Numerical study of exterior acoustic problems using a novel finite element-least square point interpolation method with perfectly matched layer

Abstract

In recent years the finite element-least square point interpolation method (FE-LSPIM) is proposed by previous researchers to solve mechanical problems. Then, FE-LSPIM is also presented by the authors in acoustic analysis. This work introduces this idea into the two-dimensional (2D) exterior acoustic problems including the perfectly matched layer (PML) method and proposes a FE-LSPIM/PML model for exterior acoustic problems. In present work, the computational region, truncated by PML, is discretized into quadrilateral element meshes, and the shape functions of quadrilateral element are utilized for partition of unity (PU) and the least-square point interpolation method (LSPIM) are utilized for local approximation. The proposed model inherits the compatibility attributes of finite element method (FEM) and LSPIM, and will greatly depress numerical dispersion error; meanwhile, the present model can deal with the exterior domain problems by combining with the PML method. Numerical example shows that, the FE-LSPIM/PML achieves better absorbing effect in PML, and higher accuracy in the computational region as compared to the corresponding FEM/PML and the Element-Free Galerkin method (EFGM)/PML. Therefore, the FE-LSPIM/PML can be well applied to solve the exterior acoustic problems.