Shape optimization of sound barrier using an isogeometric fast multipole boundary element method in two dimensions

Abstract

This study presents an isogeometric fast multipole boundary element method (IGA FMBEM) in two-dimensional (2D) acoustics and a related sensitivity-based shape optimization algorithm for sound barriers. In the isogeometric analysis, Non-Uniform Rational B-Splines (NURBS) are used to accurately represent structural geometry. The control points are set as design variables in the shape optimization procedure given that their variations can flexibly result in shape changes. Acoustic shape sensitivities with respect to control points are calculated by the sensitivity boundary integral equation (BIE) based on the direct differentiation method. The singular integrals in the sensitivity BIEs are formulated explicitly under the isogeometric discretization. The minimization of sound pressure on the reference surface is selected as design objective. The gradient-based optimization solver is finally introduced for optimization iteration after the acoustic state and sensitivity information are obtained. The fast multipole method (FMM) is applied to improve overall computational efficiency. The Burton–Miller method is adopted to conquer the fictitious eigenfrequency problem in solving exterior acoustic problems. The correctness and validity of the proposed methods are demonstrated through a number of numerical simulations, while the performance of the sensitivity-based optimization algorithm is observed in the shape optimization of a 2D Γ-shaped sound barrier.