Dispersion properties of explicit finite element methods for wave propagation modelling on tetrahedral meshes

S. Geevers; W.A. Mulder; J.J.W. van der Vegt

doi:10.1007/s10915-018-0709-7

Dispersion properties of explicit finite element methods for wave propagation modelling on tetrahedral meshes

S. Geevers (Corresponding Author), W.A. Mulder, J.J.W. van der Vegt

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Abstract

We analyse the dispersion properties of two types of explicit finite element methods for modelling acoustic and elastic wave propagation on tetrahedral meshes, namely mass-lumped finite element methods and symmetric interior penalty discontinuous Galerkin methods, both combined with a suitable Lax–Wendroff time integration scheme. The dispersion properties are obtained semi-analytically using standard Fourier analysis. Based on the dispersion analysis, we give an indication of which method is the most efficient for a given accuracy, how many elements per wavelength are required for a given accuracy, and how sensitive the accuracy of the method is to poorly shaped elements.

Original language	English
Pages (from-to)	372-396
Number of pages	25
Journal	Journal of scientific computing
Volume	77
Issue number	1
Early online date	20 Apr 2018
DOIs	https://doi.org/10.1007/s10915-018-0709-7
Publication status	Published - 1 Oct 2018

Keywords

UT-Hybrid-D
Explicit finite element method
Mass lumping
Discontinuous Galerkin method
Wave equation
Dispersion analysis
Tetrahedral mesh

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title = "Dispersion properties of explicit finite element methods for wave propagation modelling on tetrahedral meshes",

abstract = "We analyse the dispersion properties of two types of explicit finite element methods for modelling acoustic and elastic wave propagation on tetrahedral meshes, namely mass-lumped finite element methods and symmetric interior penalty discontinuous Galerkin methods, both combined with a suitable Lax–Wendroff time integration scheme. The dispersion properties are obtained semi-analytically using standard Fourier analysis. Based on the dispersion analysis, we give an indication of which method is the most efficient for a given accuracy, how many elements per wavelength are required for a given accuracy, and how sensitive the accuracy of the method is to poorly shaped elements.",

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AU - Geevers, S.

AU - Mulder, W.A.

AU - van der Vegt, J.J.W.

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N2 - We analyse the dispersion properties of two types of explicit finite element methods for modelling acoustic and elastic wave propagation on tetrahedral meshes, namely mass-lumped finite element methods and symmetric interior penalty discontinuous Galerkin methods, both combined with a suitable Lax–Wendroff time integration scheme. The dispersion properties are obtained semi-analytically using standard Fourier analysis. Based on the dispersion analysis, we give an indication of which method is the most efficient for a given accuracy, how many elements per wavelength are required for a given accuracy, and how sensitive the accuracy of the method is to poorly shaped elements.

AB - We analyse the dispersion properties of two types of explicit finite element methods for modelling acoustic and elastic wave propagation on tetrahedral meshes, namely mass-lumped finite element methods and symmetric interior penalty discontinuous Galerkin methods, both combined with a suitable Lax–Wendroff time integration scheme. The dispersion properties are obtained semi-analytically using standard Fourier analysis. Based on the dispersion analysis, we give an indication of which method is the most efficient for a given accuracy, how many elements per wavelength are required for a given accuracy, and how sensitive the accuracy of the method is to poorly shaped elements.

KW - UT-Hybrid-D

KW - Explicit finite element method

KW - Mass lumping

KW - Discontinuous Galerkin method

KW - Wave equation

KW - Dispersion analysis

KW - Tetrahedral mesh

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VL - 77

SP - 372

EP - 396

JO - Journal of scientific computing

JF - Journal of scientific computing

IS - 1

ER -

Dispersion properties of explicit finite element methods for wave propagation modelling on tetrahedral meshes

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Keywords

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