Adaptive shape optimization with NURBS designs and PHT-splines for solution approximation in time-harmonic acoustics

Abstract

In this paper, we propose the adaptive shape optimization algorithm based on the concept of Geometry Independent Field approximaTion paired with the Sequential Quadratic Programming method, applied to time-harmonic acoustics.Non-Uniform Rational Basis Splines are used for the geometry parametrization, and in the same manner, as in conventional isogeometric shape optimization, the control points of the optimized boundary serve as design variables. This preserves the tight link between the design, analysis, and optimization models. Polynomial splines over Hierarchical T-meshes are employed for the solution approximation, providing the capability to refine the solution locally and adaptively to the boundary changes during the optimization process in a step-by-step procedure controlled by the error tolerance. This leads to significant savings in terms of the number of degrees of freedom and computational time.The performance of the proposed method is demonstrated in three benchmark examples and the results are compared with the data from the literature, showing the high accuracy and efficiency of the technique. It is shown that an adaptive optimization scheme can bring over 90% reduction in both, the number of degrees of freedom and time, in comparison with the uniform refinement.