Numerical solution of a boundary value problem with effective boundary conditions for calculation of gravity

Abstract

Forward modeling of gravity field on the base of boundary-value problem solution is a promising technique against traditional summation methods. To calculate gravity of a body with known physical and geometrical properties, one can firstly solve a boundary-value problem for gravitational potential and then calculate its gradient. This approach is more common, but it requires two operations. Another approach is to solve a boundary value problem formulated directly for gravity itself. The main difficulties for methods based on boundary-value problem solution are proper boundary condition, domain size and domain discretization. For the first approach there are plenty of works dealing with these cases in contrast with the second approach. In this paper, authors discuss and compare boundary conditions of two types: the Dirichlet and Robin, in terms of approximation accuracy for the second approach using the finite element method. Calculation results are presented for a test problem, when the gravitational field is produced by a homogeneous body in the shape of a right rectangular prism. A more effective boundary condition is a Robin type condition derived from a simple asymptotic approximation of the gravitational field by the equivalent point mass.