The interior penalty discontinuous Galerkin method for elastic wave propagation: grid dispersion

Basabe, Jonás D. De; Sen, Mrinal K.; Wheeler, Mary F.

doi:10.1111/j.1365-246x.2008.03915.x

Cited by 155 publications

(95 citation statements)

References 34 publications

(74 reference statements)

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“…Rational functions [34] or sines and cosines [35] can also be considered as basis functions. Discontinuous Galerkin methods [36][37][38] allow for the use of standard high-order elements. Since the mass matrix is local, it is readily inverted.…”

Section: Discussionmentioning

confidence: 99%

New Triangular Mass-Lumped Finite Elements of Degree Six for Wave Propagation

Mulder¹

2013

PIER

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Abstract-Mass-lumped continuous finite elements allow for explicit time stepping with the second-order wave equation if the resulting integration weights are positive and provide sufficient accuracy. To meet these requirements on triangular and tetrahedral meshes, the construction of continuous finite elements for a given polynomial degree on the edges involves polynomials of higher degree in the interior. The parameters describing the supporting nodes of the Lagrange interpolating polynomials and the integration weights are the unknowns of a polynomial system of equations, which is linear in the integration weights. To find candidate sets for the nodes, it is usually required that the number of equations equals the number of unknowns, although this may be neither necessary nor sufficient. Here, this condition is relaxed by requiring that the number of equations does not exceed the number of unknowns. This resulted in two new types elements of degree 6 for symmetrically placed nodes. Unfortunately, the first type is not unisolvent. There are many different elements of the second type with a large range in their associated time-stepping stability limit. To assess the efficiency of the elements of various degrees, numerical tests on a simple problem with an exact solution were performed. Efficiency was measured by the computational time required to obtain a solution at a given accuracy. For the chosen example, elements of degree 4 with fourth-order time stepping appear to be the most efficient.

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Section: Discussionmentioning

confidence: 99%

New Triangular Mass-Lumped Finite Elements of Degree Six for Wave Propagation

Mulder¹

2013

PIER

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“…Let us quote few examples: Ainsworth et al (2006) provided a theoretical study for the 1D case; Basabe et al (2008) analysed the effects of basis functions on 2D periodic and regular quadrilateral meshes; and discussed the convergence of the DG-FEM combined with ADER time integration and 3D tetrahedral meshes. More related to our particular concern here, Delcourte et al (2009) provided a convergence analysis of the DG-FEM with a centred flux scheme and tetrahedral meshes for elastodynamics.…”

Section: Accuracy Of Dg-fem With Tetrahedral Meshesmentioning

confidence: 99%

Seismic Waves - Research and Analysis

Kanao¹

2012

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“…More specifically, the numerical algorithm can be summarized in the following steps ( Fig. 10.3): consider an elastic heterogeneous 3D medium, (i) make a partition of the computational domain based on the involved materials and/or structures to be simulated, (ii) select a suitable spectral-element discretization in each non-overlapping sub-region, and (iii) enforce the continuity of the numerical solution at the internal interfaces by treating the jumps of the displacements through a suitable DG algorithm of the interior penalty type (De Basabe et al 2008).…”

Section: Development Of the Numerical Codementioning

confidence: 99%

Physics-Based Earthquake Ground Shaking Scenarios in Large Urban Areas

Paolucci

Mazzieri

Smerzini

et al. 2014

Perspectives on European Earthquake Engineering and Seismology

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With the ongoing progress of computing power made available not only by large supercomputer facilities but also by relatively common workstations and desktops, physics-based source-to-site 3D numerical simulations of seismic ground motion will likely become the leading and most reliable tool to construct ground shaking scenarios from future earthquakes. This paper aims at providing an overview of recent progress on this subject, by taking advantage of the experience gained during a recent research contract between Politecnico di Milano, Italy, and Munich RE, Germany, with the objective to construct ground shaking scenarios from hypothetical earthquakes in large urban areas worldwide. Within this contract, the SPEED computer code was developed, based on a spectral element formulation enhanced by the Discontinuous Galerkin approach to treat non-conforming meshes. After illustrating the SPEED code, different case studies are overviewed, while the construction of shaking scenarios in the Po river Plain, Italy, is considered in more detail. Referring, in fact, to this case study, the comparison with strong motion records allows one to derive some interesting considerations on the pros and on the present limitations of such approach.

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The interior penalty discontinuous Galerkin method for elastic wave propagation: grid dispersion

Cited by 155 publications

References 34 publications

New Triangular Mass-Lumped Finite Elements of Degree Six for Wave Propagation

New Triangular Mass-Lumped Finite Elements of Degree Six for Wave Propagation

Seismic Waves - Research and Analysis

Physics-Based Earthquake Ground Shaking Scenarios in Large Urban Areas

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