Journal of Jilin University(Earth Science Edition) ›› 2015, Vol. 45 ›› Issue (4): 1217-1226.doi: 10.13278/j.cnki.jjuese.201504301

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Forward Calculation of Three Dimensional Gravity Vector Using Finite Element Method

Jiang Fuyu1, Xie Leilei1, Chang Wenkai1, Huang Yan2, Zhang Zuohong2   

  1. 1. School of Earth Sciences and Engineering, Hohai University, Nanjing 210098, China;
    2. Geology Exploration Technology Institute of Jiangsu Province, Nanjing 210048, China
  • Received:2014-10-30 Published:2015-07-26

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Abstract:

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.

Key words: variational problem, gravity vector, finite element method, data storage, calculation precision, three dimensional body

CLC Number: 

  • P631.1

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