吉林大学学报(理学版)

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时域声波散射问题单轴优化PML方法的收敛性

杨孝英1, 杜新伟2   

  1. 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
  • 收稿日期:2016-05-24 出版日期:2017-05-26 发布日期:2017-05-31
  • 通讯作者: 杜新伟 E-mail:duxw@jlu.edu.cn

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

YANG Xiaoying1, DU Xinwei2   

  1. 1. School of Basic Science, Changchun University of Technology, Changchun 130012, China; 2. Key Laboratory of[JP2]Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, Changchun 130012, China
  • Received:2016-05-24 Online:2017-05-26 Published:2017-05-31
  • Contact: DU Xinwei E-mail:duxw@jlu.edu.cn

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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.

关键词: 时域散射, 优化的PML方法, 指数收敛

Abstract: We proposed an uniaxial optimal perfectly matched layer (PML) method for solving timedomain 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 δ. 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.

Key words: optimal PML method, exponential convergence, timedomain scattering

中图分类号: 

  • O241.3
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