Meshfree Generalized Multiscale Finite Element Method

Abstract

In this paper, we propose a new multiscale approach with a meshfree coarse scale. A coarse scale is constructed on the basis of an already existing computational grid on a fine scale, depending on the heterogeneous parameters of the problem. This approach is based on the Generalized Multiscale Finite Element Method (GMsFEM), where the heterogeneous parameters of the problem are taken into account on a coarse scale using multiscale basis functions. These multiscale basis functions are constructed at an offline stage using local spectral problems. To represent the fractures on a fine grid, the Discrete Fracture Model (DFM) is used. The results of a numerical solution for two-dimensional and three-dimensional problems are presented.