A new method using the cubic B-spline curves with nominal uniform knot set toparameterize the geometry is proposed to deal with shape optimization problems.In the method, the control points of the B-spline curves are set to be thedesign variables in the optimization scheme. A knot insertion algorithm has beenintroduced in order to keep the geometry unchanged whilst increasing the numberof control points at the final optimization stage. The super-reduced idea andthe mesh refinement are also employed to deal with the equality constraint andspeed up the optimization process. The method is applied to two problems. Thefirst is a 2-dimensional Poisson problem, and the second is an airfoil designproblem. In both applications, the results show that the new method is much moreefficient when compared with the traditional methods. In the airfoil designproblem, the drag of the airfoil has been reduced significantly with much lessfunction calls.
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