Computations of boundary optimal control problems for an electrically conducting fluid

We study four optimal control problems for an electrically conducting fluid. The control is the (normal) electrical current on the boundary of the flow domain. The objectives are to match a desired velocity field, or to match a desired electrical potential field, or to minimize the potential gradient, or to minimize the vorticity in the flow domain. We develop a systematic way to use the Lagrange multiplier rules to derive an optimality system of equations from which an optimal solution can be computed, Mixed finite element methods are used to find approximate solutions for the optimality systems of equations that characterize the optimal controls. A direct method and an iterative method are proposed for solving the discrete, nonlinear optimality systems of equations. Numerical results for several examples are presented. (C) 1996 Academic Press, Inc.