论文标题
使用时空有限元元件外观微积分，用于电磁场系统的周期性稳态问题的有限元方法
A finite element method to a periodic steady-state problem for an electromagnetic field system using the space-time finite element exterior calculus
论文作者
论文摘要
本文提出了一种有限元方法，用于解决标量值和矢量值泊松方程的周期性稳态问题，这是库仑仪下麦克斯韦方程的简单还原模型。我们引入了一个新的潜在变量，我们将两个由标量和矢量价值的泊松问题组成的系统重新制定了使用标准de rham综合体中的$ \ mathbb {r}^4 $中的1型hodge-laplace问题。因此，我们可以直接将有限元的外部微积分（FEEC）理论应用于$ \ mathbb {r}^4 $中，以推断出良好的性，稳定性和收敛性。据报道，使用立方元素的数值示例验证了理论结果。
This paper proposes a finite element method for solving the periodic steady-state problem for the scalar-valued and vector-valued Poisson equations, a simple reduction model of the Maxwell equations under the Coulomb gauge. Introducing a new potential variable, we reformulate two systems composed of the scalar-valued and vector-valued Poisson problems to a single Hodge-Laplace problem for the 1-form in $\mathbb{R}^4$ using the standard de Rham complex. Consequently, we can directly apply the Finite Element Exterior Calculus (FEEC) theory in $\mathbb{R}^4$ to deduce the well-posedness, stability, and convergence. Numerical examples using the cubical element are reported to validate the theoretical results.
