3-D large-scale wave propagation modeling by spectral element method on Cray T3E multiprocessor

Seriani, G.

doi:10.1016/s0045-7825(98)00057-7

Cited by 120 publications

(62 citation statements)

References 13 publications

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“…In this respect, the SEM is related to FEMs in which mass lumping is used to avoid the costly resolution of the nondiagonal system resulting from the use of a Gauss quadrature rule [e.g., Cohen et al, 1993]. As mentioned above, a different choice is made in the Chebyshev SEM used by some authors [e.g., Priolo et al, 1994;Seriani, 1998], in which an integration rule that is exact for the polynomial basis chosen is used, with the consequence that the exactly diagonal mass matrix is lost.…”

Section: Accuracy Of the Methodsmentioning

confidence: 99%

“…Other authors [e.g., Priolo et al, 1994;Seriani, 1998] use a different implementation of the SEM based on Chebyshev polynomials. The main advantages are that the Gauss-Lobatto-Chebyshev integration rule is exact for the chosen polynomial basis, while it is only approximate in the case of GLL (see Section 3.11), and that the Gauss-LobattoChebyshev points and weights are known analytically (in the GLL version they are computed numerically).…”

Section: Numerical Integrationmentioning

confidence: 99%

“…The main disadvantage of the approach is that it does not lead to a diagonal mass matrix, and that therefore iterative solvers for large matrix systems have to be implemented and an implicit time-marching scheme is often used. This is technically difficult, but has been used successfully even in 3-D [Seriani, 1997[Seriani, , 1998]. Because an unconditionally stable implicit time scheme is used, this method is not sensitive to very high Pwave speeds in small grid cells that can drastically reduce the time step and therefore increase the cost of the explicit time scheme used in the Legendre approach.…”

Section: Numerical Integrationmentioning

confidence: 99%

“…The SEM has been used for two decades in computational fluid dynamics [Patera, 1984]. It has more recently been applied to problems related to two-dimensional (2-D) [Cohen et al, 1993;Priolo et al, 1994] and 3-D local or regional [Komatitsch, 1997;Faccioli et al, 1997;Komatitsch and Vilotte, 1998;Seriani, 1998;Komatitsch and Tromp, 1999;Komatitsch et al, 2004;Liu et al, 2004] and global [Chaljub, 2000;Komatitsch and Tromp, 2002a, b;Komatitsch et al, 2002;Chaljub et al, 2003;Chaljub and Valette, 2004] seismic wave propagation. We introduce the full complexity of the 3-D Earth, i.e., lateral variations in compressionalwave speed, shear-wave speed, and density in the mantle, a 3-D crustal model, anisotropy, ellipticity, surface topography and bathymetry, as well as the effects of the oceans, rotation, and self-gravitation.…”

Section: Introductionmentioning

confidence: 99%

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The spectral-element method in seismology

Komatitsch

Tsuboi

Tromp

2005

Geophysical Monograph Series

121

120

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We present the main properties of the spectral-element method, which is well suited for numerical calculations of synthetic seismograms for three-dimensional Earth models. The technique is based upon a weak formulation of the equations of motion and combines the flexibility of a finite-element method with the accuracy of a pseudospectral method. The mesh is composed of hexahedral elements and honors the main discontinuities in the Earth model. The displacement vector is expressed in each element in terms of high-degree Lagrange interpolants, and integrals are computed based upon Gauss-Lobatto-Legendre quadrature, which leads to an exactly diagonal mass matrix and therefore drastically simplifies the algorithm. We use a fluid-solid coupling formulation that does not require iterations at the core-mantle or inner-core boundaries. The method is efficiently implemented on parallel computers with distributed memory based upon a message-passing methodology. We present two large-scale simulations for a realistic three-dimensional Earth model computed on the Japanese Earth Simulator at periods of 5 s and longer.

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Section: Accuracy Of the Methodsmentioning

confidence: 99%

Section: Numerical Integrationmentioning

confidence: 99%

Section: Numerical Integrationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The spectral-element method in seismology

Komatitsch

Tsuboi

Tromp

2005

Geophysical Monograph Series

121

120

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“…A particular FE scheme is the spectral-element (SE) method, which is state-of-the-art in regional and global earthquake simulations at the moment (e.g., Priolo et al, 1994;Komatitsch, 1997;Seriani, 1998;Chaljub, 2000;Capdeville et al, 2003;Nissen-Meyer et al, 2008;Fichtner et al, 2009;Cupillard et al, 2012). The SE method supports computational grids of deformable hexahedral elements, to simulate fully 3-D wavefields with high-order spatial accuracy, and explicit time extrapolation schemes.…”

Section: Introductionmentioning

confidence: 99%

Regional wave propagation using the discontinuous Galerkin method

et al. 2013

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Abstract. We present an application of the discontinuous Galerkin (DG) method to regional wave propagation. The method makes use of unstructured tetrahedral meshes, combined with a time integration scheme solving the arbitrary high-order derivative (ADER) Riemann problem. This ADER-DG method is high-order accurate in space and time, beneficial for reliable simulations of high-frequency wavefields over long propagation distances. Due to the ease with which tetrahedral grids can be adapted to complex geometries, undulating topography of the Earth's surface and interior interfaces can be readily implemented in the computational domain. The ADER-DG method is benchmarked for the accurate radiation of elastic waves excited by an explosive and a shear dislocation source. We compare real data measurements with synthetics of the 2009 L'Aquila event (central Italy). We take advantage of the geometrical flexibility of the approach to generate a European model composed of the 3-D EPcrust model, combined with the depthdependent ak135 velocity model in the upper mantle. The results confirm the applicability of the ADER-DG method for regional scale earthquake simulations, which provides an alternative to existing methodologies.

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Legendre spectral finite elements for structural dynamics analysis

Sprague

Geers

2007

Commun. Numer. Meth. Engng.

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SUMMARYSpectral, hierarchical, and h-type finite elements (FEs) are compared in the context of their application to structural dynamics analysis. The Timoshenko beam, which is the 1-D analog of Mindlin-type shell elements, is used for comparison in eigenvalue and transient-response analyses. A detailed formulation of each method is presented to illustrate clearly their fundamental differences. The principal advantages of spectral FEs over low-order h-type elements are (a) far superior accuracy for a fixed number of model degrees of freedom (DOF) and (b) much higher computational efficiency at a fixed accuracy level. The principal advantages over hierarchical p-type elements are (a) a mass matrix that is inherently diagonal as opposed to full, (b) DOF that pertain directly to nodal displacements and rotations, and (c) more efficient tensor-product factorization.

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3-D large-scale wave propagation modeling by spectral element method on Cray T3E multiprocessor

Cited by 120 publications

References 13 publications

The spectral-element method in seismology

The spectral-element method in seismology

Regional wave propagation using the discontinuous Galerkin method

Legendre spectral finite elements for structural dynamics analysis

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