Cell-Based Smoothed Radial Point Interpolation Method for Underwater Acoustic Scattering Problems

Abstract

In this work, a novel cell-based smoothed radial point interpolation method (CSRPIM) is used to deal with underwater acoustic scattering problem. The nature of infinite domain has been changed by exact Dirichlet-to-Neumann (DtN) boundary condition. Owing to the use of gradient smoothing operation and consequent properly softened stiffness, the CSRPIM model is capable of reducing pollution error significantly. A theoretical analysis is carried out to elucidate the superiority in controlling pollution error of CSRPIM. By selecting virtual nodes properly in condensed shape functions, the interpolation error in the CSRPIM can also be reduced. Through several simple acoustic scattering numerical examples, advantages of CSRPIM have been verified. The results show that the CSRPIM can be applied directly to solve acoustic scattering problems and can obtain higher accuracy than traditional linear finite element method (FEM) even if in relatively high frequency range. Also, the use of linear triangular elements in the present model makes the analysis of practical underwater acoustic problems with complex shapes easier.