Edged-based smoothed point interpolation method for acoustic radiation with perfectly matched layer

Abstract

It is known that for exterior acoustics the domain-based finite element method always encounters the accuracy loss for high wavenumbers and the difficulty in dealing with the Sommerfeld radiation condition. In this work, by using the polynomial and radial bases with specific node-selection schemes, the point interpolation method with the generalized gradient smoothing technique is employed to improve the accuracy for acoustic computations. The appropriately softened acoustical stiffness of the discrete model is constructed based on the edge-based smoothing domains via the gradient smoothing technique. In addition, the perfectly matched layer technique enables the smoothed point interpolation method to investigate exterior acoustics. The complex coordinate transformation is utilized to determine the proper parameters for the perfectly matched layer through theoretical and numerical analyses. Several typical acoustic problems are analyzed, revealing that better accuracy is obtained by the present method compared with the finite element method, especially for high wavenumbers.