Title: Optimal Shape Design of Nozzel under Uncertainty in Input

In the present paper, optimal shape design of the Nozzel is considered under stochastic input flow and model uncertainty as an uncertain source. Uncertainties are considered to be random field. The paper studies general formulation of the Nozzel design and states the problem in the optimal control formulation. The problem is transformed to a fixed domain and Lagrangian method is applied to drive the optimality system. Random fields are approximated by Karhunen-Loeve expansion and collocation method with Smolyak type sparse grid is implemented for uncertainty quantification and reducing the course of dimensionality. An Academic example is studied and results are presented.

Keywords:

Shape optimization , Optimal Control , Smolyak type parse grid , Stochastic Collocation Method ,