OPTIMAL POSITIONING OF ANODES FOR CATHODIC PROTECTION

We consider an optimal control problem that arises in cathodic protect ion. The control is the position of a finite number of anodes, each wi th a prescribed current density. The goal is to obtain a desired poten tial distribution on the cathode that will prevent or reduce cathodic corrosion. The existence of an optimal solution is proven. The differe ntiability of the functional minimized is justified, and the equations satisfied by the derivative are established. Then a numerical algorit hm is proposed for computing the optimal position of the anodes. Final ly, we present some numerical results obtained by implementing the pro posed numerical algorithm with a boundary element method.