In this paper, we discuss a numerical multiscale approach for solving wave equations with heterogeneous coefficients. Our interest comes from geophysics applications and we assume that there is no scale separation with respect to spatial variables. To obtain the solution of these multiscale problems on a coarse grid, we compute global fields such that the solution smoothly depends on these fields. We present a Galerkin multiscale finite element method using the global information and provide a convergence analysis when applied to solve the wave equations. We investigate the relation between the smoothness of the global fields and convergence rates of the global Galerkin multiscale finite element method for the wave equations. Numerical examples demonstrate that the use of global information renders better accuracy for wave equations with heterogeneous coefficients than the local multiscale finite element method. © 2010 IMACS.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-CI-016-04
Acknowledgements: We are grateful to reviewers who provided many insightful comments and suggestions to improve presentation of the paper. L. Jiang would like to acknowledge partial support from Chinese NSF 10901050. Y. Efendiev would like to acknowledge a partial support from NSF and DOE. Efendiev's work was also partially supported by Award Number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST). V. Ginting's work was supported in part by the Department of Energy (DE-NT00047-30).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.