Solar dynamo

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Historical perspective on astrophysical MHD simulations

This contribution contains the introductory remarks that I presented at IAU Symposium 270 on ``Computational Star Formation" held in Barcelona, Spain, May 31 -- June 4, 2010. I discuss the historical development of numerical MHD methods in astrophysics from a personal perspective. The recent advent of robust, higher order-accurate MHD algorithms and adaptive mesh refinement numerical simulations promises to greatly improve our understanding of the role of magnetic fields in star formation.Comment: 11 pages, 5 figures, in "Computational Star Formation" held in Barcelona, Spain, May 31 - June 4, 2010", Eds. J. Alves, B. G. Elmegreen, J. M. Girart, V. Trimbl