high-order mapping, numerical fluxes along curved boundaries are computed much more accurately due to the accurate representation of the computational domain. Numerical experiments for 2D and 3D propagation problems demonstrate the applicability and benefits of the proposed high-order geometrical mapping for simulations involving curved domains.

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“…[7,5,9,13,12,15,16,33,34,8]). The readers can find more references in some recent books [2,18,35] and conference proceedings [1,3,10].…”

Section: Introductionmentioning

confidence: 99%

Superconvergence analysis for Maxwell's equations in dispersive media

Lin

2007

Math. Comp.

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Abstract. In this paper, we consider the time dependent Maxwell's equations in dispersive media on a bounded three-dimensional domain. Global superconvergence is obtained for semi-discrete mixed finite element methods for three most popular dispersive media models: the isotropic cold plasma, the one-pole Debye medium, and the two-pole Lorentz medium. Global superconvergence for a standard finite element method is also presented. To our best knowledge, this is the first superconvergence analysis obtained for Maxwell's equations when dispersive media are involved.

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High-order RKDG Methods for Computational Electromagnetics

Cited by 79 publications

References 18 publications

On high order strong stability preserving runge-kutta and multi step time discretizations

On high order strong stability preserving runge-kutta and multi step time discretizations

Improving accuracy of high-order discontinuous Galerkin method for time-domain electromagnetics on curvilinear domains

Superconvergence analysis for Maxwell's equations in dispersive media

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