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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2025 Volume 65, Number 3, Pages 376–389 (Mi zvmmf11945)

Partial Differential Equations

On the uniqueness of discrete gravity and magnetic potentials

I. È. Stepanovaa, I. I. Kolotovb, A. G. Yagolab, A. V. Shchepetilovb, A. N. Levashovb

a Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, 123995, Moscow, Russia
b Faculty of Physics, Lomonosov Moscow State University, 119991, Moscow, Russia

Abstract: The problem of the uniqueness of the solution to finite-differenced analogues of the Laplace equation in various domains of the three-dimensional space for restoring discrete gravity and magnetic potentials is considered. This approach makes it possible to determine potentials in two cases: a) when the discrete fundamental solution is known and b) if an additional a priori information on the boundary values of potentials is given.

Key words: uniqueness, fundamental solution, discrete gravity potential, discrete magnetic potential.

UDC: 550.83+550.81

Received: 18.11.2024
Revised: 18.11.2024
Accepted: 12.12.2024

DOI: 10.31857/S0044466925030111


 English version:
Computational Mathematics and Mathematical Physics, 2025, 65:3, 603–617

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© Steklov Math. Inst. of RAS, 2026