Comptes Rendus
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Three-dimensional hybrid asynchronous perfectly matched layer for wave propagation in heterogeneous semi-infinite media
Comptes Rendus. Mécanique, Volume 348 (2020) no. 12, pp. 1003-1030.

This paper presents an efficient hybrid asynchronous three-dimensional (3D) perfectly matched layer (PML) for modeling unbounded domains. The proposed unsplit explicit or implicit 3D PML formulation is implemented in the framework of a heterogeneous asynchronous time integrator. It is fully versatile in terms of time integrators and time step sizes according to partitions while conserving classical finite element formulations in the elastic domain without complex-valued stretched coordinates. Examples of a semi-infinite bar, Lamb’s test, and a soil–structure interaction problem with PML-truncated semi-infinite heterogeneous media are investigated to illustrate the efficiency of the proposed PML in terms of accuracy and CPU time.

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DOI : 10.5802/crmeca.59
Mots clés : Three-dimensional perfectly matched layers (PMLs), Unbounded domains, Wave propagation, Transient analysis, Subdomain coupling, Heterogeneous asynchronous time integrator (HATI)
Sijia Li 1, 2 ; Michael Brun 3 ; Irini Djeran-Maigre 2 ; Sergey Kuznetsov 4

1 Structural Mechanics and Coupled Systems Laboratory, Conservatoire National des Arts et Métiers, 292 rue Saint-Martin, 75141 Paris Cedex 03, France
2 Univ Lyon, INSA-Lyon, GEOMAS, 69621 Villeurbanne, France
3 LEM3 CNRS UMR 7239, Université de Lorraine, 7 rue Félix Savart, 57070 METZ, France
4 Institute for Problems in Mechanics, 119526 Moscow, Russia
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {Three-dimensional hybrid asynchronous perfectly matched layer for wave propagation in heterogeneous semi-infinite media},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {1003--1030},
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     volume = {348},
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Sijia Li; Michael Brun; Irini Djeran-Maigre; Sergey Kuznetsov. Three-dimensional hybrid asynchronous perfectly matched layer for wave propagation in heterogeneous semi-infinite media. Comptes Rendus. Mécanique, Volume 348 (2020) no. 12, pp. 1003-1030. doi : 10.5802/crmeca.59. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.59/

[1] P. Bettess Infinite elements, Int. J. Numer. Meth. Eng., Volume 11 (1977), pp. 53-64 | DOI | Zbl

[2] A. Houmat Mapped infinite p-element for two-dimensional problems of unbounded domains, Comput. Geotech., Volume 35 (2008), pp. 608-615 | DOI

[3] B. Enquist B; A. Majda Absorbing boundary conditions for the numerical simulation of waves, Math. Comput., Volume 31 (1977), pp. 629-651 | MR

[4] D. Kosloff; R. Kosloff Absorbing boundaries for wave propagation problems, J. Comput. Phys., Volume 63 (1986), pp. 363-376 | DOI | MR | Zbl

[5] J. F. Semblat; L. Lenti; A. Gandomzadeh A simple multi-directional absorbing layer method to simulate elastic wave propagation in unbounded domains, Int. J. Numer. Meth. Eng., Volume 85 (2011), pp. 1543-1563 | DOI | Zbl

[6] P. Rajagopal; M. Drozdz; E. A. Skelton On the use of the absorbing layers to simulate the propagation of elastic waves in unbounded isotropic media using commercially available finite element packages, NDT and E Int., Volume 51 (2012), pp. 30-40 | DOI

[7] E. Zafati; M. Brun; I. Djeran-Maigre; F. Prunier Design of an efficient multi-directional explicit/implicit Rayleigh absorbing layer for seismic wave propagation in unbounded domain using a strong form formulation, Int. J. Numer. Meth. Eng., Volume 106 (2015), pp. 83-112 | DOI | MR | Zbl

[8] J. P. Bérenger A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., Volume 114 (1994), pp. 185-200 | DOI | MR | Zbl

[9] W. C. Chew; W. H. Weedon A 3D perfectly matched medium from modified Maxwell’s equations with stretched coordinates, Microw. Opt. Technol. Lett., Volume 7 (1994), pp. 599-604 | DOI

[10] W. C. Chew; Q. H. Liu Perfectly matched layers for elastodynamics: a new absorbing boundary condition, J. Comput. Acoust., Volume 4 (1996), pp. 341-359 | DOI

[11] F. Collino; C. Tsogka Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media, Geophysics, Volume 66 (2001), pp. 294-307 | DOI

[12] T. Wang; X. Tang Finite-difference modeling of elastic wave propagation: a nonsplitting perfectly matched approach, Geophysics, Volume 68 (2003), pp. 1749-1755 | DOI

[13] R. Matzen An efficient finite element time-domain formulation for the elastic second-order wave equation: A non split complex frequency shifted convolutional PML, Int. J. Numer. Meth. Eng., Volume 88 (2011), pp. 951-973 | DOI | MR | Zbl

[14] U. Basu; A. Chopra Perfectly matched layers for time-harmonic elastodynamics of unbounded domains: theory and finite-element implementation, Comput. Meth. Appl. Mech. Eng., Volume 192 (2003), pp. 1337-1375 | DOI | Zbl

[15] U. Basu; A. Chopra Perfectly matched layers for transient elastodynamics of unbounded domains, Int. J. Numer. Meth. Eng., Volume 59 (2004), pp. 1039-1074 | DOI | MR | Zbl

[16] U. Basu Explicit finite element perfectly matched layer for transient three-dimensional elastic waves, Int. J. Numer. Meth. Eng., Volume 77 (2009), pp. 151-176 | DOI | MR | Zbl

[17] LS-DYNA LS-DYNA Keyword User’s Manual, Livermore Software Technology Corporation, 2019

[18] J. Mamie; W. P. Kikstra DIANA User’s Manual, DIANA FEA BV, 2016 (Version 10.1)

[19] M. Brun; E. Zafati; I. Djeran-Maigre; F. Prunier Hybrid asynchronous perfectly matched layer for seismic wave propagation in unbounded domains, Finite Elem. Anal. Des., Volume 122 (2016), pp. 1-15 | DOI | MR

[20] S. Kucukcoban; L. F. Kallivokas Mixed perfectly-matched-layers for direct transient analysis in 2D elastic heterogeneous media, Comput. Meth. Appl. Mech. Eng., Volume 200 (2011), pp. 57-76 | DOI | MR | Zbl

[21] A. Fathi; B. Poursartip; L. F. Kallivokas Time-domain hybrid formulations for wave simulations in three-dimensional PML-truncated heterogeneous media, Int. J. Numer. Meth. Eng., Volume 101 (2015), pp. 165-198 | DOI | MR | Zbl

[22] M. Brun; A. Gravouil; A. Combescure Two FETI-based heterogeneous time step coupling methods for Newmark and α-schemes derived from the energy method, Comput. Meth. Appl. Mech. Eng., Volume 283 (2015), pp. 130-176 | DOI | MR | Zbl

[23] A. Gravouil; A. Combescure; M. Brun Heterogeneous asynchronous time integrators for computational structural dynamics, Int. J. Numer. Meth. Eng., Volume 102 (2015), pp. 202-232 | DOI | MR | Zbl

[24] Q. H. Liu Perfectly matched layers for elastic waves in cylindrical and spherical coordinates, J. Acoust. Soc. Am., Volume 105 (1999), pp. 2075-2084 | DOI

[25] J. M. Carcione; D. Kosloff Representation of matched-layer kernels with viscoelastic mechanical models, Int. J. Numer. Anal. Model., Volume 10 (2013), pp. 221-232 | MR | Zbl

[26] S. Li; M. Brun; I. Djeran-Maigre; S. Kuznetsov Hybrid asynchronous absorbing layers based on Kosloff damping for seismic wave propagation in unbounded domains, Comput. Geotech., Volume 109 (2019), pp. 69-81 | DOI

[27] I. Harari; U. Albocher Studies of FE/PML for exterior problems of time-harmonic elastic waves, Comput. Meth. Appl. Mech. Eng., Volume 195 (2006), pp. 3854-3879 | DOI | MR | Zbl

[28] A. Gravouil; A. Combescure A multi-time-step explicit–implicit method for non-linear structural dynamics, Int. J. Numer. Meth. Eng., Volume 50 (2001), pp. 199-225 | DOI | Zbl

[29] N. M. Newmark A method of computation for structural dynamics, J. Eng. Mech. Div. (ASCE), Volume 85 (1959), pp. 67-94

[30] A. Combescure; A. Gravouil A numerical scheme to couple subdomains with different time-steps for predominantly linear transient analysis, Comput. Meth. Appl. Mech. Eng., Volume 191 (2002), pp. 1129-1157 | DOI | Zbl

[31] T. J. R. Hughes The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1987 | Zbl

[32] T. Belytschko; W. K. Liu; B. Moran Nonlinear Finite Elements for Continua and Structures, Wiley, New York, 2000 | Zbl

[33] H. Lamb Proceedings of the 38th Royal Society of London, 72, Royal Society of London, London, 1903, pp. 128-130

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