Improving the performance of perfectly matched layers by means of <i>hp</i>‐adaptivity

Abstract

Abstract We improve the performance of the Perfectly Matched Layer (PML) by using an automatic h p ‐adaptive discretization. By means of h p ‐adaptivity, we obtain a sequence of discrete solutions that converges exponentially to the continuum solution. Asymptotically, we thus recover the property of the PML of having a zero reflection coefficient for all angles of incidence and all frequencies on the continuum level. This allows us to minimize the reflections from the discrete PML to an arbitrary level of accuracy while retaining optimal computational efficiency. Since our h p ‐adaptive scheme is automatic, no interaction with the user is required. This renders tedious parameter tuning of the PML obsolete. We demonstrate the improvement of the PML performance by h p ‐adaptivity through numerical results for acoustic, elastodynamic, and electromagnetic wave‐propagation problems in the frequency domain and in different systems of coordinates. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 832–858, 2007