A numerical method for designing acoustic cloak with arbitrary shapes

In this paper, we propose a numerical method to evaluate the material parameters of acoustic cloaks with arbitrary shapes. The transformation of the cloak layer assumed to be harmonic, so it can be uniquely determined by Laplace's equation together with proper boundary conditions. The material parameters in the transformed space are then calculated based on the relation between the pure stretches in deformation and mass density as well as bulk modulus. The calculation of the transformed material parameters and the numerical validation for an arbitrary acoustic cloak can be well integrated in a two-step model with help of the finite-element software COMSOL Multiphysics. Numerical examples are provided to illustrate these ideas.