摘要
在弹性波传播的数值模拟中,吸收边界被广泛应用于截取有限空间进行无限空间问题的分析.完全匹配层(perfect matched layer,PML)吸收边界较其它吸收边界条件具有更优越的吸收性能,已被成功应用于直角坐标系下的弹性波方程正演模拟.考虑极坐标系下二阶弹性波动方程,通过采用辅助函数的方法,提出了一种非分裂格式的完全匹配层吸收边界条件.并且基于Galerkin近似技术,给出了非对称以及轴对称条件下的时域有限元计算格式.通过数值算例分析了该极坐标系下分裂格式的完全匹配层吸收边界的有效性.
In the solving of the elastic wave equations with the numerical approximation tech- niques, the absorbing boundary conditions had been widely used to truncate the infinite-space simulation to a finite-space one. The perfect matched layer （PML） technique as an absorbing boundary condition had exhibited excellent absorbing efficiency in the forward simulation of the elastic wave equation formulated in rectangular coordinates. Based on the stretched coordinate concept, an advanced non-splitting-field perfect matched layer （ non-splitting PML） equation for elastic waves was formulated in the polar coordinate system. Through the introduction of inte- grated complex variables in the radial direction into the auxiliary functions, the PML formula- tion was extended in polar coordinates in view of the 2nd-order elastic wave equation with dis- placements as basic unknowns. In addition, aimed at the time-domain cases and with the finite- element method for space discretization, the finite-element time-domain （FETD） scheme in standard displacement-based formulation was presented. The scheme for the special cases in axisymmetric polar coordinates was also given. The effectiveness and validity of the present non-splitting PML formulation are demonstrated with several numerical examples.
出处
《应用数学和力学》
CSCD
北大核心
2015年第9期956-969,共14页
Applied Mathematics and Mechanics
基金
国家自然科学基金(11162008
51368038)
甘肃省环境保护厅科研基金(GSEP-2014-23)
甘肃省教育厅研究生导师基金(1103-07)~~
关键词
完全匹配层
极坐标系
吸收边界条件
时域有限元
perfect matched layer
polar coordinate system
absorbing boundary condition
time-domain finite element
