A generalized multiscale finite element method for elastic wave propagation in fractured media

2016 ◽  
Vol 7 (2) ◽  
pp. 163-182 ◽  
Author(s):  
Eric T. Chung ◽  
Yalchin Efendiev ◽  
Richard L. Gibson ◽  
Maria Vasilyeva
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Elastic Wave ◽  
Fractured Media ◽  
Elastic 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.

Global Multiscale Finite Element Method for Flow in Fractured Media

2014 ◽  
Vol 945-949 ◽  
pp. 1007-1010
Author(s):  
Xiao Lin Li ◽  
Guang Wei Meng ◽  
Li Ming Zhou ◽  
Feng Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fluid Flow ◽  
Accurate Solution ◽  
Fractured Media ◽  
Fine Scale ◽  
Multiscale Finite Element Method ◽  
Dual Porosity Model ◽  
Multiscale Finite Element ◽  
Element Method

Numerical simulation in fractured media is challenging because of the complex microstructure and the coupled fluid flow in porous and fractured media. In this paper, we have extended the global multiscale finite element method (GMsFEM) to study the fluid flow in fractured media with a dual porosity model. By using the fine-scale solution at t=0 to determine the boundary conditions of the basis function, local and nonlocal informations are reflected in the basis functions. As a result, an accurate solution can be achieved in the coarse scale. Numerical example demonstrate that the solution of GMsFEM is highly consistent with the fine-scale solution of FEM. Furthermore, GMsFEM provides a great computational efficiency.

Finite-element method for elastic wave propagation

1990 ◽  
Vol 6 (5) ◽  
pp. 359-368 ◽  
Author(s):  
F. J. Serón ◽  
F. J. Sanz ◽  
M. Kindelán ◽  
J. I. Badal
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Elastic Wave ◽  
Elastic Wave Propagation ◽  
Element Method
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