基于GPU并行的谱元法地震波数值模拟
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摘要
谱元法是有限元法的一个重要分支,具有对模型适应能力强、计算精度较高和易于实现等优点。有别于有限元的近似计算,谱元法的质量矩阵采用数值积分得到的对角阵,既简化了计算,又可避免计算精度的下降。以用于通用计算领域的GPU为例,介绍了在CUDA编程平台下实现谱元法地震波数值模拟并行化的方法。在实例应用中为避免浮点数据的原子操作,提高计算效率,模型被采样为串行执行的四个并行单元集合体。
Spectral element method(SEM) is one of important branches of finite element method.It can applied to complex models,with high precision and easy to realize.With the recent developed general computing device GPU and programming model CUDA,SEM seismic wave simulation is parallel implemented.In order to avoid float atomic operation and to improve efficiency,the geometrical model is resampled to four serial computed parts in which elements are executed parallel.
Spectral element method(SEM) is one of important branches of finite element method.It can applied to complex models,with high precision and easy to realize.With the recent developed general computing device GPU and programming model CUDA,SEM seismic wave simulation is parallel implemented.In order to avoid float atomic operation and to improve efficiency,the geometrical model is resampled to four serial computed parts in which elements are executed parallel.
引文
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[2]Seriani G,Priolo E.High-order spectral element method for acoustic wave modeling[C]∥Expanded Abstracts of62nd SEG Annual Int Mtg,1991:1561-1564.
[3]Seriani G,Priolo E,Carcione J,et al.High-order spectral element method for elastic wave modeling[C]∥Expanded Abstracts of62nd SEG Annual Int Mtg,1992:1258-1261.
[4]Komatitsch D,Vilotte J P.The spectral element method:An efficient tool to simulate the seismic response of2D and3D geological structures.Bulletin of the Seismological Society of America,1998,88(2):368-392.
[5]Komatitsch D,Tromp J.Introduction to the spectral element method for three-dimensional seismic wave propagation[J].Geophysics,1999,139:806-822.
[6]王童奎,李瑞华,李小凡,等.谱元法数值模拟地震波传播[J].防灾减灾工程学报,2007,7(4):470-477.
[7]林伟军.弹性波传播模拟的Chebyshev谱元法[J].声学学报,2007,32(6):525-533.
[8]Seriani G,Oliveira S P.Optimal blended spectral-element operators for acoustic wave modeling[J].Geophysics,2007,72:95-106.
[9]严珍珍,张怀,杨长春,等.汶川大地震地震波传播的谱元法数值模拟研究[J].中国科学D辑,2009,39(4):393-402.
[10]Komatitsch D,Erlebacher G,Goddeke D,et al.High-order finite-ele-ment seismic wave propagation modeling with MPI on a large GPU clus-ter[J].Journal of Computational Physics,2010,229:7692-7714.
[11]王勖成.有限单元法[M].北京:清华大学出版社,2003.
[12]廖振鹏.工程波动理论导论[M].北京:科学出版社,2002.
[13]李亚智,赵美英,万小明.有限元法基础与程序设计[M].北京:科学出版社,2011.
[14]Komatitsch D,Barnesz C,Tromp J.Wave propagation near a fluid-solid interface A spectral-element approach[J].Geophysics,2000,65:623-631.
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