SEM Wave Propagation in Complex Media with Tetrahedral to Hexahedral Mesh

Charara, Marwan; Вершинин, А. В.; Sabitov, Denis; Pekar, Grigory

doi:10.3997/2214-4609.20148951

Cited by 12 publications

(9 citation statements)

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“…Let us give the spectral element solution of the problem of stress analysis for a structural element and the results of spectral element analysis of wave propagation [13] in the elastic medium in comparison with the finite element and analytical solutions.…”

Section: Resultsmentioning

confidence: 99%

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

Konovalov

Вершинин

Зингерман

et al. 2017

Modelling and Simulation in Engineering

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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.

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Section: Resultsmentioning

confidence: 99%

“…The industrial application of the SEM is hindered by the problem of mesh generation [12,13]. Typically, for a multibody model geometry it is quite difficult to build a conformal finite element mesh consisting of hexahedral elements only for which the SEM [3] was initially developed.…”

Section: Introductionmentioning

confidence: 99%

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

Konovalov

Вершинин

Зингерман

et al. 2017

Modelling and Simulation in Engineering

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“…High order of spectral element and data locality inside an element make this method well-parallelizable on hybrid massively parallel architectures with accelerators (Komatitsch et al, 2010;Charara, Vershinin, Sabitov, & Pekar, 2011).…”

Section: Numerical Solutionmentioning

confidence: 99%

Numerical Analysis of Propagation of Nonlinear Waves in Prestressed Solids

Левин¹,

Вершинин²,

Зингерман³

2016

MAS

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The details of numerical algorithms implemented in CAE FIDESYS for the analysis of the propagation of nonlinear waves in elastic and viscoelastic bodies are discussed. It's taken into account that waves propagation lead to new strains which superimpose on existing stresses (induced anisotropy) in the media. For the formulation of problem we used the theory of repeated superposition of large strains. The details of numerical algorithms for the analysis of the propagation of nonlinear waves in elastic and viscoelastic bodies are discussed. The implementation of the spectral element method for the nonlinear dynamic problems of elasticity under finite strains is considered. Some details of parallel computing on multicore and multiprocessor systems for the problems of nonlinear dynamic elasticity are presented. The results of numerical experiments obtained in CAE Fidesys are shown, in particular: the analysis of propagation of nonlinear shock wave; the analysis of propagation of surface waves; the dynamic processes related with the origination of a hole in a weakly compressible nonlinear-viscoelastic material.

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“…An example of a successful balanced union of these features is the spectral element method (SEM) proposed by Patera (1984), and afterwards developed for solving geophysical problems since 1993 (Tromp, Komatitsch, and Liu 2008) and used, in particular, on GPU-based platforms, (Charara et al 2011). The method delivers the advantages of the finite-element technique (features 1-5) plus high accuracy, owing to the polynomial basis functions handled in cells by Gaussian integration rules (feature 1).…”

Section: Introductionmentioning

confidence: 99%

Multi‐block finite‐difference method for 3D elastodynamic simulations in anisotropic subhorizontally layered media

Sofronov

Зайцев

Dovgilovich

2015

Geophysical Prospecting

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Prediction of elastic full wavefields is required for reverse time migration, full waveform inversion, borehole seismology, seismic modelling, etc. We propose a novel algorithm to solve the Navier wave equation, which is based on multi‐block methodology for high‐order finite‐difference schemes on curvilinear grids. In the current implementation, the blocks are subhorizontal layers. Smooth anisotropic heterogeneous media in each layer can have strong discontinuities at the interfaces. A curvilinear adaptive hexahedral grid in blocks is generated by mapping the original 3D physical domain onto a parametric cube with horizontal layers and interfaces. These interfaces correspond to the main curvilinear physical contrast interfaces of a subhorizontally layered formation. The top boundary of the parametric cube handles the land surface with smooth topography. Free‐surface and solid–solid transmission boundary conditions at interfaces are approximated with the second‐order accuracy. Smooth media in the layers are approximated up to sixth‐order spatial schemes. All expected properties of the developed algorithm are demonstrated in numerical tests using corresponding parallel message passing interface code.

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SEM Wave Propagation in Complex Media with Tetrahedral to Hexahedral Mesh

Cited by 12 publications

References 0 publications

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

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

Numerical Analysis of Propagation of Nonlinear Waves in Prestressed Solids

Multi‐block finite‐difference method for 3D elastodynamic simulations in anisotropic subhorizontally layered media

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