Multiscale model reduction of the wave propagation problem in viscoelastic fractured media

We apply a generalized multiscale finite element method to solve the Helmholtz problem related to viscoelastic wave propagation in fractured media in the frequency domain. This approach allows the incorporation of explicit fractures in the simulation in a computationally efficient scheme. In the fine-scale, the method is based on the symmetric interior penalty discontinuous Galerkin (SIPG) method and uses the linear-slip model to represent the fractures. The coarse-scale solution employs a selected subset of the basis functions within the SIPG framework to achieve faster results with reduced degrees of freedom. We consider elastic and viscoelastic material properties for the background medium and different fracture distributions for testing the proposed computational multiscale method. The numerical results show that the multiscale basis functions can efficiently capture the fine-scale features of the medium with significant dimension reduction of the system and provide accurate solutions.