时域声波散射问题单轴优化PML方法的收敛性  

Convergence of Uniaxial Optimal PML Method for Time-Domain Acoustic Scattering Problems

作　　者：杨孝英[1] 杜新伟[2] 

机构地区：[1]长春工业大学基础科学学院,长春130012 [2]吉林大学符号计算与知识工程教育部重点实验室,长春130012

出　　处：《吉林大学学报（理学版）》2017年第3期587-593,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11271159);吉林大学符号计算与知识工程教育部重点实验室项目(批准号:93k172012Z01)

摘　　要：基于Laplace变换和频域的复坐标拉伸,给出一种解时域声波散射问题的单轴优化完美匹配层(PML)方法.该方法在矩形区域中构造单轴优化PML,为各项异性散射体的散射问题提供一种较灵活有效的计算方法,并且该方法在吸收函数中引入一个小参数ε0,使得散射问题的优化PML方法的计算不再依赖PML层的厚度δ.结果表明,只要参数ε0充分小,优化的PML解指数即收敛于原散射问题的解.We proposed an uniaxial optimal perfectly matched layer （PML） method for solving timedomain acoustic scattering problem based on the Laplace transform and the complex coordinate stretching in the frequency domain. The uniaxial optimal PML was constructed by this method in a rectangular domain, which provided a flexible and effictive calculation method for the scattering problems of anisotropic scatters. A small parameter ε0 was introduced into the absorption function, so that the calculation of the optimal PML method for scattering problem was no longer dependent on the thickness of the PML layer ＆ The results show that the optimal PML solution converges exponentially to the solution of the original scattering problem if the parameter ε0 is sufficiently small.

关 键 词：时域散射 优化的PML方法 指数收敛 

分 类 号：O241.3[理学—计算数学]