三度体重力矢量的有限单元法正演计算

以重力位在场源内部满足泊松方程为依据,以重力矢量满足第三类边界条件为切入点,推导了与三度体重力矢量满足的边值问题相对应的变分问题,进而利用有限单元法实现了对变分问题的求解.立方体模型试验结果表明:文中提出的新的系数矩阵存储方式较之传统方式能够更有效地节约存储空间,且为利用预条件共轭梯度技术更加快速地求解线性方程组提供了保障;重力矢量的计算精度与边界长度及单元网格的边长息息相关,其计算效率则主要取决于所要计算的节点总数和大型稀疏线性方程组求解算法的优劣;一般情况下,当单元的边长小于场源体边长的1/10、边界长度大于场源体长度的7.5倍时,能够获得理想的结果.

Forward Calculation of Three Dimensional Gravity Vector Using Finite Element Method

Variational problem of three dimensional gravity vector was deduced to meet the boundary value based on Poisson equation and the third boundary condition,and the solution of variational problem is further implemented by using the finite element method.The results of the cubic model test show that the proposed new coefficient matrix storage strategy is more effective to save storage space than a traditional approach;this,in turn,makes it possible to quickly solve liner equations by using the preconditioned conjugate gradient technology.The calculation precision of the gravity vector is closely related to the boundary length and unit grid;while the computational efficiency mainly depends on the total number of nodes and the algorithm used in solving a large sparse system of linear equation.In general,when the length of unit grid is less than 1/10 of the body length,and the boundary length is greater than 7.5 times of the length of the source,a desired result can be achieved.