间断的Galerkin方法在地震波场数值模拟中的应用概述

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

通过数值求解描述地震波传播的微分方程来模拟波的传播角度而言,在日趋繁荣的地震波场数值模拟方法的探索中,间断的Galerkin方法(Discontinuous Galerkin,DG)是继有限差分法、伪谱法、有限元法以及谱元法之后出现的另一种有效的数值模拟方法,该方法从2005年以来在地震波场模拟中得到了迅速发展,给这一学科注入了新的活力.但是从国内的发展来看,在地震波场数值模拟方面还没有得到足够的关注.尤其是现有的综述性文献都忽略了这一方法得到的有益的成果,本文将重点介绍间断的Galerkin方法的发展及其在地震波场数值模拟的最新应用研究.

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 EG method and its latest application in modeling of the seismic wavefields.