论文标题
麦克斯韦方程的混合电网方程
A Yee-like finite element scheme for Maxwell's equations on hybrid grids
论文作者
论文摘要
研究了一种新的有限元方法，用于在混合二维网格上近似麦克斯韦方程。适当的基础函数和数值正交的选择会导致对角线质量矩阵，从而可以通过显式方法有效地整合时间。在纯粹的矩形网格上，提出的方案与良好的拟合和FDTD方法一致。在三角形上引入的其他内部自由度可以使质量倾斜，而没有对这些元素形状的通常限制。开发了该方法的完整错误分析，并提出了数值测试以进行插图。
A novel finite element method for the approximation of Maxwell's equations over hybrid two-dimensional grids is studied. The choice of appropriate basis functions and numerical quadrature leads to diagonal mass matrices which allow for efficient time integration by explicit methods. On purely rectangular grids, the proposed schemes coincide with well-established FIT and FDTD methods. Additional internal degrees of freedom introduced on triangles allow for mass-lumping without the usual constraints on the shape of these elements. A full error analysis of the method is developed and numerical tests are presented for illustration.
