Efficient PML for the wave equation
For computational scientists simulating wave propagation in unbounded media, this provides a more efficient PML implementation that avoids reformulating the wave equation into a first-order system.
The authors propose a PML formulation for the wave equation in its second-order form, requiring only two auxiliary variables in 2D and four in 3D, which is cheaper and simpler than existing first-order approaches. Numerical examples demonstrate accuracy and long-time stability.
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. Since our formulation requires no higher derivatives, it is also easily coupled with standard finite difference or finite element methods. Strong stability is proved while numerical examples in two and three space dimensions illustrate the accuracy and long time stability of our PML formulation.