Dispersion analysis of spectral element methods for elastic wave propagation

Seriani, G.; Oliveira, Saulo P.

doi:10.1016/j.wavemoti.2007.11.007

Cited by 134 publications

(73 citation statements)

References 20 publications

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“…Then, we identify the numerical eigenvalues ξ P and ξ S , corresponding to the physical frequencies, by computing the numerical velocities obtained for each eigenvalue and comparing them to the real values of c P and c S , respectively. We remark that the computed eigenvalues approximating ω S1 and ω S2 are not exactly the same but their difference is negligible (Seriani & Oliveira 2008;Zyserman & Gauzellino 2005). In the following we will select ξ S as that eigenvalue, between the two physically relevant, that leads to the worst approximation of c S .…”

Section: Dispersion Analysismentioning

confidence: 99%

“…For the acoustic case, the dispersion properties of high-order DG methods have been analyzed in Ainsworth (2004a) and in Ainsworth et al (2006), while time-stepping stability of continuous and discontinuous finite element methods has been addressed in Mulder et al (2014). In the elastic case, the dispersive behavior of spectral element methods has been analyzed in Seriani & Oliveira (2008) using a Rayleigh quotient approximation of the eigenvalue problem resulting from the dispersion analysis. Dispersion and dissipation properties of DGSE approximation on quadrilateral grids have been studied using a plane wave analysis in De Basabe et al (2008) and Antonietti et al (2012).…”

Section: Introductionmentioning

confidence: 99%

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Dispersion-dissipation analysis of 3-D continuous and discontinuous spectral element methods for the elastodynamics equation

Ferroni¹,

Antonietti²,

Mazzieri³

et al. 2017

Geophysical Journal International

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SUMMARYIn this paper we present a three dimensional dispersion and dissipation analysis for both the semi discrete and the fully discrete approximation of the elastodynamics equation based on the plane wave method. For space discretization we compare different approximation strategies, namely the continuous and the discontinuous spectral element method on both tetrahedral and hexahedral elements. For time discretization we employ a leapfrog time integration scheme. Several numerical results are presented and discussed.

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Section: Dispersion Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dispersion-dissipation analysis of 3-D continuous and discontinuous spectral element methods for the elastodynamics equation

Ferroni¹,

Antonietti²,

Mazzieri³

et al. 2017

Geophysical Journal International

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“…As stated in [46], the spectral method [63], the spectral element method [65,[90][91][92][93][94][95][96] and the spectral finite element method [45,[97][98][99] and each of the following references have been developed to solve wave propagation problems. Analysing the literature resources, it is sometimes difficult to recognise whether a method belongs to one or another of these methods.…”

Section: Methods Examplementioning

confidence: 99%

Spectral Methods for Modelling of Wave Propagation in Structures in Terms of Damage Detection—A Review

Palacz

2018

Applied Sciences

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Modern methods of detection and identification of structural damage direct the activities of scientific groups towards the improvement of diagnostic methods using for example the phenomenon of mechanical wave propagation. Damage detection methods that use mechanical wave propagation in structural components are extremely effective. Many different numerical approaches are used to model this phenomenon, but, due to their universal nature, spectral methods are the most commonly used, of which there are several types. This paper reviews recent research efforts in the field to show basic differences and effectiveness of the two most common spectral methods used for modelling the wave propagation problem in terms of damage detection.

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“…Ãk is the wave number [31]. k ¼ jkj is a scalar quantity in one dimension,k ¼ jkjðcos ; sin Þ in two dimensions andk ¼ jkjðcos cos 0; sin cos 0; sin 0Þ in three dimensions.…”

Section: Fixed-! Methods For Dispersionmentioning

confidence: 99%

Space-time spectral element method solution for the acoustic wave equation and its dispersion analysis

Geng

Qin

Zhang

et al. 2017

Acoust. Sci. & Tech.

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This paper presents the solution for the continuous space-time spectral element method (CSTSEM) based on Chebyshev polynomials for the acoustic wave equation. Acoustic wave propagation in various dimensions is simulated using quadrilateral, hexahedral, and tesseract elements. The convergence is studied for 1+1-dimensional wave propagation. The extended 2+1-and 3+1-dimensional wave equations are also numerically solved by CSTSEM and the dispersion characteristics are investigated. A fixed-! (! is the angular frequency) method is proposed for computing the dispersion of space-time coupled methods. CSTSEM is verified as a simple, practical isotropic algorithm with low dispersion and high accuracy.

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Dispersion analysis of spectral element methods for elastic wave propagation

Cited by 134 publications

References 20 publications

Dispersion-dissipation analysis of 3-D continuous and discontinuous spectral element methods for the elastodynamics equation

Dispersion-dissipation analysis of 3-D continuous and discontinuous spectral element methods for the elastodynamics equation

Spectral Methods for Modelling of Wave Propagation in Structures in Terms of Damage Detection—A Review

Space-time spectral element method solution for the acoustic wave equation and its dispersion analysis

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