A discontinuous Galerkin based multiscale method for heterogeneous elastic wave equations

In this paper, we develop a local multiscale model reduction strategy for the elastic wave equation in strongly heterogeneous media, which is achieved by solving the problem in a coarse mesh with multiscale basis functions. We use the interior penalty discontinuous Galerkin (IPDG) to couple the mult...

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Bibliographic Details
Published inJournal of computational physics Vol. 518; p. 113294
Main Authors Wang, Zhongqian, Chung, Eric, Li, Zishang
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.12.2024
Subjects
CEM-GMsFEM
Discontinuous Galerkin
Elastic wave equations
CEM-GMsFEM
Discontinuous Galerkin
Elastic wave equations
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Summary:In this paper, we develop a local multiscale model reduction strategy for the elastic wave equation in strongly heterogeneous media, which is achieved by solving the problem in a coarse mesh with multiscale basis functions. We use the interior penalty discontinuous Galerkin (IPDG) to couple the multiscale basis functions that contain important heterogeneous media information. The construction of efficient multiscale basis functions starts with extracting dominant modes of carefully defined spectral problems to represent important media feature, which is followed by solving a constraint energy minimization problem. Then a Petrov-Galerkin projection and systematization onto the coarse grid are applied. As a result, an explicit and energy-conserving scheme is obtained for fast online simulation. The method exhibits both coarse-mesh and spectral convergence as long as one appropriately chooses the oversampling size. We rigorously analyze the stability and convergence of the proposed method. Numerical results are provided to show the performance of the multiscale method and confirm the theoretical results.
ISSN:0021-9991
DOI:10.1016/j.jcp.2024.113294