Acoustic shape optimization based on isogeometric boundary element method with subdivision surfaces

Abstract

This study proposes a new acoustic shape optimization approach by combining isogeometric subdivision surfaces with the boundary element method. The geometry of the structural boundary is constructed by the Catmull–Clark subdivision surfaces, which are able to provide multiresolution subdivision hierarchy models to meet different precision requirements. The acoustic propagation in the unbounded domain is simulated using the boundary element method. The control points in subdivision meshes are set as design variables, and the minimization of sound pressure at the observation points is selected as the design objective. The acoustic shape sensitivities are calculated by the sensitivity boundary integral equation based on the direct differentiation method. In each iteration the geometry is updated from a direct optimized shape, then a secondary processing is considered to obtain smooth surfaces. Compared with the conventional optimization methods, we eliminate jagged geometry by multiresolution approach without needing the cumbersome meshing procedure and volume parameterization. Several numerical experiments demonstrate the effectiveness and validity of the developed shape optimization approach.