M. N. Dmitriev, V. V. Lisitsa, “Application of M-PML absorbing boundary conditions to the numerical simulation of wave propagation in anisotropic media. Part I: reflectivity”, Sib. Zh. Vychisl. Mat., 14:4 (2011), 333–344; Num. Anal. Appl., 4:4 (2011), 271

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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2011, Volume 14, Number 4, Pages 333–344 (Mi sjvm446)

This article is cited in 22 scientific papers (total in 22 papers)

Application of M-PML absorbing boundary conditions to the numerical simulation of wave propagation in anisotropic media. Part I: reflectivity

M. N. Dmitriev^ab, V. V. Lisitsa^a

^a A. A. Trofimuk Institute of Petroleum Geology and Geophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University, Novosibirsk

Full-text PDF (254 kB) Citations (22)

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Abstract: This paper presents a detailed study of the construction of reflectionless boundary conditions for anisotropic elastic problems. A Multiaxial Perfectly Matched Layer (M-PML) approach is considered. With a proper stabilization parameter, the M-PML ensures solution stability for arbitrary anisotropic media. It is proved that this M-PML modification is not perfectly matched, and the reflectivity the M-PML exceeds that of the standard PML. Moreover, the reflection coefficient linearly depends on the stabilization parameter. A problem of constructing an optimal stabilization parameter is formulated as follows: find a minimal possible parameter that ensures stability. This problem is considered in a second paper on this work.

Key words: anisotropy, reflectionless boundary conditions, perfectly matched layer, elastic wave equations.

Received: 17.12.2010
Revised: 26.01.2011

English version:
Numerical Analysis and Applications, 2011, Volume 4, Issue 4, Pages 271–280
DOI: https://doi.org/10.1134/S199542391104001X

Bibliographic databases:

Document Type: Article

UDC: 519.63

Language: Russian

Citation: M. N. Dmitriev, V. V. Lisitsa, “Application of M-PML absorbing boundary conditions to the numerical simulation of wave propagation in anisotropic media. Part I: reflectivity”, Sib. Zh. Vychisl. Mat., 14:4 (2011), 333–344; Num. Anal. Appl., 4:4 (2011), 271–280

Citation in format AMSBIB

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\transl

\jour Num. Anal. Appl.

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\crossref{https://doi.org/10.1134/S199542391104001X}

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Linking options:

https://www.mathnet.ru/eng/sjvm446

https://www.mathnet.ru/eng/sjvm/v14/i4/p333

Cycle of papers

Application of M-PML absorbing boundary conditions to the numerical simulation of wave propagation in anisotropic media. Part I: reflectivity
M. N. Dmitriev, V. V. Lisitsa
Sib. Zh. Vychisl. Mat., 2011, 14:4, 333–344
Application of absorbing boundary conditions M-PML for numerical simulation of wave propagation in anisotropic media. Part II: Stability
M. N. Dmitriev, V. V. Lisitsa
Sib. Zh. Vychisl. Mat., 2012, 15:1, 45–54

This publication is cited in the following 22 articles:

Wei Zhong, Tielin Liu, “An Implementation Method of the Complex Frequency-Shifted Uniaxial/Multi-Axial PML Technique for Viscoelastic Seismic Wave Propagation”, Journal of Earthquake Engineering, 28:4 (2024), 885
Te-chao Zhang, Xiao-shan Cao, Si-yuan Chen, “Gradient viscoelastic virtual boundary for numerical simulation of wave propagation”, Computers & Mathematics with Applications, 147 (2023), 202
Zhinan Xie, Yonglu Zheng, Paul Cristini, Xubin Zhang, “Multi-axial unsplit frequency-shifted perfectly matched layer for displacement-based anisotropic wave simulation in infinite domain”, Earthq. Eng. Eng. Vib., 22:2 (2023), 407
Wang Yu., Bai M., Yang L., Zhao X., Saad O.M., Chen Ya., “An Unsplit Cfs-Pml Scheme For the Second-Order Wave Equation With Its Application in Fractional Viscoacoustic Simulation”, IEEE Trans. Geosci. Remote Sensing, 60 (2022)
Pled F., Desceliers Ch., “Review and Recent Developments on the Perfectly Matched Layer (Pml) Method For the Numerical Modeling and Simulation of Elastic Wave Propagation in Unbounded Domains”, Arch. Comput. Method Eng., 29:1 (2022), 471–518
Yingjie Gao, Meng-Hua Zhu, “Application of the Reflectionless Discrete Perfectly Matched Layer for Acoustic Wave Simulation”, Front. Earth Sci., 10 (2022)
Yiwen He, Ting Wu, Yu-Po Wong, Temesgen Bailie Workie, Jingfu Bao, Ken-ya Hashimoto, 2022 IEEE MTT-S International Conference on Microwave Acoustics and Mechanics (IC-MAM), 2022, 74
Poursartip B., Fathi A., Tassoulas J.L., “Large-Scale Simulation of Seismic Wave Motion: a Review”, Soil Dyn. Earthq. Eng., 129 (2020), 105909
Zhao Zh., Chen J., “Complex Frequency-Shifted Multi-Axial Perfectly Matched Layer For Frequency-Domain Seismic Wavefield Simulation in Anisotropic Media”, Geophys. Prospect., 67:5 (2019), 1329–1344
Li J., Innanen K.A., Wang B., “A New Second Order Absorbing Boundary Layer Formulation For Anisotropic-Elastic Wavefield Simulation”, Pure Appl. Geophys., 176:4 (2019), 1717–1730
Lisitsa V., Kolyukhin D., Tcheverda V., “Statistical Analysis of Free-Surface Variability'S Impact on Seismic Wavefield”, Soil Dyn. Earthq. Eng., 116 (2019), 86–95
Koskela J., Plessky V., Willemsen B., Turner P., Hammond B., Fenzi N., “Hierarchical Cascading Algorithm For 2-D Fem Simulation of Finite Saw Devices”, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 65:10 (2018), 1933–1942
Koskela J., Plessky V., 2018 IEEE International Ultrasonics Symposium (Ius), IEEE International Ultrasonics Symposium, IEEE, 2018
Gao K., Huang L., “Optimal Damping Profile Ratios For Stabilization of Perfectly Matched Layers in General Anisotropic Media”, Geophysics, 83:1 (2018), T15–T30
Julius Koskela, Victor Plessky, 2018 IEEE International Ultrasonics Symposium (IUS), 2018, 1
Fathi A., Poursartip B., Kallivokas L.F., “Time-Domain Hybrid Formulations For Wave Simulations in Three-Dimensional Pml-Truncated Heterogeneous Media”, Int. J. Numer. Methods Eng., 101:3 (2015), 165–198
Ping P. Zhang Yu. Xu Y., “A Multiaxial Perfectly Matched Layer (M-Pml) for the Long-Time Simulation of Elastic Wave Propagation in the Second-Order Equations”, J. Appl. Geophys., 101 (2014), 124–135
Metivier L., Brossier R., Labbe S., Operto S., Virieux J., “a Robust Absorbing Layer Method For Anisotropic Seismic Wave Modeling”, J. Comput. Phys., 279 (2014), 218–240
Tago J., Metivier L., Virieux J., “Smart Layers: a Simple and Robust Alternative To Pml Approaches For Elastodynamics”, Geophys. J. Int., 199:2 (2014), 700–706
Liu You-Shan, Teng Ji-Wen, Liu Shao-Lin, Xu Tao, “Explicit Finite Element Method with Triangle Meshes Stored by Sparse Format and its Perfectly Matched Layers Absorbing Boundary Condition”, Chinese J. Geophys.-Chinese Ed., 56:9 (2013), 3085–3099

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Sibirskii Zhurnal Vychislitel'noi Matematiki

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