Skip to main content
Earth, Planets and Space
Download PDF

A hybridized mixed finite element domain decomposed method for two dimensional magnetotelluric modelling

Earth, Planets and Space volume 51, pages 297–306 (1999)Cite this article

Abstract

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.

References

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Coggon, J. H., Electromagnetic and electrical modelling by the finite element method, Geophysics, 36, 132–155, 1971.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Douglas, J., Jr., F. Hurtado, and F. Pereira, On the numerical simulation of waterflooding of heterogeneous petroleum reservoirs, Comput. Geosci., 1, 155–190, 1997.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Newman, G. and D. Alumbaugh, Three-dimensional massively parallel electromagnetic inversion—I. Theory, Geophys. J. Int., 128, 345–354, 1997.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Sheen, D., Approximation of electromagnetic fields: Part I. Continuous Problems, SIAM J. Appl. Math., 57, 1716–1736, 1997.

    Article  Google Scholar 

  • Travis, B. J. and A. D. Chave, A moving finite element method for magnetotelluric modelling, Phys. Earth Planet. Inter., 53, 432–443, 1989.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Depto. de Física, Fac. de Cs. Exactas, U.N.L.P., Calle 49 y 115, 1900, La Plata, Argentina

    F. I. Zyserman

  2. CONICET, Depto. de Geofísica Aplicada, Fac. de Cs. Astronómicas y Geofísicas, U.N.L.P., Paseo del Bosque s/n, 1900, La Plata, Argentina

    L. Guarracino & J. E. Santos

  3. Department of Mathematics, Purdue University, W. Lafayette, IN, 47907, USA

    J. E. Santos

Authors
  1. F. I. Zyserman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Guarracino
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. E. Santos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to F. I. Zyserman.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

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

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1186/BF03352233

Keywords

  • Domain Decomposition
  • Domain Decomposition Method
  • Absorb Boundary Condition
  • Finite Element Space
  • Interior Boundary