Efficient PML for the wave equation

Understand

In the last decade, the perfectly matched layer (PML) approach has proved a flexible and accurate method for the simulation of waves in unbounded media.

• Most PML formulations, however, usually require wave equations stated in their standard second-order form to be reformulated as first-order systems, thereby introducing many additional unknowns.
• To circumvent this cumbersome and somewhat expensive step, we instead propose a simple PML formulation directly for the wave equation in its second-order form.
• Inside the absorbing layer, our formulation requires only two auxiliary variables in two space dimensions and four auxiliary variables in three space dimensions; hence it is cheap to implement.