Geometric Computational Electrodynamics with Variational Integrators and Discrete Differential Forms
Geometric Computational Electrodynamics with Variational Integrators and Discrete Differential Forms
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DOI：
10.1007/978-1-4939-2441-7_19
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发表时间：
2007-07
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影响因子：
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通讯作者：
A. Stern;Y. Tong;M. Desbrun;J. Marsden
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文献类型：
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作者：
A. Stern;Y. Tong;M. Desbrun;J. Marsden
In this paper, we develop a structure-preserving discretization of the Lagrangian framework for electrodynamics, combining the techniques ofvariational integratorsanddiscrete differential forms. This leads to a general family of variational, multisymplectic numerical methods for solving Maxwell’s equations that automatically preserve key symmetries and invariants. In doing so, we show that Yee’s finite-difference time-domain (FDTD) scheme and its variants are multisymplectic and derive from a discrete Lagrangian variational principle. We also generalize the Yee scheme to unstructured meshes, not just in space but in 4-dimensional spacetime, which relaxes the need to take uniform time steps or even to have a preferred time coordinate. Finally, as an example of the type of methods that can be developed within this general framework, we introduce a newasynchronous variational integrator(AVI) for solving Maxwell’s equations. These results are illustrated with some prototype simulations that show excellent numerical behavior and absence of spurious modes, even for an irregular mesh with asynchronous time stepping.
