Symplectic and multisymplectic numerical methods for Maxwell’s equations

Sun, Yajuan; Tse, P. S. P.

doi:10.1016/j.jcp.2010.12.006

Cited by 54 publications

(32 citation statements)

References 32 publications

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“…Maxwell's equations in (2.1) have another natural multi-symplectic formulation [16,19] which require no extra variables,…”

Section: ð3:3þmentioning

confidence: 99%

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

Cai¹,

Wang²,

Song³

2013

Journal of Computational Physics

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“…Maxwell's equations in (2.1) have another natural multi-symplectic formulation [16,19] which require no extra variables,…”

Section: ð3:3þmentioning

confidence: 99%

“…In this section, we follow the dispersion analysis for the two dimensional Maxwell's equations in [16]. There is a large amount of literature on the dispersion analysis of numerical methods for Maxwell's equations (for example, see [31,32] for the dispersion analysis of FDTD methods and ADI methods).…”

Section: Dispersion and Non-dissipation Propertymentioning

confidence: 99%

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

Cai¹,

Wang²,

Song³

2013

Journal of Computational Physics

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“…It is well known that the differential form of the time-domain Maxwell's equations is as follows (see [12,44]):…”

Section: Introductionmentioning

confidence: 99%

A POD reduced-order finite difference time-domain extrapolating scheme for the 2D Maxwell equations in a lossy medium

Luo

Gao

2016

Journal of Mathematical Analysis and Applications

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This paper is concerned with establishing a reduced-order finite difference time-domain (FDTD) extrapolating scheme based on proper orthogonal decomposition (POD) method for the two-dimensional (2D) Maxwell equations in a lossy medium. For this purpose, we first review the classical FDTD scheme and associated results for the 2D Maxwell equations in a lossy medium. And then, we formulate three sets of POD bases by means of the solutions obtained from the classical FDTD scheme on the very short time interval, establish the POD reduced-order FDTD extrapolating scheme, and furnish the error estimates among the POD reduced-order FDTD solutions and the classical FDTD solutions as well as the accuracy solution for the 2D Maxwell equations in a lossy medium. Finally, we enumerate two numerical examples to confirm that the POD reduced-order FDTD extrapolating scheme is feasible and efficient for simulating the phenomena for the electric and magnetic fields in a lossy medium.

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“…Naturally, it is desirable to propose a numerical scheme preserved these features in the discrete sense as much as possible. To achieve this some structure-preserving numerical algorithms were proposed in [12][13][14][15]. These methods have attractive properties, however most of them are of low-order accuracy in both time and space.…”

Section: Introductionmentioning

confidence: 99%

Numerical Analysis of AVF Methods for Three-Dimensional Time-Domain Maxwell’s Equations

2015

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We propose two schemes [AVF(2) and AVF(4)] for Maxwell's equations, by discretizing the Hamiltonian formulation with Fourier pseudospectral method for spatial discretization and average vector field method for time integration. Both AVF(2) and AVF(4) hold the two Hamiltonian energies automatically, while being energy-, momentum-and divergence-preserving, unconditionally stable, non-dissipative and spectral accurate. Rigorous error estimates are obtained for the proposed schemes. The numerical dispersion relations are also investigated. Numerical experiments support well the theoretical analysis results. The proposed schemes are valid for the regular domain, but invalid for the domain with complex geometries.

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Symplectic and multisymplectic numerical methods for Maxwell’s equations

Cited by 54 publications

References 32 publications

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

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

A POD reduced-order finite difference time-domain extrapolating scheme for the 2D Maxwell equations in a lossy medium

Numerical Analysis of AVF Methods for Three-Dimensional Time-Domain Maxwell’s Equations

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