半解析高阶有限谱元法及其在波导介质层PBG 结构滤波器优化设计中的应用

摘要

本文采用高阶有限谱单元对分层结构的横截面进行半解析离散。将结构中沿纵向均匀的区段视为子结构，运用基于 Riccati 方程的精细积分算法求出其出口刚度阵。网格拼装后即可对分层介质问题进行求解。半解析高阶谱单元的采用可以避免著名的龙格现象，该算法的数值精度能随着基函数的阶数的增加呈指数级提高。即高阶有限谱单元能够达到任意需要的精度。数值算例证明这种方法具有很高的精度与效率。在高精度高效率分析的基础上建立了滤波器的优化设计模型，利用遗传算法对优化模型进行全局优化，得到了PBG 结构滤波性能全局最优的设计参数。%2D spectral elements were employed to discretize the cross section of a layered structure,the structure was divided into several substructures homogeneous along the longitudinal direction .A Riccati equation based high precision integration (HPI)method was utilized to perform integration along the the longitudinal direction, which was the undiscretized direction,to generate the stiffness matrix of the whole layered structure.The spectral element can avoid the well-known Runge phenomenon and achieve spectral accuracy,which means the numerical results can converge exponentially as the increase of interpolation order of basis functions.Numerical examples demonstrate the high efficiency and accuracy of the proposed method.Genetic Algorithm was used to optimize PBG structure based on the Semi-Analytical Spectral Element Method.