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Article information
2022 , Volume 27, ¹ 4, p.63-76
Arkhipov D.A., Shurina E.P.
Analysis of the toroidal coil approximation technique for the electromagnetic simulations
Objective. In well-logging applications, the electromagnetic field is generated by the toroidal or solenoidal coils. The physically correct and efficient approximation of these coils is of utmost importance. In this paper, we propose two techniques to approximate the toroidal coil: the electric source and the magnetic source. Methods. In the frequency domain the electromagnetic field is governed by the second-order partial differential equation for the electric or magnetic fields. The computational scheme is based on the vector finite element method with a hierarchical basis of the complete second order. The tetrahedral discretization of the computational domain is non-uniform. When approximating the toroidal coil as an electric current density in the coil winding, the finite element mesh must capture the geometry of the winding. For a coil with multiple winding turns, it results in an extremely fine mesh, which leads to large linear systems, hence, poor solver performance. To overcome this, we develop a new technique for approximating a toroidal coil as a magnetic current density in the core of the coil. This approach does not require including the winding into the finite element mesh. Therefore, the size of the resulting linear system is independent of the number of turns in the coil winding. Results. The article shows that the magnetic current density in the generator coil does not depend on the host medium, but is determined only by the geometric (core size and number of turns) and electrophysical characteristics of the toroidal source core. The paper presents the distribution of the electromagnetic field strength for both formulations in a homogeneous medium. Conclusion. The behavior of the electromagnetic field is the same for both methods of source approximation, but the magnetic formulation does not depend on the geometry of the toroidal coil therefore the computational mesh does no
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Keywords: vector finite element method, electromagnetic field, toroidal coil, current density, Maxwell equations
doi: 10.25743/ICT.2022.27.4.005
Author(s):
Arkhipov Dmitry Aleksandrovich
Position: Junior Research Scientist
Office: Trofimuk Institute of Petroleum Geology and Geophysics of Siberian Branch Russian Academy of Sciences
Address: 630090, Russia, Novosibirsk, Koptug aven., 3
E-mail: d_arhipov@list.ru
Shurina Ella Petrovna
Dr. , Professor
Position: General Scientist
Office: Novosibirsk State Technical University, Trofimuk Institute of Petroleum Geology and Geophysics SB RAS
Address: 630073, Russia, Novosibirsk, Karl Marx Ave. 20
Phone Office: (343) 223-72-95
E-mail: shurina@online.sinor.ru
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Bibliography link:
Arkhipov D.A., Shurina E.P. Analysis of the toroidal coil approximation technique for the electromagnetic simulations // Computational technologies. 2022. V. 27. ¹ 4. P. 63-76
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