Numerical simulation of acoustic wave propagation in layered media with a generalized multiscale finite element method

2014 ◽  
Author(s):  
Mikhail Artemyev* ◽  
Richard L. Gibson ◽  
Wing Tat Leung
Keyword(s):  
Numerical Simulation ◽  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Acoustic Wave ◽  
Layered Media ◽  
Acoustic 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.

Sign in / Sign up

Export Citation Format

Share Document