Computational Technology for the Basis and Coefficients of Geodynamo Spectral Models in the Maple System

Gleb Vodinchar () and Liubov Feshchenko
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Gleb Vodinchar: Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, 7, Mirnaya Str., Paratunka, Kamchatka 684034, Russia
Liubov Feshchenko: Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, 7, Mirnaya Str., Paratunka, Kamchatka 684034, Russia

Mathematics, 2023, vol. 11, issue 13, 1-34

Abstract: Spectral models are often used in the study of geodynamo problems. Physical fields in these models are presented as stationary basic modes combinations with time-dependent amplitudes. To construct a model it is necessary to calculate the modes parameters, and to calculate the model coefficients (the Galerkin coefficients). These coefficients are integrals of complex multiplicative combinations of modes and differential operators. The paper proposes computing technology for the calculation of parameters, the derivation of integrands and the calculation of the integrals themselves. The technology is based on computer algebra methods. The main elements for implementation of technology in the Maple system are described. The proposed computational technology makes it possible to quickly and accurately construct fairly wide classes of new geodynamo spectral models.

Keywords: geodynamo; magneto-convection; spectral models; Galerkin method; computer algebra applications; symbolic computation; Maple system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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