Implementation of a fast finite element solver for multiphase problems using hardware accelerator

Abstract

Numerical simulation of a shield tunnelling construction enables a reliable prognosis of the construction process and the impact of the process on the surrounding ground. For ground contains partially saturated soil, which consists of groundwater, two-phase FEM formulation is required to model the soil accurately. For the construction maintenance phase, the compressed air is used at the shield heading face to prevent water inflow. In this case, partially soil saturated consist of three components: soil grains, pore water and pore air. Consequently, a fully coupled finite element formulation for partially saturated soil as a three-phase material are of mandatory usage for the model. The derived coupled simulations of partially saturated soil in shield tunnelling using compressed air lead to a block-structured system of equations. The coefficient stiffness matrix is sparse, non-symmetric and ill-conditioned which are difficult to solve using traditional solvers. An iterative solver based on Krylov subspace method is employed to solve the system with less computation cost than a direct solver. In addition, efficient preconditioners act as means to improve the condition of the system matrix and accelerate the convergence behaviour of the iterative solver. Graphics Processing Unit (GPU), a new high-profile parallel processor with hundreds of microprocessors on a single card, makes large scale parallel algorithms possible on a personal desktop user. In this thesis, a GPU-accelerated iterative solver is developed to provide a robust solver for solving large sparse system. For this new iterative solver, several Krylov iterative methods with different preconditioners are developed based on CUDA support libraries. In detail, BiCGSTAB and GMRES solvers are implemented on GPU and ILU(0), ILUT preconditioner is developed on CPU. Furthermore, a parallel GPU-based block-preconditioning technique has also been developed to integrate with the new iterative solver to specifically address the block-structure matrix. Finally, scaling strategy is applied for the block-matrix to improve the condition of the system matrix.