scholarly journals An Efficient Multiscale Finite‐Element Method for Frequency‐Domain Seismic Wave Propagation

2018 ◽  
Vol 108 (2) ◽  
pp. 966-982 ◽  
Author(s):  
Kai Gao ◽  
Shubin Fu ◽  
Eric T. Chung
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Frequency Domain ◽  
Seismic Wave ◽  
Seismic Wave Propagation ◽  
Multiscale Finite Element Method ◽  
Multiscale Finite Element ◽  
Element Method

scholarly journals Generalized Multiscale Finite Element Method for Elastic Wave Propagation in the Frequency Domain

Computation ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 63 ◽  
Author(s):  
Uygulana Gavrilieva ◽  
Maria Vasilyeva ◽  
Eric T. Chung
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Elastic Wave ◽  
Coarse Grid ◽  
Basis Functions ◽  
Interface Conditions ◽  
Multiscale Finite Element Method ◽  
Multiscale Finite Element ◽  
Element Method

In this work, we consider elastic wave propagation in fractured media. The mathematical model is described by the Helmholtz problem related to wave propagation with specific interface conditions (Linear Slip Model, LSM) on the fracture in the frequency domain. For the numerical solution, we construct a fine grid that resolves all fracture interfaces on the grid level and construct approximation using a finite element method. We use a discontinuous Galerkin method for the approximation by space that helps to weakly impose interface conditions on fractures. Such approximation leads to a large system of equations and is computationally expensive. In this work, we construct a coarse grid approximation for an effective solution using the Generalized Multiscale Finite Element Method (GMsFEM). We construct and compare two types of the multiscale methods—Continuous Galerkin Generalized Multiscale Finite Element Method (CG-GMsFEM) and Discontinuous Galerkin Generalized Multiscale Finite Element Method (DG-GMsFEM). Multiscale basis functions are constructed by solving local spectral problems in each local domains to extract dominant modes of the local solution. In CG-GMsFEM, we construct continuous multiscale basis functions that are defined in the local domains associated with the coarse grid node and contain four coarse grid cells for the structured quadratic coarse grid. The multiscale basis functions in DG-GMsFEM are discontinuous and defined in each coarse grid cell. The results of the numerical solution for the two-dimensional Helmholtz equation are presented for CG-GMsFEM and DG-GMsFEM for different numbers of multiscale basis functions.

Complex topography and media implementation using hp-adaptive DG-FEM for seismic wave modeling

2020 ◽  
Author(s):  
Yang Xu ◽  
Xiaofei Chen ◽  
Dechao Han ◽  
Wei Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Seismic Wave ◽  
Seismic Wave Propagation ◽  
Seismic Inversion ◽  
Complex Topography ◽  
Propagation Law ◽  
The Impact ◽  
Element Method

<p>Numerical simulation of seismic wavefield is helpful to understand the propagation law of seismic wave in complex media. In addition, accurate simulation of seismic wave propagation is of great importance for seismic inversion. The discontinuous Galerkin finite element method(DG-FEM) combines the advantages of finite element method(FEM) and finite volume method(FVM) to effectively simulate the propagation characteristics of seismic waves in complex medium.</p><p>In this study, we use the hp-adaptive DG -FEM to perform accurate simulation of seismic wave propagation in complex topography and medium, and compare the results with the analytical solution of the Generalized Reflection/Transmission(GRT) coefficient method. Furthermore, ADE CFS-PML is modified and applied to DG-FEM, which greatly reduces the impact of artificial boundaries.</p>

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