Dispersion error reduction for interior acoustic problems using the radial point interpolation meshless method with plane wave enrichment functions

Abstract

In acoustic analyses the standard radial point interpolation meshless method (RPIM) is able to outperform the classic finite element method (FEM) because the numerical dispersion can be significantly mitigated by increasing the size of the interpolation domain. However, this operation usually leads to a surge in computational cost. In this work an enriched RPIM (e-RPIM) is developed by using the general multiple wave patterns but no extra degrees of freedom are needed. In this enriched scheme the traditional radial basis function interpolation is augmented by a set of plane wave enrichment functions which helps to reflect the oscillation characteristics of the wave propagation. This e-RPIM can obviously alleviate the numerical dispersion and yield satisfactory solution accuracy by using a relatively small size interpolation domain. Although extra computational cost is required in constructing the enriched interpolation shape functions, the computational efficiency of the original RPIM is evidently improved by the proposed e-RPIM if the computation accuracy is taken into consideration. Several numerical experiments validate that the proposed e-RPIM is a promising competitor to the standard RPIM and FEM in acoustic analyses.