大地测量混合边值问题的自然边界元解法

Natural Boundary Element Method for the Geodetic Mixed Boundary Value Problems

在物理大地测量边值问题的球近似下,将大地测量混合边值问题转化为Neumann外问题,用自然边界元法,对Neumann外问题进行自然边界归化,得到自然边界积分方程,再求自然边界积分方程的数值解.在球界面下,利用自然边界元方法,将大地测量混合边值问题的求解,转化为线性方程组的求解,而线性方程组的解存在惟一稳定,因而大地测量混合边值问题的解存在惟一稳定.

We study a new numerical solution method for the geodetic mixed boundary value problems, which is natural boundary element method. In sphere approximation,the geodetic mixed boundary value problems can be transformed into the Neumann boundary value problem over exterior spherical domain. The natural boundary reduction is applied to deal with the Neumann boundary value problem. By expansion in spherical harmonies, the natural integral equation of the Neumann boundary value problem over exterior spherical domain is obtained. Then the solution to the geodetic mixed boundary value problems can be transformed into linear equations solution. By solving the linear equations, it is concluded that the solution of the geodetic mixed boundary value problems is existence, uniqueness and stability.