A Novel Virtual Node Selection Scheme of Cell-Based Smoothed Radial Point Interpolation Method (CS-RPIM) for Mid-Frequency Acoustic Problems

Abstract

Due to the “overly-stiff” nature, it has been proved that the finite element method (FEM) is inevitable to suffer from the dispersion error when solving mid-frequency acoustic problems. In order to overcome this defect, in this study, a novel virtual node selection scheme of changing the virtual node’s position with a parameter is proposed, which is used to construct the condensed shape function of the cell-based radial point interpolation method (CS-RPIM) to soften the stiffness of discrete model. Based on the generalized gradient smoothing technique (GGST) and the condensed shape function technique, the present method provides a “close-to-exact” stiffness for discrete system model, which controls the dispersion error from the root. Several numerical examples have been researched to verify the performance of the proposed method in mid-frequency acoustic simulations. Moreover, with the excellent robustness, the present method lays a good foundation for solving complex practical engineering problems.