Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

Kai Gao, Shubin Fu, Richard L. Gibson, Eric T. Chung, Yalchin R. Efendiev

Research output: Contribution to journalArticlepeer-review

44 Scopus citations

Abstract

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both boundaries and the interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale medium property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.
Original languageEnglish (US)
Pages (from-to)161-188
Number of pages28
JournalJournal of Computational Physics
Volume295
DOIs
StatePublished - Apr 16 2015

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Computer Science Applications

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