Some examples of the application of high-performance computing for time-domain full-wave simulations in underwater acoustics using a spectral-element method

2018 ◽  
Vol 143 (3) ◽  
pp. 1926-1926
Author(s):  
Paul Cristini ◽  
Dimitri Komatitsch ◽  
Alexis Bottero
Keyword(s):  
High Performance Computing ◽  
Time Domain ◽  
High Performance ◽  
Spectral Element Method ◽  
Underwater Acoustics ◽  
Spectral Element ◽  
Full Wave ◽  
Performance Computing ◽  
Element Method

scholarly journals The Implementation of Spectral Element Method in a CAE System for the Solution of Elasticity Problems on Hybrid Curvilinear Meshes

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Dmitriy Konovalov ◽  
Anatoly Vershinin ◽  
Konstantin Zingerman ◽  
Vladimir Levin
Keyword(s):  
Mathematical Simulation ◽  
High Performance ◽  
Spectral Element Method ◽  
New Technologies ◽  
Spectral Element ◽  
High Tech ◽  
Engineering Analysis ◽  
Elasticity Problems ◽  
Cae System ◽  
Element Method

Modern high-performance computing systems allow us to explore and implement new technologies and mathematical modeling algorithms into industrial software systems of engineering analysis. For a long time the finite element method (FEM) was considered as the basic approach to mathematical simulation of elasticity theory problems; it provided the problems solution within an engineering error. However, modern high-tech equipment allows us to implement design solutions with a high enough accuracy, which requires more sophisticated approaches within the mathematical simulation of elasticity problems in industrial packages of engineering analysis. One of such approaches is the spectral element method (SEM). The implementation of SEM in a CAE system for the solution of elasticity problems is considered. An important feature of the proposed variant of SEM implementation is a support of hybrid curvilinear meshes. The main advantages of SEM over the FEM are discussed. The shape functions for different classes of spectral elements are written. Some results of computations are given for model problems that have analytical solutions. The results show the better accuracy of SEM in comparison with FEM for the same meshes.

An Efficient High Performance Parallelization of a Discontinuous Galerkin Spectral Element Method

2013 ◽  
pp. 37-47 ◽  
Author(s):  
Christoph Altmann ◽  
Andrea D. Beck ◽  
Florian Hindenlang ◽  
Marc Staudenmaier ◽  
Gregor J. Gassner ◽  
...  
Keyword(s):  
Discontinuous Galerkin ◽  
High Performance ◽  
Spectral Element Method ◽  
Spectral Element ◽  
Element Method

scholarly journals Time domain room acoustic simulations using the spectral element method

2019 ◽  
Vol 145 (6) ◽  
pp. 3299-3310 ◽  
Author(s):  
Finnur Pind ◽  
Allan P. Engsig-Karup ◽  
Cheol-Ho Jeong ◽  
Jan S. Hesthaven ◽  
Mikael S. Mejling ◽  
...  
Keyword(s):  
Time Domain ◽  
Spectral Element Method ◽  
Spectral Element ◽  
Element Method

scholarly journals Removing the CFL stability criterion of the explicit time-domain very high degree spectral-element method with eigenvalue perturbation

Geophysics ◽  
2021 ◽  
pp. 1-29
Author(s):  
Chao Lyu ◽  
Yann Capdeville ◽  
Gang Lv ◽  
Liang Zhao
Keyword(s):  
Time Domain ◽  
Stability Criterion ◽  
Spectral Element Method ◽  
Waveform Inversion ◽  
Spectral Element ◽  
Time Step ◽  
Transform Method ◽  
Time Dispersion ◽  
The Stability ◽  
Element Method

The explicit time-domain spectral-element method (SEM) for synthesizing seismograms hasgained tremendous credibility within the seismological community at all scales. Althoughthe recent introduction of non-periodic homogenization has addressed the spatial meshing difficulty of the mechanical discontinuities, the Courant-Friedrichs-Lewy (CFL) stability criterionstrictly constrains the maximum time step, which still puts a great burden on the numericalsimulation. In the explicit time-domain SEM, the source of instability of using a time stepbeyond the stability criterion is that some unstable eigenvalues of the updated matrix are largerthan what can be accurately simulated. We succeed in removing the CFL stability condition inthe explicit time-domain SEM by combining the forward time dispersion-transform method,the eigenvalue perturbation, and the inverse time dispersion-transform method. Our theoretical analyses and numerical experiments both in the homogeneous, moderate and strong heterogeneous models, show that this combination can precisely simulate waveforms with timesteps dozens of the CFL limit even towards the Nyquist limit especially for the efficient veryhigh degree SEM, which abundantly saves the iteration times without suffering from the time-dispersion error. It demonstrates a potential application prospect in some situations such as thefull waveform inversion which requires multiple numerical simulations for the same model.

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