Inverse Acoustic Scattering from a Bounded Homogeneous Penetrable Obstacle

We consider time domain acoustic scattering from a bounded homogeneous penetrable obstacle. The problem is reduced to a system of time-dependent integral equations on the boundary of the scatter. Our aim is to determine the location and shape of the obstacle. Using convolution quadrature in time combined with the nonlinear integral equation method, we obtain the Helmholtz equation with complex wave numbers. Then the iterative scheme is presented to solve the nonlinear boundary integral equations, and the fully discrete system is given. Numerical experiments are presented to show the effectiveness of the proposed method.