Mixed perfectly-matched-layers for direct transient analysis in 2D elastic heterogeneous media

Kucukcoban, Sezgin; Kallivokas, Loukas F.

doi:10.1016/j.cma.2010.07.013

Cited by 89 publications

(84 citation statements)

References 76 publications

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“…12 shows the relative errors of the two approaches, defined as the percent deviation of the absolute values when compared to those of the exact solution. Clearly, the PML approach is substantially more accurate than the PB approach, with errors below 5% up to distances 25 x   , while the errors in the second approach exceed 10% even before a distance 5 x   , and it becomes intolerable at larger distances. When consideration is also given to the fact that in this example the PML model has only half the number of degrees of freedom of the PB model, it is clear that TLM+PML approach outperforms the TLM+PB approach by a vast margin.…”

Section: Pml Vs Paraxial Boundaries (Pb)mentioning

confidence: 99%

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Perfectly matched layers in the thin layer method

Barbosa

Park

Kausel

2012

Computer Methods in Applied Mechanics and Engineering

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This paper explores the coupling of the Perfectly Matched Layer technique (PML) with the Thin Layer Method (TLM), the combination of which allows making highly efficient and accurate simulations of layered half-spaces of infinite depth subjected to arbitrary dynamic sources anywhere. It is shown that with an appropriate complex stretching of the thickness of the thinlayers, one can assemble a system of layers which fully absorbs and attenuates waves for any angle of propagation. An extensive set of numerical experiments show that the TLM+PML performance is clearly superior to that of a standard TLM model with paraxial boundaries augmented with buffer layers (TLM+PB). This finding strongly suggests that the proposed combination may in due time constitute the preferred choice for this class of problems.

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Section: Pml Vs Paraxial Boundaries (Pb)mentioning

confidence: 99%

“…In more recent years, the PML has also been used widely for problems of elastic wave propagation in both structural mechanics and in geophysics [3,9,10,13,42]. A good literature review on the subject can be found in [25].…”

Section: Introductionmentioning

confidence: 99%

Perfectly matched layers in the thin layer method

Barbosa

Park

Kausel

2012

Computer Methods in Applied Mechanics and Engineering

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“…However, the second term vanishes since the stretch function (5) is not defined for the static case of ω = 0 [12]. Consequently, substitutingû i = −iωÛ i in the last term of (10) and taking inverse Fourier transform (−iω ⇒ ∂/∂t) of this, results in…”

Section: Formulation Of Pml For Elastic Wave Propagationmentioning

confidence: 99%

“…Despite the absence of a rigorous methodology for their choice [9,12], polynomial functions are often used as indicated below for the damping parameter:…”

Section: Complex Coordinates Stretchingmentioning

confidence: 99%

“…Subsequent to these electromagnetic wave applications, many PML formulations have been introduced for elastic wave propagation [6][7][8][9][10][11][12]. Amongst these, the splitfield formulations that are typically described by systems of first order equations with double (for 2D) or triple (for 3D) the number of stress-velocity physical equations (nine equations in all for the 3D case) .…”

Section: Introductionmentioning

confidence: 99%

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A second-order, perfectly matched layer formulation to model 3D transient wave propagation in anisotropic elastic media

Assi

Cobbold

2016

Journal of the Acoustical Society of America

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Numerical simulation of wave propagation in an infinite medium is made possible by surrounding a finite region by a perfectly matched layer (PML). Using this approach a generalized three-dimensional (3D) formulation is proposed for timedomain modeling of elastic wave propagation in an unbounded lossless anisotropic medium. The formulation is based on a second-order approach that has the advantages of, physical relationship to the underlying equations, and amenability to be implemented in common numerical schemes. Specifically, our formulation uses three second-order equations of the displacement field and nine auxiliary equations, along with the three time histories of the displacement field. The properties of the PML, which are controlled by a complex two-parameter stretch function, are such that it acts as near perfect absorber. Using finite element method (FEM) 3D numerical results are presented for a highly anisotropic medium. An extension of the formulation to the particular case of a Kelvin-Vogit viscoelastic medium is also presented.

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A supervised approach for improving the dimensionless frequency estimation for time‐domain simulations of building structures on embedded foundations

Kusanovic,

Ayoubi,

Seylabi

et al. 2024

Earthq Engng Struct Dyn

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The analysis of soil–structure interaction (SSI) problems has been established successfully in recent decades. In particular, the solution in the frequency domain provides an exact and efficient method for computing the response of the coupled system. Despite this, the state of practice as a first attempt to incentivize time domain analyses compatible with standard finite element packages introduces the so‐called dimensionless flexible‐base frequency. This frequency, which depends solely on the structure‐to‐soil‐period ratio, allows transforming the frequency domain analyses into time domain analyses using frequency‐independent soil impedance values. However, if such frequency exists for the combined system, it must depend on several physical variables. In this work, we propose a supervised approach to obtain the flexible‐base dimensionless frequency at which the frequency‐independent soil impedance should be used. The analysis is carried out using five dimensionless parameters, and the importance of each one to the estimation of the dimensionless flexible‐base frequency is investigated. We use an inverse problem based on ensemble Kalman inversion (EnKI) to obtain the optimal frequency of the interaction. The data obtained are then employed in a machine‐learning framework to map a set of dimensionless parameters to such a frequency. The generated mapping is finally verified, and a significant improvement in time‐domain simulations is shown compared to the state of practice.

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Mixed perfectly-matched-layers for direct transient analysis in 2D elastic heterogeneous media

Cited by 89 publications

References 76 publications

Perfectly matched layers in the thin layer method

Perfectly matched layers in the thin layer method

A second-order, perfectly matched layer formulation to model 3D transient wave propagation in anisotropic elastic media

A supervised approach for improving the dimensionless frequency estimation for time‐domain simulations of building structures on embedded foundations

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