- Open Access
A hybridized mixed finite element domain decomposed method for two dimensional magnetotelluric modelling
Earth, Planets and Space volume 51, pages297–306(1999)
A numerical algorithm to solve the 2D forward problem in magnetotellurics is presented. The method solves Maxwell’s equations as a first order system of partial differential equations employing an iterative hybridized mixed domain decomposed finite element procedure. Absorbing boundary conditions are used on the artificial boundaries, diminishing undesired reflection effects and allowing the use of substantially smaller computational domains. Although the algorithm presented can be implemented onboth serial and parallel computers, its capabilities are fully utilized on the latters. Results obtained on an IBM SP/2 parallel supercomputer of Purdue University are shown. Also the accuracy of the numerical method is verified by comparison with both numerical and analytical solutions provided by well known methods.
Aprea, C., J. R. Booker, and J. Torquil Smith, The forward problem of electromagnetic induction: accurate finite-difference approximations for two-dimensional discrete boundaries with arbitrary geometry, Geophys. J. Int., 129, 29–40, 1997.
Arnold, D. N. and F. Brezzi, Mixed and nonconforming finite element methods: implementation, postprocessing and error estimates, R.A.I.R.O. Modélisation, Mathématique et Analyse Numérique, 19, 7–32, 1985.
Coggon, J. H., Electromagnetic and electrical modelling by the finite element method, Geophysics, 36, 132–155, 1971.
Després, B., P. Joly, and J. E. Roberts, A domain decomposition method for the harmonic Maxwell equations, in Iterative Methods in Linear Algebra, edited by R. Beauwens and P. de Groen, pp. 475–484, Elsevier Science Publishers B. V. (North-Holland), Amsterdam, 1992.
Douglas, J., Jr., P. J. Paes Leme, J. E. Roberts, and J. Wang, A parallel iterative procedure applicable to the approximate solution of second order partial differential equations by mixed finite element methods, Numer. Math., 65, 95–108, 1993.
Douglas, J., Jr., F. Pereira, and L.-M. Yeh, A parallelizable characteristic scheme for two phase flow I: single porosity models, Comp. Appl. Math., 14, 1, 73–96, 1995.
Douglas, J., Jr., F. Hurtado, and F. Pereira, On the numerical simulation of waterflooding of heterogeneous petroleum reservoirs, Comput. Geosci., 1, 155–190, 1997.
Fraeijs de Veubeke, B. X., Displacement and equilibrium models in the finite element method, in Stress Analysis, edited by O. C. Zienkiewicz and G. Holister, pp. 275–284, Wiley, New York, 1965.
Fraeijs de Veubeke, B. X., Stress function approach, in International Congress on the Finite Element Method in Structural Mechanics, pp. 321–332, Bournemouth, 1975.
Hohmann, G. W., Three dimensional EM modelling, Geophys. Surv., 6, 27–54, 1983.
Lee, K. H. and H. F. Morrison, A solution for TM-mode plane waves incident on a two-dimensional inhomogeneity, Geophysics, 50, 466–472, 1985.
Newman, G. and D. Alumbaugh, Three-dimensional massively parallel electromagnetic inversion—I. Theory, Geophys. J. Int., 128, 345–354, 1997.
Pu, X. H., A. K. Agarwal, and J. T. Weaver, Magnetic field solutions of E-polarization induction problems, J. Geomag. Geoelectr., 45, 859–872, 1993.
Santos, J. E., Global and domain decomposed mixed methods for the solution of Maxwell’s equations with application to Magnetotellurics, Numerical Methods for Partial Differential Equations, 14, 407–437, 1998.
Sheen, D., Approximation of electromagnetic fields: Part I. Continuous Problems, SIAM J. Appl. Math., 57, 1716–1736, 1997.
Travis, B. J. and A. D. Chave, A moving finite element method for magnetotelluric modelling, Phys. Earth Planet. Inter., 53, 432–443, 1989.
Wannamaker, P. E., J. A. Stodt, and L. Rijo, A stable finite element solution for two-dimensional magnetotelluric modelling, Geophys. J. R. Astr. Soc., 88, 277–296, 1987.
Weaver, J. T., B. V. Le Quang, and G. Fischer, A comparison of analytic and numerical results for a two dimensional control model in electromagnetic induction.—I. B-polarization calculations, Geophys. J. R. Astr. Soc., 82, 263–277, 1985.
Weaver, J. T., X. H. Pu, and A. K. Agarwal, Improved methods for solving the magnetic field in E-polarization induction problems with fixed and staggered grids, Geophys. J. Int., 126, 437–446, 1996.
About this article
Cite this article
Zyserman, F.I., Guarracino, L. & Santos, J.E. A hybridized mixed finite element domain decomposed method for two dimensional magnetotelluric modelling. Earth Planet Sp 51, 297–306 (1999). https://doi.org/10.1186/BF03352233
- Domain Decomposition
- Domain Decomposition Method
- Absorb Boundary Condition
- Finite Element Space
- Interior Boundary