Partition of Unity Finite Element Method applied to exterior problems with Perfectly Matched Layers

Abstract

The Partition of Unity Finite Element Method (PUFEM) is now a well established and efficient method used in computational acoustics to tackle short-wave problems. This method is an extension of the classical finite element method whereby enrichment functions are used in the approximation basis in order to enhance the convergence of the method whilst maintaining a relatively low number of degrees of freedom. For exterior problems, the computational domain must be artificially truncated and special treatments must be followed in order to avoid or reduce spurious reflections. In recent papers, different Non-Reflecting Boundary Conditions (NRBCs) have been used in conjunction with the PUFEM. An alternative is to use the Perfectly Match Layer (PML) concept which consists in adding a computational sponge layer which prevents reflections from the boundary. In contrast with other NRBCs, the PML is not case specific and can be applied to a variety of configurations. The aim of this work is to show the applicability of PML combined with PUFEM for solving the propagation of acoustic waves in unbounded media. Performances of the PUFEM-PML are shown for different configurations ranging from guided waves in ducts, radiation in free space and half-space problems. In all cases, the method is shown to provide acceptable results for most applications, similar to that of local approximation of NRBCs.