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Article information
2014 , Volume 19, ¹ 6, p.108-121
Epov M.I., Shurina E.P., Mikhaylova E.I.
Analysis of numerical schemes for modeling of electromagnetic field in media with contrast inclusions in a wide frequency range
Purpose. The purpose of this paper is a comparative analysis of variational formulations of the discontinuous Galerkin method (DG-method) for solution of the Helmholtz equation in a wide frequency range (from 100 kHz to 1 GHz) in a medium with contrast small inclusions of various shapes. Methodology. The Helmholtz equation for electric field is solved on unstructured tetrahedral mesh with vector basis functions of the first order in a medium with microinclusions. The following variational formulations are considered: the conforming vector Galerkin method, the nonconforming (discontinuous) Galerkin method based on various modifications of the IP approach. Findings. On the basis of the developed computational schemes for domains with various types of microinclusions, we analyze the wave formation process depending on the electrophysical properties of the medium and the excitation frequency of the electromagnetic field. The estimation error for the solution was obtained by various modifications of the discontinuous Galerkin method. Originality/value. Based on the results of numerical experiments we show that the IP DG-method without averaging and the IIP DG-method (the incomplete interior penalty method) are the most effective and stable approaches in the wide frequency range. We found the irrelevance of the iterative methods for solving the discrete analogues of variational formulations of discontinuous Galerkin method (in the space H(curl,Ω )).
[full text]
Keywords: The vector finite element method, discontinuous Galerkin method, composite material, microinclusions
Author(s):
Epov Mihail Ivanovich
Dr. , Academician RAS, Professor
Position: Director
Office: A.A. Trofimuk Institute of Petroleum Geology and Geophysics SB RAS
Address: 630090, Russia, Novosibirsk, Akademika Koptyuga Prosp. 3
Phone Office: (383)330-13-81
E-mail: EpovMI@ipgg.sbras.ru
SPIN-code: 5421-0812Shurina 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
Mikhaylova Ekaterina Igorevna
Position: Junior Research Scientist
Office: Trofimuk Institute of Petroleum Geology and Geophysics Siberian Branch of Russian Academy of Sciences
Address: 630073, Russia, Novosibirsk, 20, Prospekt K. Marksa
Phone Office: (383) 333-29-00
E-mail: mik_kat@ngs.ru
SPIN-code: 1745-6057 References:
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Bibliography link:
Epov M.I., Shurina E.P., Mikhaylova E.I. Analysis of numerical schemes for modeling of electromagnetic field in media with contrast inclusions in a wide frequency range // Computational technologies. 2014. V. 19. ¹ 6. P. 108-121
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