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Mathematical modeling
Numerical solution of a boundary value problem with effective boundary conditions for calculation of gravity
D. Kh. Ivanovab, P. N. Vabishchevichcd a M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 48 Kulakovsky Street, Yakutsk 677000, Russia
b Yakutsk Branch of the Regional Scientificand Educational Mathematical Center "Far Eastern Center of Mathematical Research", 48 Kulakovsky Street, Yakutsk 677000, Russia
c Nuclear Safety Institute of RAS, 52 B. Tulskaya Street, Moscow 115191, Russia
d Academy of Science of the Republic of Sakha (Yakutia), 33 Lenin Ave., Yakutsk 677007, Russia
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.
Keywords:
gravitational field, Poisson equation, approximate boundary condition, finite element method.
Received: 25.11.2020 Revised: 22.01.2021 Accepted: 26.02.2021
Citation:
D. Kh. Ivanov, P. N. Vabishchevich, “Numerical solution of a boundary value problem with effective boundary conditions for calculation of gravity”, Mathematical notes of NEFU, 28:1 (2021), 93–113
Linking options:
https://www.mathnet.ru/eng/svfu313 https://www.mathnet.ru/eng/svfu/v28/i1/p93
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