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Review on application of the discontinuous Galerkin method for modeling of the seismic wavefield

WANG Wen-shuai1,3,ZHANG Huai2,LI Xiao-fan1(1.Institute of Geology and Geophysics,Chinese Academy of Sciences,Beijing 100029,China; 2.Graduate University of Chinese Academy of Sciences,Beijing 100049,China; 3.School of Mathematics and Computer Science,Ningxia University,Yinchuan 750021,China)  
In the past years,a number of different numerical methods have been developed in order to solve the seismic wave equations,such as finite difference method,pseudospectral method,finite element method and spectral element method etc.In these methods,discontinuous Galerkin(DG) method is one of the effective methods,which is of an intelligent combination of finite element and the finite volume methods,utilizing a space of basis and test functions that mimics the finite element method but satisfying the equation in as sense close to the finite volume method,appears to offer many of the desired properties as allowing for jumps of material parameters and the solutions across the element interfaces.The discontinuous Galerkin method together with a time integration approach using arbitrary high-order derivatives(ADER) has been further developed rapidly for modeling of seismic wave propagation since 2005.However,from the perspective of development in our country,it does not gained enough attention,especially in seismic modeling.In this paper,it will focus on the development of DG method and its latest application in modeling of the seismic wavefields.
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