• absorbing boundary conditions;
  • acoustic;
  • perfectly matched layer;
  • second-order equation


In the context of simulations of wave propagations in unbounded domain, absorbing boundary conditions are often used to truncate the simulation domain to a finite space. Perfectly matched layer (PML) has proven to be an excellent absorbing boundary conditions. However, as this technique was primarily designed for the first-order equation system, it cannot be applied to the second-order equation system directly. In this paper, based on a complex-coordinate stretching technique, we developed a novel, efficient auxiliary-differential equation form of the complex-frequency shifted-PML for the second-order equation system. This facilitates the use of complex-frequency shifted-PML in acoustic simulations based upon wave equations of second-order form. Compared with previous state-of-the-art methods, the proposed one has the advantage of simpler implementation. It is an unsplit-field scheme that can be extended to higher-order discretization schemes conveniently. Numerical results from both homogeneous and heterogeneous computational domains are provided to illustrate the validity of the method. Copyright © 2013 John Wiley & Sons, Ltd.