A coupled hybrid smoothed radial point interpolation method for computing underwater acoustic scattering

Abstract

The discrete model in the standard finite element method (FEM) always exhibits stiffer behavior than the actual continuous model. This leads to an unavoidable dispersion error that increases rapidly with the wave number. To overcome this issue in underwater acoustic scattering problems, a coupled hybrid smoothed radial point interpolation method (CHSRPIM) is proposed to reduce the dispersion error. In CHSRPIM, the modified Dirichlet-to-Neumann boundary condition is imposed on an artificial boundary to ensure that the acoustic wave correctly travels outward, and a hybrid acoustic stiffness is created using the local gradient smoothing operation to soften the stiffness. To obtain a very close-to-actual stiffness of the original model, a cell-based radial point interpolation method with three real and four virtual nodes is devised to create the acoustic shape function. The major benefit of the CHSRPIM is that, for a given mesh, the dispersion error is effectively reduced compared with that of the FEM without increasing the degrees of freedom. The performance of the proposed method is numerically evaluated. Numerical experiments are conducted to investigate the properties of the proposed method. The simulation results indicate that the CHSRPIM possesses superior computational performance and can significantly improve accuracy; therefore, it has good potential for resolving practical acoustic scattering problems in engineering.