A BE-based shape optimization method enhanced by topological derivative for sound scattering problems

This paper presents a BE-based shape optimization method for acoustic problems in the context of shape design of sound insulating walls. In order to avoid the convergence to a local minimal solution around an initial shape, the topological derivative is introduced. Based on the global distribution of the topological derivative, new shape or topology are attained by nucleating small scattering bodies. Evaluation of the topological derivative is achieved within the framework of the boundary element analysis. To cope with the topological change due to the nucleation and cutting of thin branches, shape is updated by the aid of the level set approach during the optimization process. Through numerical examples, it is proved that the developed method can find a shape with good performance irrespective of its initial shape.