Dispersive properties of the Natural Element Method

The Natural Element Method (NEM) is a meshfree numerical method for the solution of partial differential equations. In the natural element method, natural neighbor coordinates, which are based on the Voronoi tesselation of a set of nodes, are used to construct the interpolant. The performance of NEM in two-dimensional linear elastodynamics is investigated. A standard Galerkin formulation is used to obtain the weak form and a central-difference time integration scheme is chosen for time history analyses. Two different applications are considered: vibration of a cantilever beam and dispersion analysis of the wave equations. The NEM results are compared to finite element and analytical solutions. Excellent dispersive properties of NEM are observed and good agreement with analytical solutions is obtained.