CAJ | 학술논문

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-?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-?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-?法节点有限元和棱边法有限元的计算结果，验证了A-?法节点有限元的正确性和有效性。
기우절점적유한원방법구유망격부분、구조고계기함수용역적우점。유우재절점상정의장량，절점유한원경괄용우다물리문제。단절점유한원방법직접구해전자장회출현위해，장량재불균균개질중불련속등문제。기우절점적A-?방법가이유효피면전통절점유한원방법존재적문제。본문연구A-?방법적공정응용，연구개역화폐역문제중여하설치관우시세화표세함수적변계조건，특별시파도문제화이상도체구적산사문제，토론료단구변계조건，복사변계조건적사용방법。대우이상도체변계조건채용료조항변계조건，여단구조건배합，극복방정적기이성。수치실험비교분석료A-?법절점유한원화릉변법유한원적계산결과，험증료A-?법절점유한원적정학성화유효성。
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-?method can effectively avoid problems caused by the traditional nodal-based finite element method. This paper focuses on A-?method 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-? nodal finite element method.