An Analysis of the Discontinuous Galerkin Method for Wave Propagation Problems

Hu, Fang Q.; Hussaini, M. Y.; Rasetarinera, Patrick

doi:10.1006/jcph.1999.6227

Cited by 251 publications

(118 citation statements)

References 31 publications

Supporting

Mentioning

112

Contrasting

Unclassified

Order By: Relevance

“…Other methods include spectral and pseudospectral techniques (e.g., Carcione, 1994), which are characterized by high accuracy, or finite-element methods (FEMs), which have been successfully used for seismicwave simulations in 3D sedimentary basins because of their geometrical flexibility (e.g., Bao et al, 1998). The ADER-DG method (e.g., Arnold, 1982;Falk and Richter, 1999;Hu et al, 1999;Rivière and Wheeler, 2003;Monk and Richter, 2005;Käser and Dumbser, 2006) exploits the geometrical advantages offered by tetrahedral meshes and thus appears promising because of improved flexibility in the mesh creation step when compared to other high-order methods, while preserving comparable accuracy. However, from a computational perspective it is significantly more expensive.…”

Section: Introductionmentioning

confidence: 99%

Spectral-Element Simulations of Seismic Waves Generated by the 2009 L'Aquila Earthquake

Magnoni¹,

Casarotti²,

Michelini³

et al. 2013

Bulletin of the Seismological Society of America

View full text Add to dashboard Cite

We adopt a spectral-element method (SEM) to perform numerical simulations of the complex wavefield generated by the 6 April 2009 M w 6.3 L'Aquila earthquake in central Italy. The mainshock is represented by a finite-fault solution obtained by inverting strong-motion and Global Positioning System data, testing both 1D and 3D wavespeed models for central Italy. Surface topography, attenuation, and the Moho discontinuity are also accommodated. Including these complexities is essential to accurately simulate seismic-wave propagation. Three-component synthetic waveforms are compared to corresponding velocimeter and strong-motion recordings. The results show a favorable match between data and synthetics up to ∼0:5 Hz in a 200 km × 200 km × 60 km model volume, capturing features mainly related to topography or low-wavespeed basins. We construct synthetic peak ground velocity maps that, for the 3D model, are in good agreement with observations, thus providing valuable information for seismic-hazard assessment. Exploiting the SEM in combination with an adjoint method, we calculate finite-frequency kernels for specific seismic arrivals. These kernels capture the volumetric sensitivity associated with the selected waveform and highlight prominent effects of topography on seismic-wave propagation in central Italy.

show abstract

Section: Introductionmentioning

confidence: 99%

Spectral-Element Simulations of Seismic Waves Generated by the 2009 L'Aquila Earthquake

Magnoni¹,

Casarotti²,

Michelini³

et al. 2013

Bulletin of the Seismological Society of America

View full text Add to dashboard Cite

show abstract

“…In these preliminary papers we addressed some restricted inverse problems and dealt mainly with the computational challenges associated with poroelastic inverse problems. For the 25 forward model we used the SPECFEM2D code based on the spectral element method due to Morency and Tromp, [11]. However issues with the SPECFEM2D code (discussed later in the paper) led us to developing the discontinuous Galerkin (DG) formulation discussed in this paper.…”

Section: Introductionmentioning

confidence: 99%

“…Since then the method has been extensively analysed [22,23,24,25,26,27]. Furthermore, the DG method and many variants have been applied to many problems, including first-and second-order hyperbolic problems such as Maxwell's equations and the elastic and acoustic wave equations [28,29,30, 31, 40 …”

Section: Introductionmentioning

confidence: 99%

A discontinuous Galerkin method for poroelastic wave propagation: The two-dimensional case

Ward

Lähivaara

Eveson

2017

Journal of Computational Physics

View full text Add to dashboard Cite

“…2,3,4,5,6,7 The spectral error for the semi-discrete scheme and h ! 0 is found to converge at h 2p+3 , for the absolute dispersion error, and h 2p+1 for the dissipation error.…”

Section: Introductionmentioning

confidence: 99%

Performance of the DGM for the Linearized Euler Equations With Non-Uniform Mean-Flow

Williamschen

Gabard

Bériot

2015

21st AIAA/CEAS Aeroacoustics Conference

View full text Add to dashboard Cite

A dispersion analysis of the fully-discrete, nodal discontinuous Galerkin method (DGM) for the solution of the time-domain linearized Euler equations (LEE) is performed. Two dispersion analysis methods are developed, considering both uniform and non-uniform mean-flow e↵ects. Convergence studies are performed for the dispersion, dissipation, and nodal solution errors of the acoustic, entropy, and vorticity modes. The accuracy and stability of the DGM are analyzed in the context of aeroacoustic applications, and guidelines are proposed for the choice of optimal discretizations. Computational costs are estimated for a model problem and related to the choice of the element size, polynomial order, and time step. Results indicate that temporal error can become a dominant source of error for high accuracy requirements and long distance wave propagation. The stability of the scheme is analyzed for a shear layer mean flow profile. Aliasing-type errors are found to contribute to the formation of numerical instabilities which are further strengthened by increases in the polynomial order.

show abstract

An Analysis of the Discontinuous Galerkin Method for Wave Propagation Problems

Cited by 251 publications

References 31 publications

Spectral-Element Simulations of Seismic Waves Generated by the 2009 L'Aquila Earthquake

Spectral-Element Simulations of Seismic Waves Generated by the 2009 L'Aquila Earthquake

A discontinuous Galerkin method for poroelastic wave propagation: The two-dimensional case

Performance of the DGM for the Linearized Euler Equations With Non-Uniform Mean-Flow

Contact Info

Product

Resources

About