Generalized Multiscale Discontinuous Galerkin Method for Helmholtz Problem in Fractured Media

摘要

In this work, we consider wave propagation in fractured media. The mathematical model is described by Helmholtz problem related to wave propagation with specific interface conditions on the fracture in the frequency domain. We use a discontinuous Galerkin method for the approximation by space that help to weakly impose interface conditions on fractures. Such approximations lead to the large system of equations and computationally expensive. In this work, we construct a coarse grid approximation for effective solution using Generalized Multiscale Discontinuous Galerkin Method (GMsDGM). In this method, we construct a multiscale space using solution of the local spectral problems in each coarse elements. The results of the numerical solution for the two-dimensional problem are presented for model problems of the wave propagation in fractured media.