Gradient Projection, Constraints and Surface Regularization Methods in Adjoint Shape Optimization

This paper deals with the treatment of various problems that are present in adjoint-based shape optimization applications, in which a parameterization of the surface is absent. A general implicit smoothing algorithm is used to reduce high-frequency noise which might be present in the gradients that are calculated using a continuous adjoint solver. The implicit smoother allows the definition of patches on the shape that need to remain fixed during shape optimization and automatically secures surface gradient continuity between constrained and deformable patches. Along with the gradient smoothing, a surface mesh regularization algorithm is presented and used to support high-quality elements and mesh uniformity during each optimization step. In the end, the capability and the effectiveness of the method are demonstrated in various industrial test cases.

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