论文标题
三个用于3-D空腔谐振器的数值特征材料，充满各向异性和非导导介质
Three Numerical Eigensolvers for 3-D Cavity Resonators Filled With Anisotropic and Nonconductive Media
论文作者
论文摘要
本文主要研究了各向异性和非导导介质的经典共振空腔问题，这是线性矢量麦克斯韦的特征值问题。基于最低阶和标准线性元件的边缘元素的有限元方法用于解决此类3-D闭合腔问题。为了消除数值模拟中虚假的零模式，高斯定律支持的无差异条件在弱的意义上实现了。有限元离散后，需要解决具有线性约束条件的广义特征值问题。惩罚方法，增强方法和投影方法用于在数值线性代数中解决这一困难问题。本文还给出了这三种计算方法的优点和缺点。此外，我们证明，只要各向异性材料不是磁性损失，增强方法就没有虚假模式。基于奇异值分解技术的投影方法可用于解决谐振腔问题。此外，投影方法{不能}引入任何虚假模式。最后，进行了几项数值实验以验证我们的理论结果。
This paper mainly investigates the classic resonant cavity problem with anisotropic and nonconductive media, which is a linear vector Maxwell's eigenvalue problem. The finite element method based on edge element of the lowest-order and standard linear element is used to solve this type of 3-D closed cavity problem. In order to eliminate spurious zero modes in the numerical simulation, the divergence-free condition supported by Gauss' law is enforced in a weak sense. After the finite element discretization, the generalized eigenvalue problem with a linear constraint condition needs to be solved. Penalty method, augmented method and projection method are applied to solve this difficult problem in numerical linear algebra. The advantages and disadvantages of these three computational methods are also given in this paper. Furthermore, we prove that the augmented method is free of spurious modes as long as the anisotropic material is not magnetic lossy. The projection method based on singular value decomposition technique can be used to solve the resonant cavity problem. Moreover, the projection method {cannot} introduce any spurious modes. At last, several numerical experiments are carried out to verify our theoretical results.
