An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes - I. The two-dimensional isotropic case with external source terms

By Martin Käser, Michael Dumbser. 2006

432 citations recorded by the source corpus.

Subfields: Computational Mechanics, Geophysics

View Paper: https://www.semanticscholar.org/paper/1fd51153162b2e8a063a3c224295e9520d4f953d

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Citations in the corpus

The finite-difference and finite-element modeling of seismic wave propagation and earthquake motion (2007, methodology): “…element methods (BIEM and BEM), for example Bouchon and Sánchez-Sesma (2007), spectral-element method (SPEM), for example Komatitsch et al. (2004) and Chaljub et al. (2007), and the arbitrary high-order derivative – discontinuous Galerkin method (ADER-DG), for example Käser and Dumbser (2006).”
A Stable Finite Difference Method for the Elastic Wave Equation on Complex Geometries with Free Surfaces (2007, neutral): “Other methods include the well-established spectral element method [7, 13, 20], the pseudospectral method [8] and the discontinuous Galerkin method [12].”
Stable Grid Refinement and Singular Source Discretization for Seismic Wave Simulations (2009, methodology): “The composite grid discretization developed here, together with the generalization of the method to curvilinear grids [2], which enables accurate modeling of free surfaces on realistic (nonplanar) topography, makes the finite difference method a very attractive alternative to the recently developed ”
An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes — II. The three-dimensional isotropic case (2006, methodology): “We especially point out, that allowing jumps in the numerical solution may be useful with respect to dynamic rupture simulations or to the treatment of large jumps in material properties as shown in (Käser & Dumbser 2005).”
An implicit staggered‐grid finite‐difference method for seismic modelling (2009, methodology): “…FE methods based on spectral element (e.g. Komatitsch & Vilotte 1998; De Basabe & Sen 2007) and discontinuous Galerkin (e.g. Rivière & Wheeler 2003; Käser & Dumbser 2006; De Basabe et al. 2008) methods are being investigated aggressively by the seismological community, FD-based methods still…”
An arbitrary high-order Discontinuous Galerkin method for elastic waves on unstructured meshes — III. Viscoelastic attenuation (2007, background): “A more detailed discussion of the choice of frequency ranges and the corresponding sampling frequencies can be found in ( Graves & Day 2003 ).”
Seismic imaging: From classical to adjoint tomography (2012, methodology): “Discontinuous Gerlekin (DG) methods also gained popularity in seismology in recent years (e.g., Castro and Käser, 2010; Dumbser and Käser, 2006; Hermann et al., 2010; Käser and Dumbser, 2006).”
An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes - IV. Anisotropy (2007, methodology): “This ordering is chosen in order to be consistent with the formulation introduced in previous work (Käser & Dumbser 2006; Dumbser & Käser 2006; Käser, Dumbser, de la Puente & Igel 2006).”
Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems (2007, methodology): “For efficient algorithms to do the Cauchy–Kovalewski procedure, we refer to [11,26,12].”
3‐D finite‐difference, finite‐element, discontinuous‐Galerkin and spectral‐element schemes analysed for their accuracy with respect to P‐wave to S‐wave speed ratio (2011, background): “…Journal International C© 2011 RAS Downloaded from https://academic.oup.com/gji/article-abstract/187/3/1645/617234 by guest on 27 July 2018 Käser 2006; Käser & Dumbser 2006; Dumbser et al. 2007; Käser et al. 2007, 2008; de la Puente et al. 2007, 2008; De Basabe et al. 2008; de la Puente 2008;…”