ACOUSTIC SHAPE OPTIMIZATION BASED ON ISOGEOMETRIC BEM WITH ADJOINT VARIABLE METHOD

Abstract

The isogeometric analysis (IGA) has been applied to the boundary element method (BEM), forming the IGA BEM. In this work, we introduce the IGA BEM to 2D acoustic shape optimization. The key treatment is the acoustic sensitivity analysis using the adjoint variable method (AVM). Compared with the direct differentiation method (DDM), the AVM is more suitable for problems with a large number of design variables. The gradient-based optimization solver is applied in order to update the design variables during the optimization iteration process and the Burton-Miller method is adopted to conquer the fictitious eigen-frequency problem in solving exterior acoustic problems. An example of scattering by an infinite rigid cylinder is presented to demonstrate the improved accuracy of IGA BEM. Then we verify the efficiency of the developed sensitivity algorithms through the example and demonstrate their potential in solving large-scale engineering problems. Finally, an optimization example is provided to validate the proposed optimization procedure. Numerical tests show that the optimal results are strongly frequency dependent.