  Perfectly Matched Layer (PML) is a widely adopted non-reflecting boundary
treatment for wave simulations. Reducing numerical reflections from a
discretized PML has been a long lasting challenge. This paper presents a new
discrete PML for the multi-dimensional scalar wave equation which produces no
numerical reflection at all. The reflectionless discrete PML is discovered
through a straightforward derivation using Discrete Complex Analysis. The
resulting PML takes an easily-implementable finite difference form with compact
stencil. In practice, the discrete waves are damped exponentially in the PML,
and the error due to domain truncation is maintained at machine zero by a
moderately thick PML. The numerical stability of the proposed PML is also
demonstrated.

Numerical Analysis