Topology optimization of bounded acoustic problems using the hybrid finite element-wave based method

This paper presents an alternative topology optimization method for bounded acoustic problems that uses the hybrid finite element-wave based method (FE-WBM). The conventional method for the topology optimization of bounded acoustic problems is based on the finite element method (FEM), which is limited to low frequency applications due to considerable computational efforts. To this end, we propose a gradient-based topology optimization method that uses the hybrid FE-WBM whereby the entire domain of a problem is partitioned into design and non-design domains. In this respect, the FEM is used as a design domain of topology optimization, and the WBM is used as a non-design domain to increase computational efficiency. The adjoint variable method based on the hybrid FE-WBM is also proposed as a means of computing design sensitivities. Numerical examples are presented to demonstrate the effectiveness of the proposed method. We compare the optimized design obtained from the proposed method to that obtained from the conventional method in terms of objective function values, optimized topologies and computational efficiency. The optimization results show that the proposed method can perform more efficient topology optimization than conventional method and can thus be applied to much higher frequency applications that conventional method takes considerable computation time to manage.