A hybrid finite element-least square point interpolation method for solving acoustic problems

This paper presents a finite element-least square point interpolation method (FE-LSPIM) for solving 2D acoustic problem by synthesizing the attractive features of finite element and least-square point interpolation shape functions using the concepts of partition of unity (PU) methods. In the present method, the acoustic domain is discretized using quadrilateral element, and the shape functions of the quadrilateral element are used for PU and the least-square point interpolation method (LSPIM) for local approximation. This enables the proposed method to inherit the compatibility properties of finite element method and the quadratic polynomial completeness properties of meshfree methods, so that the finite element-least-square point interpolation method (FE-LSPIM) will greatly reduce the numerical dispersion error because the numerical dispersion error is essentially caused by the “overly-stiff” nature of the FEM model. Numerical results for benchmark problems show that, the FE-LSPIM achieves more accurate results and higher convergence rates as compared with the corresponding finite elements and Element-free Galerkin method (EFGM), especially for high wave number and irregular meshes.