论文部分内容阅读
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 caused by lithography laser interferometer mirror thermal deformation, thus affecting the accuracy of lithography. In this paper, a fast boundary element method based on quadratic element is used to simulate the large-scale temperature field of the laser interferometer mirror. The introduction of discontinuous elements can effectively deal with the corner problem; a new fast multipole algorithm is used to accelerate the boundary element method. Create a unified quadratic unit multipole expansion format to handle mixed boundaries. The numerical example analyzes the calculation accuracy and efficiency of the fast multipole BEM, and compares it with the conventional one. The large-scale temperature field of the laser interferometer is calculated and compared with the finite element method. The results show that the fast multipole BEM based on quadratic elements can solve large-scale three-dimensional heat transfer problems with high accuracy.