2022 , Volume 27, № 1, p.21-38

Purpose. We consider numerical calculation of the vertical component of the gravity force produced by the ore body using solution of an auxiliary boundary value problem (BVP) for the Poisson equation in a bounded domain.

Methodology. Auxiliary BVP can be posed according to the gravitational potential or the vertical gravity force itself supplied by a homogeneous Robin boundary condition. The use of Green’s third formula to the solution of the BVP leads to an equivalent definition of the vertical gravity force based on the calculation of the surface integral. The numerical solution of the auxiliary BVP is based on standard finite element method, the calculation of the surface integral relies on Gauss quadrature formula. In the surface integral, Green’s function for the Laplace operator in an unbounded domain is evaluated using a polynomial approximation or an analytical representation.

Findings. Numerical calculations of a model problem with a homogeneous prismatic body has shown that the method based on the solution of the auxiliary BVP for the vertical gravity force itself with a large value of the scalar parameter in the Robin boundary condition and analytical representation of the Green’s function in the surface integral is the most effective method for approximating the vertical gravity force. For this method, we obtained the second order convergence rate.

Originality/value. The considered auxiliary BVP with the Robin boundary condition allows obtaining a sufficiently good approximation of the vertical gravity force