Mixed GMsFEM for the simulation of waves in highly heterogeneous media
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摘要
Numerical simulations of waves in highly heterogeneous media have important applications, but direct computations are prohibitively expensive. In this paper, we develop a new generalized multiscale finite element method with the aim of simulating waves at a much lower cost. Our method is based on a mixed Galerkin type method with carefully designed basis functions that can capture various scales in the solution. The basis functions are constructed based on some local snapshot spaces and local spectral problems defined on them. The spectral problems give a natural ordering of the basis functions in the snapshot space and allow systematically enrichment of basis functions. In addition, by using a staggered coarse mesh, our method is energy conserving and has block diagonal mass matrix, which are desirable properties for wave propagation. We will prove that our method has spectral convergence, and present numerical results to show the performance of the method.
论文关键词:Wave propagation,Heterogeneous media,Multiscale method,Energy conservation,Mixed method
论文评审过程:Received 7 September 2015, Revised 15 January 2016, Available online 13 April 2016, Version of Record 30 April 2016.
论文官网地址:https://doi.org/10.1016/j.cam.2016.04.001