A Dynamic Parametrization Scheme for Shape Optimization Using Quasi-Newton Methods

Abstract

A variable parametrization scheme is developed and demonstrated for shape optimization using quasi-Newton methods. The scheme performs adaptive parametrization renement while preserving the approximate Hessian of the shape optimization problem and enables free-form shape design using quasi-Newton optimization methods. Using a Bspline parametrization, the scheme is validated using a 1-D shape approximation problem and is shown to improve eciency and optimal solution quality compared to the traditional quasi-Newton method. The scheme is also applied to a 3-D test problem, demonstrating the feasibility of free-form shape optimization using parametrization renement and a method for partially constraining the degrees of freedom.