A 3-D spectral-element method using mixed-order curl conforming vector basis functions for electromagnetic fields
A 3-D spectral-element method using mixed-order curl conforming vector basis functions for electromagnetic fields
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DOI：
10.1109/tmtt.2005.860502
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发表时间：
2006-01
影响因子：
4.3
通讯作者：
Joon-Ho Lee;Tian Xiao;Qing Huo Liu
中科院分区：
文献类型：
--
作者：
Joon-Ho Lee;Tian Xiao;Qing Huo Liu
提出了一种基于Gauss-Lobatto-Legendre多项式的三维谱元法求解矢量电磁波方程。为了抑制虚假的解决方案，混合阶旋度一致的向量基函数中使用的SEM。这种方法的优点包括它的高阶精度和对角质量矩阵，由于使用正交勒让德多项式。因此，所提出的方法导致一个规则的特征值问题，而不是一个广义特征值问题，大大减少了计算机的内存需求和CPU时间相比，传统的高阶有限元法（FEM）。特征值问题的数值算例验证了插值阶数的谱精度，并表明SEM上级FEM。用混合边界条件对波导模型进行了分析，其结果与参考值吻合得很好。所有的数值结果表明，SEM是一个有效的替代有限元电磁场
A three-dimensional spectral-element method (SEM) based on Gauss-Lobatto-Legendre polynomials is proposed to solve vector electromagnetic-wave equations. To suppress spurious solutions, mixed-order curl conforming vector basis functions are used in the SEM. The advantages of this method include its high-order accuracy and its diagonal mass matrix due to the use of orthogonal Legendre polynomials. Thus, the proposed method leads to a regular eigenvalue problem rather than a generalized eigenvalue problem, greatly reducing the computer memory requirement and CPU time in comparison with the conventional high-order finite-element method (FEM). Numerical examples of eigenvalue problems verify the spectral accuracy with the interpolation orders and show that the SEM is superior to the FEM for the class of problems considered. A waveguide model is analyzed with mixed boundary conditions and its results are in excellent agreement with reference values. All numerical results show that the SEM is an efficient alternative to the FEM for electromagnetic fields