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.

Highlights

  • Solving exterior radiation and scattering problems continues to be very challenging especially when the frequency increases or, equivalently when the size of the domain of interest is large

  • The technique which can be seen as an extension of classical FEM allows a unified treatment of radiation conditions which is applicable to a variety of configurations ranging from periodic structures, waveguides [19], infinite and halfspace problems [20]. The aim of this this paper is to show the applicability of Perfectly Match Layer (PML) combined with Partition of Unity Finite Element Method (PUFEM) for solving the propagation of acoustic waves in unbounded media

  • The average characteristic size of PUFEM elements is 50 cm, except in the vicinity of the top part of the barrier where the size of the elements are limited by geometric features

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Summary

Introduction

Solving exterior radiation and scattering problems continues to be very challenging especially when the frequency increases or, equivalently when the size of the domain of interest is large. The BEM only requires the discretization of the surface of the scattering (or radiating) object and this naturally leads to a substantial reduction of degree of freedoms. These advantages are counterbalanced by a couple of drawbacks: the method yields fully populated matrices with complex-valued coefficients which leads to high computational expenses, and it is limited to wave problems in homogeneous domains. Volume discretization methods such as the Finite-Element-Method (FEM) allow to consider the propagation of waves in complex and nonhomogeneous Langlois et al.: Acta Acustica 2020, 4, 16 to solve acoustic wave scattering in 2 and 3 dimensions [9, 10], flow acoustic and other wave propagation problems [11,12,13]

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