Acoustic topology optimization of porous material distribution based on an adjoint variable FMBEM sensitivity analysis

Abstract

We develop an acoustic topology optimization approach in this work for the surface design of structures covered by porous materials. The fast multipole boundary element method (FMBEM) is employed for the sound scattering analysis. The acoustic absorption characteristics of porous materials are numerically modeled using the Delany–Bazley–Miki empirical model. Based on the solid isotropic material with penalization (SIMP) method, the optimization is performed by setting the artificial element densities of porous material as the design variables, minimizing the sound pressure or the dissipated sound power as the design objective. As a key treatment in this study, we develop a fast sensitivity analysis approach based on an adjoint variable method (AVM) and the fast multipole method (FMM) to calculate the sensitivities of the objective function with respect to a large number of design variables. The FMM is applied to accelerate the vector-matrix product required by the AVM. According to the gradient information, the method of moving asymptotes (MMA) is used for solving the optimization problem to find the optimal solution. We validate the proposed topology optimization approach through numerical examples of acoustic scattering over a single cylinder and multi cylinders, and demonstrate its ability to handle large-scale problems.