Convergence of finite element A–ϕ method for solving time-dependent Maxwell’s equations

Ma, Changfeng

doi:10.1016/j.amc.2005.10.007

Cited by 4 publications

(1 citation statement)

References 15 publications

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“…The susceptibilities χ (1) and χ (3) also assume constant values, but may be different in different tests. The electric and magnetic fields are initialized by taking the projections [50, equation (31)] of the exact electric and magnetic fields, where the exact fields given by [59]…”

Section: Implementation Of the Energy Conserving Backward Euler-type mentioning

confidence: 99%

Energy-Stable Time-Domain Finite Element Methods for the 3D Nonlinear Maxwell's Equations

Anees

Angermann

2020

IEEE Photonics J.

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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. The new capabilities of these methods are to efficiently model linear and nonlinear effects of the electrical polarization. The novel strategy has been developed to bring under control the discrete nonlinearity model in space and time. It results in energy stable discretizations both at the semi-discrete and the fully discrete levels, with spatial discretization using edge and face elements (Nédeléc-Raviart-Thomas formulation). In particular, the proposed time discretization schemes are unconditionally stable with respect to a specially defined nonlinear electromagnetic energy, which is an upper bound of the electromagnetic energy commonly used. The approaches presented prove to be robust and allow the modeling of 3D optical problems that can be directly derived from the full system of Maxwell's nonlinear equations, and allow the treatment of complex nonlinearities and geometries of various physical systems coupled with electromagnetic fields.

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Section: Implementation Of the Energy Conserving Backward Euler-type mentioning

confidence: 99%

Energy-Stable Time-Domain Finite Element Methods for the 3D Nonlinear Maxwell's Equations

Anees

Angermann

2020

IEEE Photonics J.

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Finite element analysis of an A–ϕ method for time-dependent Maxwell’s equations based on explicit-magnetic-field scheme

Ma¹,

Wang²

2007

Applied Mathematics and Computation

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Analysis of Wireless Power Transfer System Based on 3-D Finite-Element Method Including Displacement Current

Zhang

Zhao

et al. 2012

IEEE Trans. Magn.

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Convergence of finite element A–ϕ method for solving time-dependent Maxwell’s equations

Cited by 4 publications

References 15 publications

Energy-Stable Time-Domain Finite Element Methods for the 3D Nonlinear Maxwell's Equations

Energy-Stable Time-Domain Finite Element Methods for the 3D Nonlinear Maxwell's Equations

Finite element analysis of an A–ϕ method for time-dependent Maxwell’s equations based on explicit-magnetic-field scheme

Analysis of Wireless Power Transfer System Based on 3-D Finite-Element Method Including Displacement Current

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