Shape optimization with level set-based method using a reaction diffusion equation for 2D sound barrier

A level set-based method using a reaction diffusion equation is applied for optimization problems of two dimensional (2D) sound barriers. The level set method is employed to implicitly represent the sound barrier structure, which distinguishes the material and void domains by the value of the level set function. The boundary element method is employed to solve acoustic problems governed by Helmholtz equation. Topological derivatives are computed by the boundary integral equation combined with the adjoint variable method. The distribution of level set function is iteratively updated based on the reaction diffusion equation to find the optimal structure. For the existent floating scatterers in the optimization process and the sharp and narrow parts on the surface of the sound barrier, we propose a filtering algorithm to remove floating scatterers and develop a method to achieve a smooth surface of the sound barrier. The shape optimization of sound barriers is achieved using these techniques, integrating the level set-based topology optimization method. Numerical tests are provided to demonstrate the validity and effectiveness of the proposed methods.