Convergence of a Discontinuous Galerkin scheme for the mixed time domain Maxwell's equations in dispersive media.
Convergence of a Discontinuous Galerkin scheme for the mixed time domain Maxwell's equations in dispersive media.
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DOI：
10.1093/imanum/drs008
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发表时间：
2013-04
影响因子：
2.1
通讯作者：
S. Lanteri;C. Scheid
中科院分区：
文献类型：
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作者：
S. Lanteri;C. Scheid
本研究采用不连续Galerkin时域（DGTD）方法求解色散传播介质中的时域麦克斯韦方程组。德拜模型用于描述介质的色散行为。所得到的方程组求解中心通量间断Galerkin制定的空间离散和二阶蛙跳计划的集成时间。色散模型的数值处理依赖于辅助微分方程（ADE）的方法类似于在时域有限差分（FDTD）方法中所采用的。通过能量估计得到了稳定性估计，并证明了半离散和全离散情况下的收敛性。
This study is concerned with the solution of the time domain Maxwell's equations in a dispersive propagation media by a Discontinuous Galerkin Time Domain (DGTD) method. The Debye model is used to describe the dispersive behaviour of the media. The resulting system of equations is solved using a centered flux discontinuous Galerkin formulation for the discretization in space and a second order leap-frog scheme for the integration in time. The numerical treatment of the dispersive model relies on an Auxiliary Differential Equation (ADE) approach similarly to what is adopted in the Finite Difference Time Domain (FDTD) method. Stability estimates are derived through energy estimations and the convergence is proved for both the semi-discrete and the fully discrete case.