A Nonlocal Operator Method for Partial Differential Equations with Application to Electromagnetic Waveguide Problem
A Nonlocal Operator Method for Partial Differential Equations with Application to Electromagnetic Waveguide Problem
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DOI：
10.32604/cmc.2019.04567
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
T. Rabczuk;H. Ren;X. Zhuang
中科院分区：
文献类型：
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作者：
T. Rabczuk;H. Ren;X. Zhuang
提出了一种基于变分原理的新型非局部算子理论来求解偏微分方程。常见的微分算子以及变分形式是在非局部算子的上下文中定义的。当前的非局部公式允许轻松简单地组装切线刚度矩阵，这对于波导问题等特征值分析是必需的。该公式应用于求解基于电场的微分电磁矢量波方程。控制方程被转换为非局部积分形式。引入沙漏能量泛函来消除零能量模式。最后，通过测试三个经典基准问题来验证所提出的方法。
A novel nonlocal operator theory based on the variational principle is proposed for the solution of partial differential equations. Common differential operators as well as the variational forms are defined within the context of nonlocal operators. The present nonlocal formulation allows the assembling of the tangent stiffness matrix with ease and simplicity, which is necessary for the eigenvalue analysis such as the waveguide problem. The present formulation is applied to solve the differential electromagnetic vector wave equations based on electric fields. The governing equations are converted into nonlocal integral form. An hourglass energy functional is introduced for the elimination of zeroenergy modes. Finally, the proposed method is validated by testing three classical benchmark problems.