Development of Partition of Unity Finite Element Method for the Modelling of Acoustic Waves Propagating through Porous Domain

Abstract

The numerical simulation of propagating sound fields in two dimensions using Partition of Unity Finite Element Method(PUFEM) technique is implemented in this work. PUFEM is one of the most practical methods developed to alleviate high computational cost of conventional Finite Element Method when we deal with the medium and high frequency problem. The main idea of PUFEM is to expand the finite element approximation space by incorporating a group of wave functions which are solutions of the governing equation into the target problem. With the intention of further accelerating the computational process, an advanced 2D Exact Integration Technique(EIT) for accelerating the computation process of highly oscillating integrals is proposed and the related PUFEM triangular element is created. The performance and practical interest of this new PUFEM element combined with EIT are evaluated for the wave propagation problem where a porous absorber is included.