Multi-axial unsplit frequency-shifted perfectly matched layer for displacement-based anisotropic wave simulation in infinite domain

作     者：Xie Zhinan Zheng Yonglu Paul Cristini Zhang Xubin Xie Zhinan;Zheng Yonglu;Paul Cristini;Zhang Xubin

作者机构：Key Laboratory of Earthquake Engineering and Engineering VibrationInstitute of Engineering MechanicsChina Earthquake AdministrationHarbin 150080China Key Laboratory of Earthquake Disaster MitigationMinistry of Emergency ManagementHarbin 150080China Aix Marseille UniversityCNRSCentrale MarseilleLMAMarseille F-13353France 

出 版 物：《Earthquake Engineering and Engineering Vibration》 (地震工程与工程振动（英文刊）)

年 卷 期：2023年第22卷第2期

页      面：407-421页

核心收录：

学科分类：08[工学] 0708[理学-地球物理学] 081304[工学-建筑技术科学] 0813[工学-建筑学] 0701[理学-数学] 

基　　金：Scientific Research Fund of Institute of Engineering Mechanics,China Earthquake Administration under Grant No.2021EEEVL0102 National Natural Science Foundation of China under Grant Nos.U2039209 and 51808516 the National Key R&D Program of China under Grant No.2018YFC1504004 Distinguished Young Scholars Program of the Natural Science Foundation of Heilongjiang province,China under Grant No.YQ2020E005。 

主　　题：computational seismology seismic anisotropy wave propagation elastodynamics 

摘      要：Multi-axial perfectly matched layer(M-PML),known to have lost the perfect-matching property owing to multi-axial coordinate stretching,has been numerically validated to be long-time stable and it is thus used extensively in linear anisotropic wave simulation and in isotropic cases where the PML becomes unstable.We are concerned with the construction of the M-PML for anisotropic wave simulation based on a second order wave equation implemented with the displacement-based numerical method.We address the benefit of the incorrect chain rule,which is implicitly adopted in the previous derivation of the M-PML.We show that using the frequency-shifted stretching function improves the absorbing efficiency of the M-PML for near-grazing incident waves.Then,through multi-axial complex-coordinate stretching the second order anisotropic wave equation in a weak form,we derive a time-domain multi-axial unsplit frequency-shifted PML(M-UFSPML)using the frequency-shifted stretching function and the incorrect chain rule.A new approach is provided to reduce the number of memory variables needed for computing convolution terms in the M-UFSPML.The obtained M-UFSPML is well suited for implementation with a finite element or the spectral element method.By providing several typical examples,we numerically verify the accuracy and long-time stability of the implementation of our M-UFSPML by utilizing the Legendre spectral element method.