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间断的Galerkin方法在地震波场数值模拟中的应用概述

ISSN号：1004-2903
期刊名称：地球物理学进展
时间：2013.2.15
页码：171-179
分类：P315[天文地球—地震学;天文地球—固体地球物理学;天文地球—地球物理学]
作者机构：[1]中国科学院地质与地球物理研究所,北京100029, [2]中国科学院研究生院地球动力学实验室,北京100049, [3]宁夏大学数学计算机学院,银川750021
相关基金：国家自然科学基金项目（41174047,41204041）; 国家重点基础研究发展规划项目（2008CB425701）; 十一五863计划信息技术领域面向地球系统模式研究的高性能计算支撑软件系统重点项目（2010AA012402）联合资助
相关项目：地震激发地球自由震荡的高精度保结构数值模拟方法研究

关键词：波场模拟, 有限元法, 间断的Galerkin方法, 有限体积法, seismic wavefield modeling, finite element method, discontinuous C, alerkin method, finite volume method

中文摘要：

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.

英文摘要：

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.

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