https://doi.org/10.26089/NumMet.v27r219

Numerical simulation of global electrical circuit problems with non-classical boundary conditions

Authors

  • Ivan G. Mileshin
  • Alexey V. Kalinin
  • Alla A. Tyukhtina

Keywords:

global electrical circuit
ionospheric potential
finite element method
HYPRE

Abstract

This paper examines approaches to solving problems arising in modeling the Earth’s global electrical circuit. For these problems, nonstandard stationary elliptic boundary-value formulations with nonclassical boundary conditions are formulated. Aparallel algorithm based on the finite element method is presented for the numerical solution of these problems. Calculation results for the model problem are presented, and the efficiency of MPI parallelization for the presented problems is discussed.


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Published

2026-05-29

Issue

Vol. 27 (2026): Issue 2.

Section

Methods and algorithms of computational mathematics and their applications

Authors

Ivan G. Mileshin

Lomonosov Moscow State University, Sarov branch of Lomonosov Moscow State University

• Assistant

Alexey V. Kalinin

National Research Lobachevsky State University of Nizhny Novgorod

• Professor, Head of Department

Alla A. Tyukhtina

National Research Lobachevsky State University of Nizhny Novgorod

• Associate Professor

References

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  10. A. Kalinin, A. Tyukhtina, and I. Mileshin, “Justification and Implementation of the Galerkin Method for Solving Non-classical Mathematical Problems of the Atmospheric Electricity Theory,” in 24th International Conference Mathematical Modeling and Supercomputer Technologies (MMST 2024), Nizhni Novgorod, Russia, November mbox18–21, 2024. Communications in Computer and Information Science. Vol. 2363. (Springer Nature, Cham 2025), pp. 198–212.
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  11. HYPRE.
    https://computing.llnl.gov/projects/hypre-scalable-linear-solvers-multigrid-methods/software/ Cited May 7, 2026.

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Copyright (c) 2026 И. Г. Милешин, А. В. Калинин, А. А. Тюхтина

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This work is licensed under a Creative Commons Attribution 4.0 International License.