Unconditionally stable time stepping method for mixed finite element maxwell solvers

被引：0
|
作者：
Crawford, Zane D. [1 ,2 ]
Li, Jie [1 ]
Christlieb, Andrew [2 ]
Shanker, Balasubramaniam [1 ]
机构：
[1] Department of Electrical and Computer Engineering, Michigan State University, East Lansing,MI, United States
[2] Department of Computational Science, Mathematics, and Engineering, Michigan State University, East Lansing,MI, United States
来源：
Progress In Electromagnetics Research C | 2020年 / 103卷
关键词：
Time domain finite element methods (TD-FEM) for computing electromagnetic fields are well studied. TD-FEM solution is typically effected using Newmark-Beta methods. One of the challenges of TD-FEM is the presence of a DC null-space that grows with time. This can be overcome by solving Maxwell equations directly. One approach; called time domain mixed finite element method (TDMFEM); discretizes Maxwell’s equations using appropriate spatial basis sets and leapfrog time stepping. Typically; the basis functions used to discretize field quantities have been low order. It is conditionally stable; and there is a strong link between time step size and mesh dependent eigenvalues; much like the Courant-Friedrichs-Lewy (CFL) condition. This implies that the time step sizes can be very small. To overcome this challenge; we use the Newmark-Beta approach. The principal contribution of this work is the development of; and rigorous proof of; unconditional stability for higher order TD-MFEM for different boundary conditions. Further; we analyze nullspaces of the resulting system; and demonstrate stability and convergence. All results are compared against the conditionally stable leapfrog approach. © 2020; Electromagnetics Academy. All rights reserved;
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页码：17 / 30
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