Analysis of the interior acoustic wave propagation problems using the modified radial point interpolation method (M-RPIM)

Abstract

Although the radial point interpolation method (RPIM), which is a typical meshless numerical technique, usually behaves much better than the conventional FEM in addressing the numerical dispersion error issue for acoustic computation and more accurate solutions can generally be yielded with the identical node distributions, the related numerical error still can not be completely removed and further improvements are still required. In this work, we proposed a modified RPIM (M-RPIM) to enhance the abilities of the original RPIM in suppressing the numerical dispersion error. In this M-RPIM, a simple and straightforward scheme is employed to ensure that the integrands in performing the numerical integration are continuously differentiable, while in the original RPIM the quadrature cells usually do not align with the shape function supports and then results in the discontinuously differentiable numerical approximation in the quadrature cells, hence considerable numerical integration error can be generated. Since the discontinuously differentiable entities in the system stiffness matrix can be completely avoided in the present M-RPIM, it is found that the numerical dispersion can be markedly suppressed and more accurate numerical solutions can be yielded than the original RPIM in solving acoustic problems. It should be pointed out that the numerical treatments and conclusions in this work are also applicable for most of other meshfree approximations which are similar to the RPIM.