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.

在声学分析中，标准径向点插值无网格方法 (RPIM) 能够胜过经典的有限元方法 (FEM)，因为可以通过增加插值域的大小来显着减轻数值离散。但是，此操作通常会导致计算成本激增。在这项工作中，通过使用一般的多波模式开发了丰富的 RPIM (e-RPIM)，但不需要额外的自由度。在这种丰富的方案中，传统的径向基函数插值通过一组平面波丰富函数来增强，这有助于反映波传播的振荡特性。这种 e-RPIM 通过使用尺寸相对较小的插值域可以明显缓解数值离散并产生令人满意的解算精度。虽然构建丰富的插值形状函数需要额外的计算成本，但如果考虑计算精度，则提出的 e-RPIM 明显提高了原始 RPIM 的计算效率。几个数值实验验证了所提出的 e-RPIM 在声学分析中是标准 RPIM 和 FEM 的有希望的竞争对手。