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多孔介质瞬态分析中非分裂PML及时域有限元实现

周凤玺 高贝贝

周凤玺, 高贝贝. 多孔介质瞬态分析中非分裂PML及时域有限元实现[J]. 应用数学和力学, 2016, 37(2): 195-209. doi: 10.3879/j.issn.1000-0887.2016.02.008
引用本文: 周凤玺, 高贝贝. 多孔介质瞬态分析中非分裂PML及时域有限元实现[J]. 应用数学和力学, 2016, 37(2): 195-209. doi: 10.3879/j.issn.1000-0887.2016.02.008
ZHOU Feng-xi, GAO Bei-bei. A Non-Splitting PML for Transient Analysis of Poroelastic Media and Its Finite Element Implementation[J]. Applied Mathematics and Mechanics, 2016, 37(2): 195-209. doi: 10.3879/j.issn.1000-0887.2016.02.008
Citation: ZHOU Feng-xi, GAO Bei-bei. A Non-Splitting PML for Transient Analysis of Poroelastic Media and Its Finite Element Implementation[J]. Applied Mathematics and Mechanics, 2016, 37(2): 195-209. doi: 10.3879/j.issn.1000-0887.2016.02.008

多孔介质瞬态分析中非分裂PML及时域有限元实现

doi: 10.3879/j.issn.1000-0887.2016.02.008
基金项目: 国家自然科学基金(11162008;51368038);甘肃省环境保护厅基金(GSEP-2014-23);甘肃省教育厅研究生导师基金(1103-07)
详细信息
    作者简介:

    周凤玺(1979—),男,副教授,博士,博士生导师(通讯作者. E-mail: geolut@163.com).

  • 中图分类号: O347.4

A Non-Splitting PML for Transient Analysis of Poroelastic Media and Its Finite Element Implementation

Funds: The National Natural Science Foundation of China(11162008;51368038)
  • 摘要: 在波场的数值模拟中,完全匹配层(perfectly matched layer, PML)已经被证明是一种十分有效的吸收技术,并得到了广泛的应用.为了解决具有无限域的多孔介质中2阶弹性波动方程数值模拟中的吸收边界问题,提出了一种非分裂格式的PML(nonsplitting perfectly matched layer, NPML).首先,基于Biot多孔介质波动理论,建立了以固相和流相位移表示的2阶动力控制方程,其中考虑了固体颗粒和孔隙流体的可压缩性、惯性以及孔隙流体的粘性.其次,根据复伸展坐标变换的定义,通过Laplace变换获得了非分裂格式PML的频域表达式.然后,借助辅助函数将该方程变换到时间域内,得到了一种有效的非分裂PML.最后,基于Galerkin近似方法,给出了其时域有限元计算格式.通过数值算例分析了该非分裂格式的PML在饱和介质动力响应分析中的有效性.
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出版历程
  • 收稿日期:  2015-05-25
  • 修回日期:  2015-09-30
  • 刊出日期:  2016-02-15

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