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 

机构地区：[1]Key Laboratory of Earthquake Engineering and Engineering Vibration,Institute of Engineering Mechanics,China Earthquake Administration,Harbin 150080,China [2]Key Laboratory of Earthquake Disaster Mitigation,Ministry of Emergency Management,Harbin 150080,China [3]Aix Marseille University,CNRS,Centrale Marseille,LMA,Marseille F-13353,France

出　　处：《Earthquake Engineering and Engineering Vibration》2023年第2期407-421,共15页地震工程与工程振动（英文刊）

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。

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.

关 键 词：computational seismology seismic anisotropy wave propagation ELASTODYNAMICS 

分 类 号：TU311.3[建筑科学—结构工程]