Abstract：It is well known that the standard finite element method (FEM) is unreliable to compute approximate solutions of the Helmholtz equation for high wave numbers due to the numerical dispersion. The cell-based smoothed radial point interpolation method (CS-RPIM) is extended to solve the 2D acoustic problem and the formulation of CS-RPIM is presented for the two-dimensional acoustic problem. In present method, the acoustic domain is discretized using triangular background cells, and each cell is further divided into several smoothing cells, the acoustic gradient smoothing technique is implemented to each smoothing cell. 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 CS-RPIM will greatly reduce the numerical dispersion error and obtain accurate results for acoustic problems because of the properly softened stiffness. Numerical examples have been studied, including a tube and a 2D problem of a car acoustic problem and the results show that the CS-RPIM achieves more accurate results and higher convergence rates as compared with the corresponding finite elements, especially for high wave number.
姚凌云;于德介;臧献国. 声学数值计算的分区光滑径向点插值无网格法[J]. , 2011, 30(10): 188-192.
YAO ling-yun;YU de-jie; ZANG xian-guo. Numerical computation for acoustic problem using a cell-based smoothed radial point interpolation method. , 2011, 30(10): 188-192.
2011, Vol. 30 
