COMPUTATIONS OF BOUNDARY OPTIMAL-CONTROL PROBLEMS FOR AN ELECTRICALLYCONDUCTING 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 fie ld, or to match a desired electrical potential field, or to minimize t he 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 solutio n can be computed, Mixed finite element methods are used to find appro ximate solutions for the optimality systems of equations that characte rize the optimal controls. A direct method and an iterative method are proposed for solving the discrete, nonlinear optimality systems of eq uations. Numerical results for several examples are presented. (C) 199 6 Academic Press, Inc.