激光干涉仪反射镜三维温度场的快速多极边界元分析  

FAST MULTIPOLE BOUNDARY ELEMENT ANALYSIS OF 3-D TEMPERATURE FIELD OF PLANE MIRROR

作　　者：高令飞[1] 王海涛[2] 张鸣[1] 朱煜[1] 

机构地区：[1]清华大学精密仪器与机械学系,北京100084 [2]清华大学核能与新能源技术研究院,北京100084

出　　处：《工程力学》2012年第11期365-369,共5页Engineering Mechanics

基　　金：863项目(2009AA04Z148);973项目(2009CB724205)

摘　　要：温差造成光刻机激光干涉仪反射镜热变形,从而影响光刻机的精度。该文将基于二次单元的快速边界元法用于激光干涉仪反射镜的大规模温度场模拟。不连续单元的引入可以有效处理角点问题;新型快速多极算法用于边界元法的加速求解。建立统一的二次单元多极展开格式以处理混合边界。数值算例分析了快速多极边界元法的计算精度和效率,并和常规算法比较;使用该算法对激光干涉仪反射镜进行了大规模温度场计算,并和有限元法比较。结果表明:基于二次单元的快速多极边界元法可以高精度求解大规模三维传热问题。Temperature difference leads to thermal deformation of the plane mirror, therefore affecting its working efficiency. In this paper, the fast boundary element method （BEM） based on quadratic element is applied for large-scale thermal analysis of the plane mirror. An introduction of the discontinuous element can treat the corner problem efficiently, and the new version of the fast multipole method is adopted to accelerate the BEM solution. A unified multipole expansion form for quadratic element is established to deal with mixed boundary conditions. In the numerical examples, both accuracy and efficiency of the fast multipole BEM are investigated and compared with the conventional algorithm. The proposed method is used to large-scale temperature calculation of the plane mirror and compared with finite element results. It is shown that the fast multipole BEM based on quadratic element is capable of large-scale 3-D thermal analysis with high accuracy.

关 键 词：边界元 快速多极 二次单元 温度场 大规模 

分 类 号：O343.6[理学—固体力学]