A variable parametrization scheme is developed and demonstrated for shape optimization using quasi-Newton methods. The scheme performs adaptive parametrization refinement while preserving the approximate Hessian of the shape optimization problem and enables free-form shape design using quasi-Newton optimization methods. Using a B-spline parametrization, the scheme is validated using a 1-D shape approximation problem and is shown to improve efficiency 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 refinement and a method for partially constraining the degrees of freedom.
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