基于节点的有限元方法具有网格剖分、构造高阶基函数容易的优点。由于在节点上定义场量，节点有限元更适用于多物理问题。但节点有限元方法直接求解电磁场会出现伪解，场量在不均匀介质中不连续等问题。基于节点的A-ϕ方法可以有效避免传统节点有限元方法存在的问题。本文研究A-ϕ方法的工程应用，研究开域和闭域问题中如何设置关于矢势和标势函数的边界条件，特别是波导问题和理想导体球的散射问题，讨论了端口边界条件，辐射边界条件的使用方法。对于理想导体边界条件采用了阻抗边界条件，与端口条件配合，克服方程的奇异性。数值实验比较分析了A-ϕ法节点有限元和棱边法有限元的计算结果，验证了A-ϕ法节点有限元的正确性和有效性。%The advantages of the nodal -based finite element method are convenient for mesh partition and high order basis functions construction. As field quantities defined on nodes,the nodal-based finite element method is more suitable for multi -physics problems. However, the nodal element for solving electromagnetic fields directly will appear spurious solutions and fields discontinuities in inhomogeneous media. Nodal-based A-ϕmethod can effectively avoid problems caused by the traditional nodal-based finite element method. This paper focuses on A-ϕmethod for engineering applications,which researches the boundary conditions setting of the vector potential and scalar potential function s in open and closed domains. Especially, for the waveguide problem and the EM wave scattering problem of perfectly conducting sphere,the applications of the port boundary condition and radiation boundary condition are discussed. The perfectly conducting boundary conditionis are dealt with impedance boundary condition accompanied with port conditions to overcome the singularity of the equations. In numerical experiments, the results obtained by the nodal element method are compared with the results of the edge element method,verifying the validity and effectiveness of the A-ϕ nodal finite element method.
展开▼
