Research On GPU Parallel Computation Of EFG Method And Its Topology Optimization

Element-free Galerkin(EFG) method not only has the advantage of getting rid of the shackles of the grid, but has good stability calculation and fast convergence and high precision, etc. Another, EFG method topology optimization can effectively solve the reconfigurable mesh and other issues, which are aroused by finite element method topology optimization. More importantly, EFG method topology optimization can effectively eliminate checkerboard phenomenon. Therefore, more and more attention of scholars has been attracted by EFG method and its topology optimization. However, in large scale problems, the research and application of EFG method and its topology optimization is severely constrained by the drawback that EFG method has low computation efficiency. At the same time, Graphic Processing Unit(GPU) has been widely applied in many fields with the rapid development of paralleling computing. Therefore, according to the shortcoming of low efficiency and time-consuming, this paper carries out the GPU parallel computing research of EFG method and its topology optimization. The main research contents are summarized as follows:Firstly, the three-dimension EFG structure analysis method was studied and applied. In the two-dimensional, we introduced triangular element to instead of the EFG traditional algorithm’s quadrilateral elements. Meanwhile, we introduced tetrahedral element to instead of hexahedral element in the three-dimensional. On the other hand, in order to achieve the integral calculation of EFG method, the Hammer integral was used to replace the Gauss integral which is the integral method of the EFG traditional algorithm. And the relevant formula was detailedly derived. Another, the feasibility of the algorithm was verified by the analysis of numerical examples.Secondly, the GPU parallel computing of EFG method was investigated. Based on the thought of interacting nodes pairs, a joint assembly scheme and its GPU parallel algorithm of the general stiffness matrix and the general punishment stiffness matrix and the preprocessing matrix was raised. Moreover, an accelerated algorithm of EFG method which couples GPU and Preconditioned Conjugate Gradient(PCG) method was presented. The derivation process of correlation formula and the flowchart of this accelerated algorithm were given in this paper. Then through the analysis of numerical examples, the convergence and time-consuming which is PCG method solve the general discrete control equation of EFG method were discussed, and the effect that the number of discrete nodes in the solving domain impact on the size of GPU’s block and speedup was considered.Finally, the GPU parallel computing of EFG topology optimization was deliberated. Based on the thought of interacting nodes pairs, a parallel algorithm of objective function sensitivity was proposed. And a GPU parallel algorithm of the objective function sensitivity and Optimization Criterion(OC) method was designed when Compute Unified Device Architecture(CUDA) had been combined. Then this paper proposed a GPU parallel algorithm of EFG topology optimization and gave its algorithm flowchart. Moreover, the feasibility and effectiveness of the above algorithm was confirmed by this paper. And 24 times speedup was achieved. At the last, the effect which is the number of discrete nodes in the solving domain impact on the speedup and the optimization results were discussed.In this paper, the computing time-consuming of EFG method and its topology optimization is significantly reduced by the GPU parallel algorithm. And the computational efficiency is greatly improved. Moreover, the research results have an important theoretical reference value and engineering significance when EFG method and its topology optimization are applied to the engineering problems.