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Global optimization, level set dynamics, incomplete sensitivity and regularity control

We aim to optimize aerodynamic shapes using an incomplete sensitivity concept and regularization (projection) when control parameters are characteristic functions as in level set and immersed boundary approaches. The projection operator is also used to define a rotation operator over the unit sphere in the admissible space to improve sensitivity definition from the incomplete sensitivity. Hence, the direction of descent is found as a solution of a one-dimensional minimization problem. This is suitable for large dimension control spaces, avoids an adjoint formulation and is particularly interesting for sensitivity evaluation for black-box solvers. The approach is applied to various shape design in supersonic regime with level sets.