Review and Recent Developments on the Perfectly Matched Layer (PML) Method for the Numerical Modeling and Simulation of Elastic Wave Propagation in Unbounded Domains

Autor: Christophe Desceliers, Florent Pled
Přispěvatelé: Laboratoire Modélisation et Simulation Multi-Echelle (MSME), Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel
Jazyk: angličtina
Rok vydání: 2021
Předmět:
Discretization
Differential equation
Wave propagation
Computer science
MSC : 35L05
35L20
35B35
65M60
65M12
74J05
74J10
74S05
74H15
FOS: Physical sciences
02 engineering and technology
Physics - Classical Physics
01 natural sciences
Domain (mathematical analysis)
Absorbing layers (ALs)
Mathematics::Numerical Analysis
Time-domain analysis
Finite Element Method (FEM)
[PHYS.MECA.STRU]Physics [physics]/Mechanics [physics]/Structural mechanics [physics.class-ph]
Elastic wave propagation
[PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph]
0202 electrical engineering
electronic engineering
information engineering
Applied mathematics
0101 mathematics
[PHYS.MECA.VIBR]Physics [physics]/Mechanics [physics]/Vibrations [physics.class-ph]
Absorbing boundary conditions (ABCs)
Perfectly matched layers (PMLs)
Applied Mathematics
Isotropy
Finite difference
Classical Physics (physics.class-ph)
[SPI.MECA.VIBR]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Vibrations [physics.class-ph]
Finite element method
Computer Science Applications
010101 applied mathematics
Unbounded domain
Perfectly matched layer
[SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph]
Elastodynamics
020201 artificial intelligence & image processing
Zdroj: Archives of Computational Methods in Engineering
Archives of Computational Methods in Engineering, Springer Verlag, 2021, ⟨10.1007/s11831-021-09581-y⟩
Archives of Computational Methods in Engineering, Springer Verlag, 2022, ⟨10.1007/s11831-021-09581-y⟩
ISSN: 1134-3060
1886-1784
Popis: International audience; This review article revisits and outlines the perfectly matched layer (PML) method and its various formulations developed over the past 25 years for the numerical modeling and simulation of wave propagation in unbounded media. Based on the concept of complex coordinate stretching, an efficient mixed displacement-strain unsplit-field PML formulation for second-order (displacementbased) linear elastodynamic equations is then proposed for simulating the propagation and absorption of elastic waves in unbounded (infinite or semi-infinite) domains. Both time-harmonic (frequency-domain) and time-dependent (timedomain) PML formulations are derived for two-and three-dimensional linear elastodynamic problems. Through the introduction of only a few additional variables governed by low-order auxiliary differential equations, the resulting mixed timedomain PML formulation is second-order in time, thereby allowing the use of standard time integration schemes commonly employed in computational structural dynamics and thus facilitating the incorporation into existing displacementbased finite element codes. For computational efficiency, the proposed timedomain PML formulation is implemented using a hybrid approach that couples a mixed (displacement-strain) formulation for the PML region with a classical (displacement-based) formulation for the physical domain of interest, using a standard Galerkin finite element method (FEM) for spatial discretization and a Newmark time scheme coupled with a finite difference (Crank-Nicolson) time scheme for time sampling. Numerical experiments show the performances of the PML method in terms of accuracy, efficiency and stability for two-dimensional linear elastodynamic problems in single-and multi-layer isotropic homogeneous elastic media.
Databáze: OpenAIRE
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