Shape optimization with adaptive Geometry Independent Field approximaTion (GIFT) in 3D time-harmonic acoustics

In this work, an adaptive shape optimization is developed using Geometry Independent Field proximaTion (GIFT) for 3D acoustics problems. The geometry -independent field approximation, using Non -uniform Rational B -splines (NURBS) to model the geometry, and Polynomial -splines over Hierarchical T -meshes (PHT-splines) to model the field space, are employed for 3D shape optimization problems in the context of time -harmonic acoustics. The adaptive optimization scheme proposed in this work combines a gradient -based optimization method with a refinement algorithm. In this case, two types of local refinement algorithms are tested: recovery -based and a residual -based algorithm. Single and multi -patch examples are studied, and it is shown that the proposed adaptive shape optimization scheme can lead to the results as the uniform optimization, but using less time and fewer degrees of freedom.