Acoustic sensitivity analysis using isogeometric BEM with wideband fast multipole method

According to the concept of isogeometric analysis (IGA), Non-Uniform Rational B-splines (NURBS) are used to describe the geometry and approximate the physical fields. This treatment circumvents the requirement to generate a mesh, which is a significant progress in reducing the gap between engineering design and analysis. Some researchers have applied the IGA to the boundary element method (BEM), forming the IGA BEM. In this work, we introduce the wideband fast multipole method (WFMM) to the IGA BEM of wideband acoustic problems to improve its numerical efficiency. The Burton-Miller method is adopted to conquer the fictitious eigen-frequency problem in solving exterior acoustic problems. Furthermore, we apply the WFMM IGA BEM to acoustic sensitivity analysis by using the direct differentiation method (DDM) and the adjoint variable method (AVM). Compared with the DDM, the AVM is more suitable for problems with a large number of design variables. An example of scattering by an infinite rigid cylinder is presented to demonstrate the acceleration and the improved accuracy of WFMM IGA BEM. Finally, we verify the efficiency of the developed sensitivity algorithms through a more engineering problem and demonstrate their potential in solving large-scale engineering problems.