Performance of the radial point interpolation method (RPIM) with implicit time integration scheme for transient wave propagation dynamics

The radial point interpolation method (RPIM) is combined with the appropriate implicit time integration technique for transient wave propagation analysis in this work. The dispersion error issue of the numerical results is investigated detailedly by performing the dispersion analysis. It is found that the RPIM with sufficiently large support domains of quadrature points is able to yield almost no spatial dispersion errors which are much lower than those from the traditional finite element (FE) approach with the identical node distributions, hence we can monotonically improve the computation accuracy of the numerical results by using the decreasing time steps, namely the present method shows the important and attractive monotonic convergence property for transient wave analysis. This property makes the present method clearly superior to the standard FE approach in transient wave analysis and much more accurate solutions can be achieved. Several typical benchmark problems of transient wave propagations are studied to assess the robust and superior performance of the present method over the conventional FE for transient wave analysis.