In this paper we apply a multilevel hybrid optimization algorithm based on a response surface methodology to control the solidification process of a double-diffusive fluid flow, during the phase-change, in the presence of electric and thermal body forces. The problem consists of a rectangular cavity subjected to a thermosolutal flow containing electrically charged particles where the patterns of the isothermal fields for the solute are prescribed. The optimization problem is formulated in terms of the electric and thermal boundary conditions that must induce such prescribed temperature profile. Thus, it is essentially an inverse problem that is solved by determining the appropriate electric and thermal boundary conditions. The electro-thermo-hydrodynamics analysis including solidification was performed using our implicit algorithm on a fixed structured grid. The optimizer is based on several deterministic and evolutionary algorithms with automatic switching among them, combining the best features of each one. The response surface methodology uses several radial basis function interpolants in order to significantly reduce the high computational cost involved during the optimization process of the electric and thermal boundary conditions. The entire numerical simulation was performed on our 96-processor Opteron based parallel computer running Linux and MPI.
