Explicit and Energy-Conserving Constraint Energy Minimizing Generalized Multiscale Discontinuous Galerkin Method for Wave Propagation in Heterogeneous Media

TL;DR

This paper introduces an explicit, energy-conserving multiscale discontinuous Galerkin method for wave propagation in heterogeneous media, combining local spectral basis functions with constraint energy minimization for efficient and accurate simulations.

Contribution

It presents a novel local multiscale model reduction technique that ensures energy conservation and convergence for wave equations in complex media.

Findings

Method is explicit and energy conserving.

Achieves coarse-mesh and spectral convergence.

Numerical tests verify stability and accuracy.

Abstract

In this work, we propose a local multiscale model reduction approach for the time-domain scalar wave equation in a heterogenous media. A fine mesh is used to capture the heterogeneities of the coefficient field, and the equation is solved globally on a coarse mesh in the discontinuous Galerkin discretization setting. The main idea of the model reduction approach is to extract dominant modes in local spectral problems for representation of important features, construct multiscale basis functions in coarse oversampled regions by constraint energy minimization problems, and perform a Petrov-Galerkin projection and a symmetrization onto the coarse grid. The method is expicit and energy conserving, and exhibits both coarse-mesh and spectral convergence, provided that the oversampling size is appropriately chosen. We study the stability and convergence of our method. We also present numerical results on the Marmousi model in order to test the performance of the method and verify the theoretical results.