GPU-accelerated smoothed particle finite element method for large deformation analysis in geomechanics

Abstract

Particle finite element method (PFEM) is an effective numerical tool for solving large-deformation problems in geomechanics. By incorporating the node integration technique with strain smoothing into the PFEM, we proposed the smoothed particle ?nite element method (SPFEM). This paper extends the SPFEM to three-dimensional cases and presents a SPFEM executed on graphics processing units (GPUs) to boost the computational efficiency. The detailed parallel computing strategy on GPU is introduced. New computation formulations related to the strain smoothing technique are proposed to save memory space in the GPU parallel computing. Several benchmark problems are solved to validate the proposed approach and to evaluate the GPU acceleration performance. Numerical examples show that with the new formulations not only the memory space can be saved but also the computational efficiency is improved. The computational cost is reduced by 70% for the double-precision GPU parallel computing with the new formulations.

A three-dimensional particle finite element model for simulating soil flow with elastoplasticity

“…Given the potential of the PFEM for investigating many practical engineering applications, the explicit 3D PFEM Fig. 2 Boundary recognition using the alpha-shape method: a cloud of points; b Delaunay triangulation; c tetrahedral mesh after deleting tetrahedrons with the diameter of their circumscribed spheres larger than ah e (a is a factor and h e is the characteristic length of the mesh) has been developed for solving both fluid [18,20] and solid problems [72]. Here, we extend the PFEM formulation developed in our previous study [64] to 3D modelling.…”

“…A 3D PFEM was developed in the framework of computational fluid dynamics to solve the Navier-Stokes equations and further applied to simulate debris flows and landslide problems [17,21], where soils are modelled as non-Newtonian fluid. A variant of the 3D PFEM model was developed for elastoplastic analysis of soils [72], where the strain field is smoothed so that first-order elements (i.e. four-node tetrahedron elements) can be used without encountering volumetric locking issues.…”

“…four-node tetrahedron elements) can be used without encountering volumetric locking issues. Additionally, the 3D PFEM model developed in [72] has been parallelised with GPUs to improve its computational efficiency given that the employed explicit FEM formulation requires very small time steps.…”

Multiple‐GPU parallelization of three‐dimensional material point method based on single‐root complex

“…The MPM, introduced to solid mechanics 5 from computational fluid dynamics, 6 was used to simulate high explosive explosions, 7 propagation of wood cracks, 8 impact between solid bodies, 9–12 fluid–structure interactions, 13 and computer animations 14–16 . In the recent decade the MPM was applied to geotechnical engineering to investigate runout of submarine landslides, 17–20 penetration and pull‐out of structures 21–23 and flow of granular materials 24–26 . Coupling analysis of pore or free water and soil, mainly used in the analysis of slope stability, 27–30 is a new trend of the MPM simulations.…”

A Lagrangian-Eulerian procedure for the coupled solution of the Navier-Stokes and shallow water equations for landslide-generated waves

“…In this new strategy, a Lagrangian finite element method, namely the Particle Finite Element Method (PFEM) [35][36][37], is used as the NFS and a standard shallow water Boussinesq model is used as the FFS. Several previous works have shown the accuracy of the PFEM to model landslides [38][39][40], also in cascading events [41][42][43][44]. In this work, we use the PFEM approach that has been successfully applied to LGW scenarios in [45] and in [28,29], where 3D simulations of the Vajont disaster were presented.…”