  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.
