基于坐标映射的类周期电磁金属阵列布局设计的灵敏度分析方法  

Mapping-based method for sensitivity analysis of quasi-periodic array

作　　者：王奇[1] 袁坷 高仁璟[1] 刘书田[1] WANG Qi;YUAN Ke;GAO Ren-jing;LIU Shu-tian(State Key Laboratory of Structural Analysis for lndustrial Equipment,alian University of Technology,Dalian 116024,China)

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,大连116024

出　　处：《计算力学学报》2022年第1期86-91,共6页Chinese Journal of Computational Mechanics

基　　金：国家重点研发计划课题(2020YFB1708303);国家自然科学基金(11802050,U1806215);深圳市技术攻关重点项目(JSGG20200102155001779)资助项目。

摘　　要：特定性能的类周期电磁金属阵列已成功应用于多种类型的电磁器件中,以实现其电磁辐射或散射性能的提升设计。类周期电磁金属阵列可描述为由多个相似形状的电磁金属单元按照特定的布局形式组合形成。布局形式由阵列的布局参数确定,通常包括每个单元的尺寸、转角以及位置参数。布局参数往往规模较大且相互独立,需要经过设计优化以满足阵列的性能要求。利用灵敏度信息可以加速设计优化,但基于差分法的灵敏度分析的计算量往往较大,特别是对于类周期电磁金属阵列的布局设计问题。提出一种基于坐标映射的类周期电磁金属阵列布局设计的灵敏度分析方法,其核心思想是,通过构建基于坐标映射的电流场基函数模型,由虚拟的单元映射出参数化的类周期电磁金属阵列布局形式,将阵列域的电磁性能变换为在虚拟的单元域内进行求解,以实现类周期电磁金属阵列的快速参数化建模及阵列布局设计的灵敏度分析。典型数值算例验证了该方法的有效性。结果表明,提出的方法能够准确得到类周期电磁金属阵列布局设计的灵敏度信息,且与传统的差分法相比求解效率有大幅提升。Function-specific quasi-periodic arrays have been integrated in many electromagnetic devices for performance improvement.In most cases a quasi-periodic array can be described as the arrangement of a series of similar array elements adjusting with the arrangement parameters.The parameters of interest include stretching,rotating,and position parameters of each array element and should be independently optimized to satisfy the array design requirement.Generally,the design optimization can be accelerated by using the sensitivity information,but the sensitivity calculation is often expensive,particularly for the case of quasi-periodic arrangement design.Thus,it is important to develop an efficient sensitivity analysis method.In this paper,a mapping-based method is proposed for predicting the radiation property of quasi-periodic array and computing its sensitivities with respect to the arrangement parameters.Through mapping transformation,the radiating problem of quasi-periodic array is modeled within a virtual single-cell domain by constructing the parametrized electric field integral equation,and the sensitivities are analytically calculated through the adjoint approach based on the geometrical parameterization of the quasi-periodic array.A typical numerical example is provided to validate the accuracy and effectiveness of the proposed method.Compared with the traditional finite difference method,the solution efficiency is greatly improved.

关 键 词：类周期阵列 电磁结构 灵敏度分析 布局优化 矩量法 

分 类 号：O224[理学—运筹学与控制论] O302[理学—数学]