Computational multiscale methods for first-order wave equation using mixed CEM-GMsFEM

TL;DR

This paper introduces a multiscale finite element method using CEM-GMsFEM to efficiently solve heterogeneous first-order wave equations, demonstrating convergence and improved computational performance.

Contribution

The paper develops a novel multiscale finite element framework employing CEM-GMsFEM for pressure-velocity wave equations, with proven convergence and enhanced efficiency.

Findings

Method achieves first-order convergence.

Numerical tests confirm accuracy and efficiency.

Framework effectively captures heterogeneity effects.

Abstract

In this paper, we consider a pressure-velocity formulation of the heterogeneous wave equation and employ the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) to solve this problem. The proposed method provides a flexible framework to construct crucial multiscale basis functions for approximating the pressure and velocity. These basis functions are constructed by solving a class of local auxiliary optimization problems over the eigenspaces that contain local information on the heterogeneity. Techniques of oversampling are adapted to enhance the computational performance. The first-order convergence of the proposed method is proved and illustrated by several numerical tests.