球谐分析及合成并行计算Parallel computation of spherical harmonic analysis and synthesis
肖华东,陆洋
摘要(Abstract):
本文介绍了球谐合成和分析问题的数值计算原理,研究分析了其内在的并行性,提出了区域划分和聚合通信的并行计算策略。基于傅立叶变换技术,应用MPI(消息传递接口)并行编程模式,实现了球谐分析及合成计算的并行化。实验结果表明,较之串行实现,并行实现大大缩短了计算时间,获得了近似线形加速比,取得很高的并行效率。
关键词(KeyWords): 球谐函数;并行计算;区域分解;FFT;MPI
基金项目(Foundation): 中国科学院基金(KZCX3-SW-132、INF105-SCE)
作者(Author): 肖华东,陆洋
参考文献(References):
- [1]Engelis,T.Spherical harmonic expansion of the Levitus sea surface topography[R].Report385,Department of Geodetic Science and Surveying,The Ohio State Uni-versity,Columbus,1987.
- [2]Lemoine F G,Kenyon S,et al.The Development of the Joint NASA GSFC and the National Imagery and Map-ping Agency(NIMA)Geopotential Model EGM96[R].Report NASA/TP-1998-206861,National Aeronautics and Space Administration,Greenbelt,MD,1998:575.
- [3]Wahr J,Molenaar M,Bryan F.Time variability of the Earth's gravity field:hydrological and oceanic effects and their possible detection using GRACE[J].Journal of Ge-ophysical Research,1998,103:30205-30209.
- [4]Lu Y,Zhang K F,Hsu H T.Development of the Regional Geopotential Model to3600Degrees through a Combination of CHAMP and Surface Gravity data[A].In:IUGG2003,Meeting of IAG Section III,Determination of the Gravity Field[C],Sapporo,Jappan,2003,June30July11.
- [5]Snir W,Otto S,Huss-Lederman S,Walker D and Dongarra J.MPI-The Complete Reference[M].The MIT Press,Cambridge,Massachusetts,London,England,1996:336.
- [6]Gropp W,Lusk E.Thakur R.Using MPI-2advanced fea-tures of the Message Interface[M].The MIT Press Cam-bridge,Massachusetts,London,England,1999:275.
- [7]Heiskanen W A,Moritz H.Physical Geodesy[M].W H Freeman and Co.,San Francisco,1967:364.
- [8]Paul M R.Recurrence Relations for Integrals of Associ-ated Legendre Functions[J].Bulletin Geodesque,1978,52(3):177-190.
- [9]Sneeuw N,Bun R.Global spherical harmonic computa-tion by two-dimensional Fourier methods[J].Journal of Geodesy,1996,70:224-232.
- [10]Colombo O L.Numerical methods for harmonic analysis on the sphere[A].In:Report No.310,Department of Geodetic Science and Surveying[C],The Ohio State University.Columbus,Ohio,1981:139.
- [11]Dilts G A.Computation of spherical harmonic expansion coefficients via FFT's[J].Journal of Computational Physics1985,57:439-453.
- [12]Mainville A.The altimetry-gravimetry problem using or-thonomal base functions[A].In:Report No.373,De-partment of Geodetic Science and Surveying[C],The Ohio State University.Columbus,Ohio,1986:203.