Numerical treatment of 2D acoustic problems with the cell-based smoothed radial point interpolation method

Abstract

This paper addresses the cell-based smoothed radial point interpolation method (CS-RPIM) for 2D acoustic problem. In present method, the acoustic domain is discretized using triangular background cells, and each cell is further divided into several smoothing cells and then the cell-based gradient smoothing operation is implemented through the smoothing cells. The pressure field function is approximated using RPIM shape functions. Supporting node selection for shape function construction uses the T2L-scheme associated with edges of the background cells. The system equations are derived using the smoothed Galerkin weak form, and the essential boundary conditions are imposed directly as in the finite element method (FEM). The cell-based gradient smoothing operation provides proper softening effect, makes the CS-RPIM model much softer than the “overly-stiff” FEM model and hence significantly reduces the numerical dispersion error. Numerical results show that the CS-RPIM achieves more accurate results and higher convergence rates as compared with the corresponding finite elements.