谱元法与透射边界的配合使用及其稳定性研究  

A COMBINATION USAGE OF TRANSMITTING FORMULA AND SPECTRAL ELEMENT METHOD AND THE STUDY OF ITS STABILITY

作　　者：戴志军[1] 李小军[1] 侯春林[2] 

机构地区：[1]中国地震局地球物理研究所,北京100080 [2]环境保护部核与辐射安全中心,北京100082

出　　处：《工程力学》2015年第11期40-50,共11页Engineering Mechanics

基　　金：973计划项目(2011CB013601);国家自然科学基金项目(91215301;61203276;61472373);中国地震局地球物理研究所基本科研项目(DQJB12B12);北京市属高等学校创新团队建设提升计划项目(IDHT20130507)

摘　　要：在无限域波动模拟中引入透射边界条件时,目前多将边界上的透射公式与内域的有限元法结合使用,其计算精度由有限元方法决定,而谱元法因结合有限元和频谱法的优势则比有限元空间域积分具有更高的计算精度。该文基于谱元法非等距网格划分特性,研究了内域的谱元法与边界上的透射公式结合的理论方法,给出了相应的透射公式使用方法,并基于建立的谱元法波动数值模型探讨了透射公式的稳定性问题。研究表明:空间域插值系数需控制在一个合理范围内,空间域插值方法相对于时间域插值方法更为稳定,高频失稳出现可能性相对较小;Gamma算子的使用可提高模拟的精度,采用Gamma算子后对于高阶透射公式仍可出现低频漂移现象,可结合降阶消漂的方式实现稳定精度高的透射边界应用。For the simulation of the problem on infinite domain, finite element method（FEM） is usually combined with transmitting formulas, and the precision of the simulation is mainly determined by the FEM methods. Spectral element method（SEM） takes advantages of both spectral method and FEM, and achieves higher precision for integration in space domain compared with FEM. This paper investigates the application of transmitting formulas in details when the interior domain uses the method of SEM. In this paper, we illustrate the use of SEM with transmitting formulas firstly. Meanwhile, the stability problem of transmitting formula is discussed in depth. The high frequency instability occurs more frequently for the interpolation in the time domain than in the space domain, and the interpolation coefficient in space domain should be in an appropriate range. Recognizing that the gamma operator is an effective measure to enhance the precision of simulation, we give a concrete method to set the value of gamma. Higher-order transmitting formulas with gamma operator may result in low-frequency drift. The paper points out that using order-reduction method is effective to get stable transmitting boundary conditions with high precision.

关 键 词：谱元法 有限元法 透射公式 透射边界 数值稳定性 

分 类 号：P315.9[天文地球—地震学]