引用本文: 张德涵, 管泽霖. 有限元法解局部重力场[J]. 武汉大学学报 ( 信息科学版), 1990, 15(2): 10-18.
Zhang Dehan, Guan Zelin. A Solution for Local Gravity Field by Using Finite Element Method[J]. Geomatics and Information Science of Wuhan University, 1990, 15(2): 10-18.
 Citation: Zhang Dehan, Guan Zelin. A Solution for Local Gravity Field by Using Finite Element Method[J]. Geomatics and Information Science of Wuhan University, 1990, 15(2): 10-18.

## A Solution for Local Gravity Field by Using Finite Element Method

• 摘要: 根据物埋大地测量边值问题的平面近似表达式,我们推导出适用于有限元法解算局部重力场的公式,然后用三维等参单元解算了一个地形模型。该模型是由地面上100m×100m的格网组成的121个结点(格网当然也可以是任意不规则的四边形)。模型中只需有结点上的重力异常。计算结果的中误差:mξ=±0.130",mη=±0.144",mξ=±10.249×10-4m,在西门子7570-C占用CPU的时间为8.15秒。通过试验证明:有限元法不仅可以解算物理大地测量的边值问题而且比其它方法计算速度快,布点灵活。方法适用于100×100km2的区域,但是它需要4个以上的空间扰动位或其派生量。

Abstract: According to the plane approximate expression of the geodetic boundary value problem,the formula for solving rocal gravity field by using the finite element method has been derived in this paper.And the three dimensions isoparametric finite element were applied to a topographical modle which consists of 121 nodes compased by grids with 100m×100m of each on the earth surface.The grids can also be arbitrary irregular quadrilaterals.The only needs of the modle are the gravity anomalies on the nodes.The mean square error of the results are mξ=±0.130" mη=±0.144" mξ=±0.249×10-4m and the CPU time(with Seiment 7570-C) was 8.15 seconds.This experiment shows that the finite element method can solve the boundary value problem of physical geodesy with advantage of being flexibler for setting up nodes and faster for computing than other methods.The method is suitable for an area around 100×100km2,but need 4 disturbing potentials or their derived quantities on the boundary outside the earth at lest.

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