Meshfree simulations of acoustic problems by a radial point interpolation method

Abstract

The classical finite element approach cannot guarantee satisfactory accuracy for acoustic problems at large wavenumbers on account of the numerical pollution error effect. This negative effect stems from the fact that the approximate wavenumbers are usually in conflict with the real wavenumbers in many numerical methods. To suppress this effect, a radial point interpolation meshless technique with a modified scheme for selecting interpolation nodes is employed in this paper. One-dimensional dispersion analysis shows that this modified scheme can effectively reduce numerical errors compared with the original scheme. The results of several numerical examples have manifested that the present method can generate more accurate and reliable solutions than the standard finite element approach and the original radial point interpolation method in the acoustic analyses.