Newmark local time stepping on high-performance computing architectures

Rietmann, Max; Grote, Marcus J.; Peter, Daniel; Schenk, Olaf

doi:10.1016/j.jcp.2016.11.012

Cited by 20 publications

(12 citation statements)

References 33 publications

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“…Dealing with small-scale heterogeneities in seismic wave simulation is a difficult task because it usually involves enormous computation costs. To handle them, Graphics Processing Unit (GPU) and/or High Performance Computing (HPC) implementations of well-established numerical techniques such as the Spectral Element method (SEM), the Discontinuous Galerkin method (DGM) and the Finite Difference method (FDM), have been proposed (Komatitsch et al 2010;Peter et al 2011;Weiss & Shragge 2013;Gokhberg & Fichtner 2016;Remacle et al 2016;Rietmann et al 2017). Furthermore, the DGM allows local time-stepping and p-adaptivity (e.g.…”

Section: Discussion a N D C O N C L U S I O N Smentioning

confidence: 99%

Non-periodic homogenization of 3-D elastic media for the seismic wave equation

Cupillard

Capdeville

2018

Geophysical Journal International

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Because seismic waves have a limited frequency spectrum, the velocity structure of the Earth that can be extracted from seismic records has a limited resolution. As a consequence, one obtains smooth images from waveform inversion, although the Earth holds discontinuities and small scales of various natures. Within the last decade, the non-periodic homogenization method shed light on how seismic waves interact with small geological heterogeneities and 'see' upscaled properties. This theory enables us to compute long-wave equivalent density and elastic coefficients of any media, with no constraint on the size, the shape and the contrast of the heterogeneities. In particular, the homogenization leads to the apparent, structure-induced anisotropy. In this paper, we implement this method in 3-D and show 3-D tests for the very first time. The non-periodic homogenization relies on an asymptotic expansion of the displacement and the stress involved in the elastic wave equation. Limiting ourselves to the order 0, we show that the practical computation of an upscaled elastic tensor basically requires (i) to solve an elastostatic problem and (ii) to low-pass filter the strain and the stress associated with the obtained solution. The elastostatic problem consists in finding the displacements due to local unit strains acting in all directions within the medium to upscale. This is solved using a parallel, highly optimized finite-element code. As for the filtering, we rely on the finiteelement quadrature to perform the convolution in the space domain. We end up with an efficient numerical tool that we apply on various 3-D models to test the accuracy and the benefit of the homogenization. In the case of a finely layered model, our method agrees with results derived from Backus. In a more challenging model composed by a million of small cubes, waveforms computed in the homogenized medium fit reference waveforms very well. Both direct phases and complex diffracted waves are accurately retrieved in the upscaled model, although it is smooth. Finally, our upscaling method is applied to a realistic geological model. The obtained homogenized medium holds structure-induced anisotropy. Moreover, full seismic wavefields in this medium can be simulated with a coarse mesh (no matter what the numerical solver is), which significantly reduces computation costs usually associated with discontinuities and small heterogeneities. These three tests show that the non-periodic homogenization is both accurate and tractable in large 3-D cases, which opens the path to the correct account of the effect of small-scale features on seismic wave propagation for various applications and to a deeper understanding of the apparent anisotropy.

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Section: Discussion a N D C O N C L U S I O N Smentioning

confidence: 99%

Non-periodic homogenization of 3-D elastic media for the seismic wave equation

Cupillard

Capdeville

2018

Geophysical Journal International

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“…Speed-ups of up to 4.5 for wave propagation in a geometrically complex volcano model were achieved (mesh with 99.8 million elements). Rietmann et al [72] developed an LTS scheme for second-order Newmark time stepping in SPECFEM3D [17], which led to a speed up of 3.9 for a simulation of the Tohoku-Oki earthquake on a mesh of 7.5 million elements.…”

Section: Dynamic Rupture Modeling Of Subduction Zone Earthquakesmentioning

confidence: 99%

“…18,43,48,49,72,75,76] allows for the simulation of various aspects of earthquake scenarios and enables researchers to answer geophysical questions complicated by the lack of sufficiently dense [79]. Middle: Unstructured tetrahedral mesh of the modeling domain, including refinement to resolve high-frequency wavepropagation and frictional failure on the fault system.…”

Section: Introductionmentioning

confidence: 99%

Extreme scale multi-physics simulations of the tsunamigenic 2004 sumatra megathrust earthquake

Uphoff

Rettenberger

Bäder

et al. 2017

Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis

122

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We present a high-resolution simulation of the 2004 Sumatra-Andaman earthquake, including non-linear frictional failure on a megathrustsplay fault system. Our method exploits unstructured meshes capturing the complicated geometries in subduction zones that are crucial to understand large earthquakes and tsunami generation. These up-to-date largest and longest dynamic rupture simulations enable analysis of dynamic source effects on the seafloor displacements.To tackle the extreme size of this scenario an end-to-end optimization of the simulation code SeisSol was necessary. We implemented a new cache-aware wave propagation scheme and optimized the dynamic rupture kernels using code generation. We established a novel clustered local-time-stepping scheme for dynamic rupture. In total, we achieved a speed-up of 13.6 compared to the previous implementation. For the Sumatra scenario with 221 million elements this reduced the time-to-solution to 13.9 hours on 86,016 Haswell cores. Furthermore, we used asynchronous output to overlap I/O and compute time.

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“…However, when the region of local mesh refinement itself contains a sub-region of even smaller elements, and so forth, any local time-step will again be overly restricted due to even smaller elements inside the "fine" region. To remedy the repeated bottleneck caused by hierarchical mesh refinement, multilevel local time-stepping methods were proposed in [19,42], which permit the use of the appropriate time-step at every level of mesh refinement. For simplicity, we restrict ourselves here to the standard (two-level) LTS-LF scheme.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Convergence Analysis of Energy Conserving Explicit Local Time-Stepping Methods for the Wave Equation

Grote¹,

Mehlin²,

Sauter

2018

SIAM J. Numer. Anal.

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Local adaptivity and mesh refinement are key to the efficient simulation of wave phenomena in heterogeneous media or complex geometry. Locally refined meshes, however, dictate a small time-step everywhere with a crippling effect on any explicit time-marching method. In [18] a leap-frog (LF) based explicit local time-stepping (LTS) method was proposed, which overcomes the severe bottleneck due to a few small elements by taking small time-steps in the locally refined region and larger steps elsewhere. Here a rigorous convergence proof is presented for the fullydiscrete LTS-LF method when combined with a standard conforming finite element method (FEM) in space. Numerical results further illustrate the usefulness of the LTS-LF Galerkin FEM in the presence of corner singularities.

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Newmark local time stepping on high-performance computing architectures

Cited by 20 publications

References 33 publications

Non-periodic homogenization of 3-D elastic media for the seismic wave equation

Non-periodic homogenization of 3-D elastic media for the seismic wave equation

Extreme scale multi-physics simulations of the tsunamigenic 2004 sumatra megathrust earthquake

Convergence Analysis of Energy Conserving Explicit Local Time-Stepping Methods for the Wave Equation

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