Инд. авторы: Epov M.I., Shurina E.P., Shtabel N.V.
Заглавие: The mathematical modeling of the electric field in the media with anisotropic objects
Библ. ссылка: Epov M.I., Shurina E.P., Shtabel N.V. The mathematical modeling of the electric field in the media with anisotropic objects // Applied Numerical Mathematics. - 2015. - Vol.93. - P.164-175. - ISSN 0168-9274.
Внешние системы: DOI: 10.1016/j.apnum.2014.06.011; РИНЦ: 23718120;
Реферат: eng: We present a numerical scheme for modeling the electric field in the media with tensor conductivity. This scheme is based on vector finite element method in frequency domain. The numerical computations of the electric field in the anisotropic medium are done. The conductivity of the anisotropic medium is positive defined dense tensor in general case. We consider the electric field from anisotropic layer, inclined anisotropic layer and some anisotropic objects in isotropic half-space.
Ключевые слова: Maxwell equations Finite element method Anisotropic media;
Издано: 2015
Физ. характеристика: с.164-175
Цитирование: 1. D. Arnold, R. Falk, R. Winther, Differential complexes and stability of finite element methods I. The de Rham complex, in: D. Arnold, P. Bochev, R. Lehoucq, R. Nicolaides, M. Shashkov (Eds.), Compatible Spatial Discretizations, in: The IMA Volumes in Mathematics and Its Applications, vol. 142, Springer, New York, 2006, pp. 23-46. 2. D.N. Arnold, R.S. Falk, R. Winther, Finite element exterior calculus: from Hodge theory to numerical stability, Bull. Am. Math. Soc. 47 (2010) 281-354. 3. R. Beck, R. Hiptmair, Multilevel solution of the time-harmonic Maxwell's equations based on edge elements, Int. J. Numer. Methods Eng. 45 (1999) 901-920. 4. A. Bossavit, I. Mayergoyz, Computational Electromagnetism: Variational Formulations, Complementarity, Edge Elements, Electromagnetism, Elsevier Science, 1998. 5. B. Donderici, F.L. Teixeira, Mixed finite-element time-domain method for transient Maxwell equations in doubly dispersive media, IEEE Trans. Microw. Theory Tech. 56 (2008) 113-120. 6. B. He, F.L. Teixeira, Differential forms, Galerkin duality, and sparse inverse approximations in finite element solutions of Maxwell equations, IEEE Trans. Antennas Propag. 55 (2007) 1359-1368. 7. R. Hiptmair, Finite elements in computational electromagnetism, Acta Numer. (2002) 237-339. 8. R. Hiptmair, From E to edge elements, The Academician 3 (2003) 23-31. 9. H.O. Lee, F.L. Teixeira, Cylindrical FDTD analysis of LWD tools through anisotropic dipping-layered Earth media, IEEE Trans. Geosci. Remote Sens. 45 (2007) 383-388. 10. Z. Ma, C. Croskey, L. Hale, The electrodynamic responses of the atmosphere and ionosphere to the lightning discharge, J. Atmos. Sol.-Terr. Phys. 60 (1998) 845-861. 11. O. Nechaev, E. Shurina, M. Botchev, Multilevel iterative solvers for the edge finite element solution of the 3D Maxwell equation, Comput. Math. Appl. 55 (2008) 2346-2362. 12. J.C. Nedelec, Mixed finite elements in R3, Numer. Math. 35 (1980) 315-341. 13. J.C. Nedelec, A new family of mixed finite elements in R3, Numer. Math. 50 (1986) 57-81. 14. N. Orlovskaya, E. Shurina, M. Epov, The modeling electromagnetic fields at the medium with anisotropic conductivity, Comput. Technol. 11 (2006) 99-116. 15. N. Orlovskaya, E. Shurina, M. Epov, Tensor coefficient of the conductivity in geophysical application, Comput. Technol. 1 (2008) 1-15. 16. Z. Ren, N. Ida, High order differential form-based elements for the computation of electromagnetic fields, IEEE Trans. Magn. 36 (2000) 1472-1478. 17. T. Rylander, J.M. Jin, Perfectly matched layer for the time domain finite element method, J. Comput. Phys. 200 (2004) 238-250, http://dx.doi.org/10.1016/j.jcp.2004.03.016. 18. E. Shurina, N. Shtabel, Analysis of vector finite element approximations of Maxwell's equations in anisotropic media, Comput. Technol. 18 (2013) 91-104 (in Russian). 19. S. Wang, R. Lee, F. Teixeira, Anisotropic-medium PML for vector FETD with modified basis functions, IEEE Trans. Antennas Propag. 54 (2006) 20-27, http://dx.doi.org/10.1109/TAP.2005.861523. 20. T. Wang, S. Fang, 3-d electromagnetic anisotropy modeling using finite differences, Geophysics 66 (2001) 1386-1398. 21. J.P. Webb, Edge elements and what they can do for you, IEEE Trans. Magn. 29 (1993) 1460-1465. 22. C. Yin, H.M. Maurer, Electromagnetic induction in a layered earth with arbitrary anisotropy, Geophysics 66 (2001) 1405-1416. 23. C. Yin, P. Weidelt, Geoelectrical fields in a layered earth with arbitrary anisotropy, Geophysics 64 (1999) 426-434. 24. L. Zhong, S. Shu, G. Wittum, J. Xu, Optimal error estimates for Nedelec edge elements for time-harmonic Maxwell's equation, J. Comput. Math. 27 (2009) 563-572.