GPS-边值问题的自然边界元数值解法

Numerical Solution of GPS-Boundary Value Problem Based on the Natural Boundary Element Method

对GPS-边值问题进行了讨论.在球近似下将GPS-边值问题转化为Neumann外问题,用自然边界元法进行自然边界归化,得到自然边界积分方程,再求自然边界积分方程的数值解.与其他边界元方法相比,自然边界元法的计算量大大减小,并且具有很好的逼近性质,能有效地处理奇异积分,是求解GPS-边值问题有效方法.

In this paper GPS-boundary value problem （Gravity-BVP） is studied. In sphere approximate, GPS/Gravity-BVP is Neumann problem over exterior spherical domains. Then the natural boundary reduction, suggested by Feng and Yu,is applied to deal with the three dimensionalproblems. By expansion in spherical harmonics, the natural integral equations of harmonic problems over exterior spherical domains are obtained. Meanwhile, a numerical method for solving geodetic BVP is developed.