Characteristics of semi- and full discretization of stabilized Galerkin meshfree method

Abstract

Stabilized conforming nodal integration (SCNI) has been developed to enhance computational efficiency of Galerkin meshfree methods. This paper employs von Neumann analyses to study the spatial semi-discretization of Galerkin meshfree methods using SCNI. Two model problems were presented with respect to the normalized phase speed and group speed for the wave equation, and normalized diffusivity for the heat equation. Both consistent and lumped mass (capacity) discretizations are considered in the study. The transient properties in the full discretization of the two model problems were also analyzed. The results show superior dispersion behavior in meshfree methods integrated by SCNI compared to the Gauss integration when consistent mass (capacity) matrix is employed in the discretization. For the lumped mass case, SCNI performance is comparable to that of the Gauss integration, but exhibits considerable reduction of computational time.