Mixed GMsFEM for the simulation of waves in highly heterogeneous media

TL;DR

This paper introduces a mixed GMsFEM that efficiently simulates waves in highly heterogeneous media by using specialized basis functions, spectral enrichment, and a staggered mesh to ensure energy conservation and computational efficiency.

Contribution

The paper develops a novel mixed GMsFEM with spectral basis enrichment and energy-conserving properties for wave simulation in complex media.

Findings

Spectral convergence of the method is proven.

Numerical results demonstrate high accuracy and efficiency.

The method conserves energy and has a block diagonal mass matrix.

Abstract

Numerical simulations of waves in highly heterogeneous media have important applications, but direct computations are prohibitively expensive. In this paper, we develop a new generalized multiscale finite element method with the aim of simulating waves at a much lower cost. Our method is based on a mixed Galerkin type method with carefully designed basis functions that can capture various scales in the solution. The basis functions are constructed based on some local snapshot spaces and local spectral problems defined on them. The spectral problems give a natural ordering of the basis functions in the snapshot space and allow systematically enrichment of basis functions. In addition, by using a staggered coarse mesh, our method is energy conserving and has block diagonal mass matrix, which are desirable properties for wave propagation. We will prove that our method has spectral convergence, and present numerical results to show the performance of the method.