The meshless analysis of wave propagation based on the Hermit-type RRKPM

Abstract

The paper presents the Hermit-type radial basis reproducing kernel particle method (Hermit-type RRKPM) for wave propagation. The Hermit-type radial basis function is employed to construct the approximating function, which can reduce the adverse effect of different reproducing kernel functions (RKFs) on computational accuracy and improve stability in the problem domain and on the boundary of the domain. Compared with the conventional reproducing kernel particle method (RKPM) and radial basis function (RBF) method, the Hermit-type RRKPM has better stability and computational accuracy. The Hermit-type RRKPM is applied to wave propagation, and integral weak form is employed to obtain a discretized system equation for wave propagation problem. The penalty method is applied to imposing the essential boundary condition, and the two-point difference method is selected for the time discretization. The accuracy and stability of the Hermit-type RRKPM are illustrated by the numerical examples.