Large-scale simulation of elastic wave propagation in heterogeneous media on parallel computers

Bao, Hesheng; Bielak, Jacobo; Ghattas, Omar; Kallivokas, Loukas F.; O’Hallaron, David R.; Shewchuk, Jonathan Richard; Xu, Jiasheng

doi:10.1016/s0045-7825(97)00183-7

Cited by 263 publications

(148 citation statements)

References 13 publications

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“…Thus, for regions such as central Italy in which topography is significant we prefer to resort to a finite-element technique, in which handling topography is natural and accurate. 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.…”

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

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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.

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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

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“…Consider a wave of the form in Equation (2) propagating in an unbounded elastic domain, the x 1 -x 2 plane, governed by Equation (1). The objective of defining a perfectly matched layer (PML) is to simulate such wave propagation by using a corresponding bounded domain.…”

Section: Perfectly Matched Layermentioning

confidence: 99%

“…Thus, if F i (x i )>0 and p i > 0, then the wave solution admitted in the PML medium is of the form of the elastic-medium solution [Equation (2)], but with an imposed spatial attenuation. This attenuation is of the form exp[−F i (x i )p i ] in the x i -direction, and is independent of the frequency if p i is.…”

Section: Perfectly Matched Layermentioning

confidence: 99%

“…The solution of the elastodynamic wave equation over an unbounded domain finds applications in soil-structure interaction analysis [1] and in the simulation of earthquake ground motion [2]. The need for realistic models often compels a numerical solution using a bounded domain, along with an artificial absorbing boundary or layer that simulates the unbounded domain beyond.…”

Section: Introductionmentioning

confidence: 99%

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Perfectly matched layers for transient elastodynamics of unbounded domains

Basu

Chopra

2004

Numerical Meth Engineering

193

116

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SUMMARYOne approach to the numerical solution of a wave equation on an unbounded domain uses a bounded domain surrounded by an absorbing boundary or layer that absorbs waves propagating outward from the bounded domain. A perfectly matched layer (PML) is an unphysical absorbing layer model for linear wave equations that absorbs, almost perfectly, outgoing waves of all non-tangential angles-ofincidence and of all non-zero frequencies. In a recent work [Computer Methods in Applied Mechanics and Engineering 2003; 192:1337-1375, the authors presented, inter alia, time-harmonic governing equations of PMLs for anti-plane and for plane-strain motion of (visco-)elastic media. This paper presents (a) corresponding time-domain, displacement-based governing equations of these PMLs and (b) displacement-based finite element implementations of these equations, suitable for direct transient analysis. The finite element implementation of the anti-plane PML is found to be symmetric, whereas that of the plane-strain PML is not. Numerical results are presented for the anti-plane motion of a semi-infinite layer on a rigid base, and for the classical soil-structure interaction problems of a rigid strip-footing on (i) a half-plane, (ii) a layer on a half-plane, and (iii) a layer on a rigid base. These results demonstrate the high accuracy achievable by PML models even with small bounded domains.

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“…Mulder et al (2014) list stability estimates for the known tetrahedral lumped elements of degrees 1 to 3 as well as for the symmetric interior-penalty discontinuous Galerkin method up to degree 4. Bao et al (1998) worked with the classic linear tetrahedral mass-lumped elements for elastic wave propagation modelling. Here, we will also include elements of degree 2 and 3.…”

mentioning

confidence: 99%

Performance of continuous mass-lumped tetrahedral elements for elastic wave propagation with and without global assembly

Mulder

Shamasundar

2016

Geophys. J. Int.

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SUMMARYWe consider isotropic elastic wave propagation with continuous mass-lumped finite elements on tetrahedra with explicit time stepping. These elements require higher-order polynomials in their interior to preserve accuracy after mass lumping and are only known up to degree 3. Global assembly of the symmetric stiffness matrix is a natural approach but requires large memory.Local assembly on the fly, in the form of matrix-vector products per element at each time step, has a much smaller memory footprint. With dedicated expressions for local assembly, our code ran about 1.3 times faster for degree 2 and 1.9 times for degree 3 on a simple homogeneous test problem, using 24 cores. This is similar to the acoustic case. For a more realistic problem, the gain in efficiency was a factor 2.5 for degree 2 and 3 for degree 3. For the lowest degree, the linear element, the expressions for both the global and local assembly can be further simplified.In that case, global assembly is more efficient than local assembly. Among the three degrees, the element of degree 3 is the most efficient in terms of accuracy at a given cost.

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Large-scale simulation of elastic wave propagation in heterogeneous media on parallel computers

Cited by 263 publications

References 13 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

Perfectly matched layers for transient elastodynamics of unbounded domains

Performance of continuous mass-lumped tetrahedral elements for elastic wave propagation with and without global assembly

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