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

Pled, Florent; Desceliers, Christophe

doi:10.1007/s11831-021-09581-y

Cited by 35 publications

(8 citation statements)

References 347 publications

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“…In the solid domain, the computational region is closed by an unsplit displacement-strain mixed PML formulation. This is similar to the work of Pled and Desceliers [21]. However, the formulation proposed here is based on the standard two-parameter stretching function, which is more efficient than the single-parameter stretching function based formulation especially when evanescent waves are present.…”

Section: Introductionsupporting

confidence: 58%

“…Fathi et al extended the two-dimensional formulation to three dimensions, and discussed several time integration schemes [20]. Pled and Desceliers reviewed the latest developments on the PML method for modelling elastic wave propagation in unbounded domains [21]. An alternative displacement-strain mixed formulation is proposed which is close to the displacement-stress mixed formulation [18][19][20], and an extended Newmark time marching scheme is introduced.…”

Section: Introductionmentioning

confidence: 99%

“…It should be noted that the coordinate stretching function used in Ref. [21] is a simplified version of the standard stretching function, with the real part fixed to be one. This could reduce the efficiency of the PML technique.…”

Section: Introductionmentioning

confidence: 99%

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Time domain numerical modelling of guided wave excitation in fluid-filled pipes

Duan

2022

Finite Elements in Analysis and Design

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Section: Introductionsupporting

confidence: 58%

Section: Introductionmentioning

confidence: 99%

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Time domain numerical modelling of guided wave excitation in fluid-filled pipes

Duan

2022

Finite Elements in Analysis and Design

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“…Furthermore, a simpler and more systematic reformulation of the PML using complex coordinate stretching technology has been developed, which has expanded the area of applications of the PML 55,56 . A comprehensive review of the PML method can be found in existing literatures 57,58 . We now focus only on the PML formulations utilized in elastodynamics.…”

Section: Introductionmentioning

confidence: 99%

Time‐domain scaled boundary perfectly matched layer for elastic wave propagation

Zhang

et al. 2023

Numerical Meth Engineering

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A novel artificial boundary method called the scaled boundary perfectly matched layer (SBPML) is proposed for the transient analysis of elastic wave propagation in unbounded domains. This method constructs a generalized perfectly matched layer (PML) around the finite interior subdomain based on a coordinate transformation inspired by the scaled boundary finite element method (SBFEM). It can model the infinite exterior subdomains of heterogeneous materials, featuring both parallel and radial straight‐line physical surfaces and interfaces. In addition, generally‐shaped (even nonconvex‐shape) artificial boundaries can be used to provide high flexibility in choosing the geometry of the finite interior subdomain. Two coordinate mapping technologies, namely the modified scaled boundary coordinate transformation from the SBFEM and the complex coordinate stretching from the PML, are successively utilized to construct the proposed method. By introducing the integral of stress as an auxiliary variable, the resulting SBPML subdomain is represented in the time domain using a mixed displacement‐stress unsplit‐field formulation. This has the added benefit of allowing for easy incorporation into standard dynamic finite element methods. The performance of the SBPML is demonstrated through several numerical examples, including P‐SV and SH wave propagation problems occurring in unbounded domains with complex geometries and heterogeneous material properties. The numerical results are evaluated in comparison to both reference solution and existing artificial boundary methods, ultimately demonstrating the flexibility, robustness, accuracy, and stability of the proposed approach.

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“…Along the same lines, Zhang et al [11] implemented the PML technique in FE software Abaqus and created a toolbox for soil‐structure interaction problems in 2D and 3D. Moreover, a detailed review of the PML method and its various formulations developed over the past 25 years for the numerical modeling and simulation of wave propagation in unbounded media can be found in [12].…”

Section: Introductionmentioning

confidence: 99%

Wave propagation in inhomogeneous media via FE/PML method

Savidis

Bergmann²,

Schepers

et al. 2022

Geotechnik

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The Perfectly Matched Layer (PML) method is an efficient approach to imposing radiation conditions at the bounded region of interest in case of wave propagation in unbounded domains. This paper presents and validates 3D FE/PML numerical schemes based on two different PML formulations for homogeneous and inhomogeneous geological media exhibiting discrete or continuous inhomogeneity. In the equation of motion for the PML domain the applied stretching behavior is expressed either as complex material properties or as complex coordinates. Both PML formulations are implemented in the FEM and verified against analytical solutions. Three different types of material inhomogeneity are considered: layered half‐space, continuously inhomogeneous half‐space with linear velocity profile and continuously inhomogeneous half‐space with nonlinear velocity profile. Sensitivity analyses are conducted, and the performance of the developed numerical schemes is investigated taking into account a broad variation of the PML parameters. Recommendations are given for the optimal values of the PML parameters for the case of homogeneous and inhomogeneous geological media.

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

Cited by 35 publications

References 347 publications

Time domain numerical modelling of guided wave excitation in fluid-filled pipes

Time domain numerical modelling of guided wave excitation in fluid-filled pipes

Time‐domain scaled boundary perfectly matched layer for elastic wave propagation

Wave propagation in inhomogeneous media via FE/PML method

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