Geodesic
Numerical modeling of seismic waves by discontinuous spectral element methods
Paola F. Antonietti1 ; Alberto Ferroni1 ; Ilario Mazzieri1 ; Roberto Paolucci2 ; Alfio Quarteroni3 ; Chiara Smerzini4 ; Marco Stupazzini5
1 MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy
2 Dipartimento di Ingegneria Civile ad Ambientale, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy
3 CMCS, Ecole Polytechnique Federale de Lausanne (EPFL), Station 8, 1015 Lausanne, Switzerland
4 Dipartimento di Ingegneria Civile ad Ambientale, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy
5 Munich Re, Munich, Königinstr. 107, 80802, Germany
ESAIM. Proceedings, Tome 61 (2018), pp. 1-37.

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We present a comprehensive review of Discontinuous Galerkin Spectral Element (DGSE) methods on hybrid hexahedral/tetrahedral grids for the numerical modeling of the ground motion induced by large earthquakes. DGSE methods combine the exibility of discontinuous Galerkin meth-ods to patch together, through a domain decomposition paradigm, Spectral Element blocks where high-order polynomials are used for the space discretization. This approach allows local adaptivity on discretization parameters, thus improving the quality of the solution without affecting the compu-tational costs. The theoretical properties of the semidiscrete formulation are also revised, including well-posedness, stability and error estimates. A discussion on the dissipation, dispersion and stability properties of the fully-discrete (in space and time) formulation is also presented. Here space dis-cretization is obtained based on employing the leap-frog time marching scheme. The capabilities of the present approach are demonstrated through a set of computations of realistic earthquake scenar-ios obtained using the code SPEED (http://speed.mox.polimi.it), an open-source code specifically designed for the numerical modeling of large-scale seismic events jointly developed at Politecnico di Milano by The Laboratory for Modeling and Scientific Computing MOX and by the Department of Civil and Environmental Engineering.
DOI : 10.1051/proc/201861001

Paola F. Antonietti 1 ; Alberto Ferroni 1 ; Ilario Mazzieri 1 ; Roberto Paolucci 2 ; Alfio Quarteroni 3 ; Chiara Smerzini 4 ; Marco Stupazzini 5

1 MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy
2 Dipartimento di Ingegneria Civile ad Ambientale, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy
3 CMCS, Ecole Polytechnique Federale de Lausanne (EPFL), Station 8, 1015 Lausanne, Switzerland
4 Dipartimento di Ingegneria Civile ad Ambientale, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy
5 Munich Re, Munich, Königinstr. 107, 80802, Germany 
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     author = {Paola F. Antonietti and Alberto Ferroni and Ilario Mazzieri and Roberto Paolucci and Alfio Quarteroni and Chiara Smerzini and Marco Stupazzini},
     title = {Numerical modeling of seismic waves by discontinuous spectral element methods},
     journal = {ESAIM. Proceedings},
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     volume = {61},
     year = {2018},
     doi = {10.1051/proc/201861001},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201861001/}
}
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Paola F. Antonietti; Alberto Ferroni; Ilario Mazzieri; Roberto Paolucci; Alfio Quarteroni; Chiara Smerzini; Marco Stupazzini. Numerical modeling of seismic waves by discontinuous spectral element methods. ESAIM. Proceedings, Tome 61 (2018), pp. 1-37. doi : 10.1051/proc/201861001. http://geodesic.mathdoc.fr/articles/10.1051/proc/201861001/

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