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In this paper, a finite element method for solving ionized fields is developed based on a novel solution philosophy. Employing the Galerkin finite element method, the solution problem of an ionized field has been formulated as an optimization problem, i.e. as a problem of minimizing an objective function whose minimum gives the solution. The effect of wind is taken into account by introducing a scalar potential of its velocity. © 1997 by John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]