A coupled FE-meshfree method for Helmholtz problems using point interpolation shape functions and edge-based gradient smoothing technique

In this paper, the point interpolation shape functions from a meshfree technique is combined with the generalized gradient smoothing technique (GGST) based on mesh grids to give a coupled FE-meshfree method for analyzing acoustic problems addressed by the Helmholtz equation. It is well-known that the numerical results of Helmholtz problems from several classical numerical approaches, such as the finite element approach, are not always sufficient to provide satisfying accuracy because of the pollution effect for relatively high wave numbers. The pollution effect may generally come from the "overly-stiff" property of the numerical models. Owing to the appropriate softening feature resulting from the edge-based gradient smoothing technique (EGST), the present coupled FE-meshfree method can effectively depress the pollution error effect of the numerical solutions. To avoid the singular issue of the moment matrix for the point interpolation shape functions used, several cell-based T-schemes are utilized for choosing nodes in the interpolation. Numerical results have validated that the present method could not only provide much more accurate solutions compared with the finite element method with the same node distribution, particularly at the relatively high frequency range, but also have higher computational efficiency with certain node selection schemes. (C) 2018 Elsevier Ltd. All rights reserved.