微波元件与加速结构的有限元分析

研究了有限元方法在二维均匀结构和轴对称加速结构中的应用,采用了带宽优化技术和子空间求解特征值方法,并给出了部分例子,结果表明该方法精度高、速度快.这些方法可直接用于三维程序、并行计算.

Study of Microwave Element and Accelerating Structure Using Finite Element Method

An analysis of the electromagnetic field in 2D uniform and axis-symmetric structures based on FEM (Finite Element Method) is presented in this paper. The equation of FEM is derived based on the Maxwell equations and variational theory. The resulting tridiagonal matrix in FEM equation is optimized to reduce band-width of the matrix and the calculation time. Subspace method is applied to solve the eigenvalue equation where the matrices are sparse and make the solver run faster. The number of eigenvalue and eigenvector can be selected by the user which makes the solver-more efficient. Irregular triangle element is used for meshing to describe the structure geometry with good approximation and improve the accuracy of the solution. Numerical results for rectangle waveguide, pill-box cavity and disc-loaded structure show that our finite element method has high accuracy, good convergence and fast running speed. Comparing with SUPERFISH program, the FEM method is advantageous in both accuracy and speed. The accuracy of our FEM is almost the same as the variational method which is used as a basic method in many fields. All strategy used here can be applied to the 3-dimension structure and other eigenvalue problems.