Numerical dispersion analysis of a multi-symplectic scheme for the three dimensional Maxwell’s equations

Cai, Wenjun; Wang, Yushun; Song, Yisheng

doi:10.1016/j.jcp.2012.09.043

Cited by 13 publications

(9 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…During the study of wave propagation on liquid-filled tubes, Johnson presented a KdV equation model with damping, named KdV-Burgers equation (Cai et al, 2013):…”

Section: Introductionmentioning

confidence: 99%

“…where is the dispersion coefficient and " is the damping coefficient. Equation (1) can be used to study a series of important physical problems which contain weakly nonlinear dispersion as well as dissipation, such as the interaction between the laser and the plasma with the short wavelength that is close to the Debye length (Kawahara, 1970;Konno and Ichikawa, 1974;Zhu and Boswell, 1989;Neumayer et al, 2008), the flow of viscous liquid in elastic tubes (Cai et al, 2013), and so on. Most of the special phenomena in the above physical problems result from the competition between the geometric dispersion and the viscous dissipation in the systems.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Competition between geometric dispersion and viscous dissipation in wave propagation of KdV-Burgers equation

Deng

2014

Journal of Vibration and Control

View full text Add to dashboard Cite

In this paper the competitive relationship between the geometric dispersion and the viscous dissipation in the wave propagation of the KdV-Burgers equation is investigated by the generalized multi-symplectic method. Firstly, the generalized multi-symplectic formulations for the KdV-Burgers equation are presented in Hamiltonian space. Then, focusing on the inherent geometric properties of the generalized multi-symplectic formulations, a 12-point difference scheme is constructed. Finally, numerical experiments are performed with fixed step-sizes to obtain the maximum damping coefficient that insures that the scheme constructed is generalized multi-symplectic, and to study the competition between the geometric dispersion and the viscous dissipation in the wave propagation of the KdV-Burgers equation. The competition phenomena are comprehensively illustrated in the wave forms as well as in the phase diagrams: for the KdV equation (a particular case of the KdV-Burgers equation without dissipation), there is a closed orbit in the phase diagram; and the closed orbit is substituted by a heteroclinic one with the appearance of the viscous dissipation; moreover, the heteroclinic orbit changes from the saddle-node type to the saddle-focus type with an increase of the damping coefficient.

show abstract

“…During the study of wave propagation on liquid-filled tubes, Johnson presented a KdV equation model with damping, named KdV-Burgers equation (Cai et al, 2013):…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Competition between geometric dispersion and viscous dissipation in wave propagation of KdV-Burgers equation

Deng

2014

Journal of Vibration and Control

View full text Add to dashboard Cite

show abstract

“…The most important character of MIs is its multi-symplecticity, and other conservative properties are preserved excellently despite of not exactly [1,5,8]. Recently, numerical dispersion of MIs was analyzed [20]. In this article, we investigate an MI for NLSEWO and its global conservative properties.…”

Section: Proposition 1 the Determined Problem (1) Satisfies The Follmentioning

confidence: 99%

Multi-symplectic preserving integrator for the Schrödinger equation with wave operator

Wang

Kong

Zhang³

et al. 2015

Applied Mathematical Modelling

View full text Add to dashboard Cite

In this article, we discuss the conservation laws for the nonlinear Schrödinger equation with wave operator under multi-symplectic integrator (MI). First, the conservation laws of the continuous equation are presented and one of them is new. The multisymplectic structure and MI are constructed for the equation. The discrete conservation laws of the numerical method are analyzed. It is verified that the proposed MI can stably simulate the Hamiltonian PDEs excellently over long-term. It is more accurate than some energy-preserving schemes though they are of the same accuracy. Moreover, the residual of mass is less than energy-preserving schemes under the same mesh partition in a long time.

show abstract

“…In Refs. [8,18,23,33,36,39], symplectic and multi-symplectic schemes of the Maxwell's equations in an isotropic, lossless and sourceless medium were proposed. In Ref.…”

Section: Introductionmentioning

confidence: 99%

A Conformal Energy-Conserved Method for Maxwell’s Equations with Perfectly Matched Layers

Jiang¹,

Cui²,

Wang³

2019

CiCP

Self Cite

View full text Add to dashboard Cite

In this paper, a conformal energy-conserved scheme is proposed for solving the Maxwell's equations with the perfectly matched layer. The equations are split as a Hamiltonian system and a dissipative system, respectively. The Hamiltonian system is solved by an energy-conserved method and the dissipative system is integrated exactly. With the aid of the Strang splitting, a fully-discretized scheme is obtained. The resulting scheme can preserve the five discrete conformal energy conservation laws and the discrete conformal symplectic conservation law. Based on the energy method, an optimal error estimate of the scheme is established in discrete L 2-norm. Some numerical experiments are addressed to verify our theoretical analysis.

show abstract

Numerical dispersion analysis of a multi-symplectic scheme for the three dimensional Maxwell’s equations

Cited by 13 publications

References 31 publications

Competition between geometric dispersion and viscous dissipation in wave propagation of KdV-Burgers equation

Competition between geometric dispersion and viscous dissipation in wave propagation of KdV-Burgers equation

Multi-symplectic preserving integrator for the Schrödinger equation with wave operator

A Conformal Energy-Conserved Method for Maxwell’s Equations with Perfectly Matched Layers

Contact Info

Product

Resources

About