Abstract
We compare the performance of two alternative algorithms which aim to construct a force-free magnetic field given suitable boundary conditions. For this comparison, we have implemented both algorithms on the same finite element grid which uses Whitney forms to describe the fields within the grid cells. The additional use of conjugate gradient and multigrid iterations result in quite effective codes.
The Grad Rubin and Wheatland Sturrock Roumeliotis algorithms both perform well for the reconstruction of a known analytic force-free field. For more arbitrary boundary conditions the Wheatland Sturrock Roumeliotis approach has some difficulties because it requires overdetermined boundary information which may include inconsistencies. The Grad Rubin code on the other hand loses convergence for strong current densities. For the example we have investigated, however, the maximum possible current density seems to be not far from the limit beyond which a force-free field cannot exist anymore for a given normal magnetic field intensity on the boundary.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Amari, T., Boulmezaoud, T.Z., and Mikić, Z.: 1999, Astron. Astrophys. 350, 1051.
Bossavit, A.: 1988, in J. Whiteman (ed.), The Mathemetics of Finite Elements and Applications, Academic Press, London, p. 137.
Boulmezaoud, T.Z. and Amari, T.: 2000, Zeitschr. für angew. Mathem. Physik. 51, 942.
Grad, H. and Rubin, H.: 1958, Proceedings of 2nd. International Conference on Peaceful Uses of Atomic Energy, 31, 190.
Grădinaru, V.C.: 2002, Ph.D. Thesis, Eberhard-Karls-Universität, Tü bingen, Tübingen, Germany.
Hiptmair, R.: 2001, Numer. Math. 90, 265.
Jänich, K.: 2001, Vektoranalysis, Springer Verlag.
Low, B.C. and Lou, Y.Q.: 1990, Astrophys. J. 352, 343.
Mikić, Z., Schnack, D.D., and van Hoven, G.: 1990, Astrophys. J., 361, 690.
Molodensky, M.M.: 1969, Soviet Astron. 12, 585.
Nédélec, J.C.: 1986, Numer. Math. 50, 57.
Régnier, S., Amari, T., and Kersalé, E.: 2002, Astron. Astrophys. 392, 1119.
Raviart, P.A. and Thomas, J.M.: 1977, Lecture Notes in Mathematics, 606, Springer Verlag.
Saad, Y.: 2003, Iterative Methods for Sparse Linear Systems, SIAM.
Sakurai, T.: 1981, Solar Phys. 69, 342.
Schrijver, C.J., DeRosa, M.L., Metcalf, T.R., Liu, Y., McTiernan, J., Régnier, S., Valori, G., Wheatland, M.S., and Wiegelmann, T.: 2006, Solar Phys. 235, 161. Author: Please update Schrijver et al. (2006).
Teixeira, F.L.: 2001, Prog. Electromagn. Res. 32, 171.
Van Hoven, G., Mok, Y., and Mikić, Z.: 1995, Astrophys. J. Lett. 440, L105.
Wheatland, M.S.: 2004, Solar Phys. 222, 247.
Wheatland, M.S., Sturrock, P.A., and Roumeliotis, G.: 2000, Astrophys. J. 540, 1150.
Wiegelmann, T.: 2004, Solar Phys. 219, 87.
Wiegelmann, T. and Inhester, B.: 2003, Solar Phys. 214, 287.
Wiegelmann, T., Inhester, B., and Sakurai, T.: 2006, Solar Phys. 233, 215. Author: Please update Wiegelmann, Inhester, and Sakurai (2005).
Yee, K.S.: 1966, IEEE Trans. Antennas Propagation AP-14, 302
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Inhester, B., Wiegelmann, T. Nonlinear Force-Free Magnetic Field Extrapolations: Comparison of the Grad Rubin and Wheatland Sturrock Roumeliotis Algorithm. Sol Phys 235, 201–221 (2006). https://doi.org/10.1007/s11207-006-0065-x
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11207-006-0065-x