物理大地测量边值问题的自然边界元解法

Numerical Solution to Geodetic Boundary Value Problems with the Natural Boundary Element Method

物理大地测量边值问题是物理大地测量学的核心问题和理论基础.在数学上表示为Laplace方程的以大地水准面为边界面的第三外部边值问题,即Stokes边值问题.文中在物理大地测量Stokes边值问题的球近似下,将Stokes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,并给出了一个算例.

Geodetic boundary value problems are very importent theories in geodesy.One of the mathematic models of geodetic boundary value problems is Stokes boundary value problem.In this paper,by sphere approximate,Stokes boundary value problem is transformed to Neumann boundary value problem over exterior spherical domains.The natural boundary reduction is applied to deal with the Neumann boundary value problems.By expansion in spherical harmonics,the natural integral equations of boundary value problems over exterior spherical domains is obtained.A numerical example is given to illustrate the method.