Application of the smoothed point interpolation methods in computational geomechanics: A comparative study

In this study, computational efficiency and performance of the smoothed point interpolation methods (SPIMs) in coupled problems of geomechanics are examined and compared with those of the standard linear finite element method (FEM). In the SPIMs, the problem domain is first discretised using a triangular background mesh, and the smoothing domains are then constructed using the cells of the background mesh. Different approaches for construction of the smoothing domains result in different SPIMs including Edge-based SPIM (ESPIM), cell-based SPIM (CSPIM), and node-based SPIM (NSPIM), each featuring different computational characteristics. For each type of the SPIM, only the simplest and most widely used supporting node selection technique is adopted in this study. The field function is approximated using shape functions constructed adopting either the polynomial point interpolation method (PIM), or radial point interpolation method (RPIM). The governing equations are derived from the equilibrium equation of the solid phase, and momentum and mass balance equations for the flow phase. The equations are then discretised in space using the generalized smoothed Galerkin (GS-Galerkin) method, and in time using the three-point time discretisation technique. The performance of the SPIMs in coupled geomechanical problems are then thoroughly assessed and compared to those of the linear FEM through extensive numerical analyses of four benchmark problems in saturated porous media covering both linear and non-linear material behaviours, and the conclusions drawn by analysing the results.