引用本文: 蒋涛, 王正涛, 李大炜, 丰海. Stokes和Hotine积分离散求和的快速算法[J]. 武汉大学学报 ( 信息科学版), 2012, 37(5): 606-609.
JIANG Tao, WANG Zhengtao, LI Dawei, FENG Hai. Fast Algorithm for the Discrete Summation of Stokes’ and Hotine’s Integral[J]. Geomatics and Information Science of Wuhan University, 2012, 37(5): 606-609.
 Citation: JIANG Tao, WANG Zhengtao, LI Dawei, FENG Hai. Fast Algorithm for the Discrete Summation of Stokes’ and Hotine’s Integral[J]. Geomatics and Information Science of Wuhan University, 2012, 37(5): 606-609.

## Fast Algorithm for the Discrete Summation of Stokes’ and Hotine’s Integral

• 摘要: 提出了一种用于Stokes积分和Hotine积分直接离散求和的快速算法。该算法将积分核表达为计算点纬度、流动点纬度和两点间经度差的函数,充分利用核函数的对称性,相同纬度的所有计算点只需计算一组核函数,计算次数远少于普通离散求和。基于EGM2008地球重力位模型的模拟实验表明,快速算法的计算效率远高于普通算法,有效解决了离散求和计算速度太慢的数值问题,且保留了球面积分的特性,可取代一维FFT用于计算Stokes积分和Hotine积分。

Abstract: A fast algorithm is proposed for the direct discrete summation of Stokes ’ and Hotine ’ s integral,the integral kernels are expressed as the functions of the latitudes of computation point and running point and the longitude-difference between them,the symmetries of the kernels are exploited so that they may only be evaluated once for all the computation points on the same latitude,the computation times of fast algorithm are far less than that of ordinary algorithm.The numerical simulation based on EGM2008 Earth gravitational model shows that the fast algorithm is far more efficient than the oridinary algorithm that the problem of numerical inefficiency can be effectively solved.Besides,the new algorithm retains the attributes of surface integral and can be used to replace 1DFFT for evaluating Stokes ’ or Hotine ’ s integral.

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