耦合GPU与PCG的EFG法并行计算及应用研究

发布时间：2018-01-17 17:04

本文关键词：耦合GPU与PCG的EFG法并行计算及应用研究　出处：《应用力学学报》2017年01期 　论文类型：期刊论文

【摘要】：针对迭代法求解无网格Galerkin法中线性方程组收敛速度慢的问题,提出了一种耦合GPU和预处理共轭梯度法的无网格Galerkin法并行算法,在对其总体刚度矩阵、总体惩罚刚度矩阵进行并行联合组装的同时即可得到对角预处理共轭矩阵,有效地节省了GPU的存储空间和计算时间;通过采用四面体积分背景网格,提高了所提算法对三维复杂几何形状问题的适应性。通过2个三维算例验证了所提算法的可行性,且预处理共轭梯度法与共轭梯度法相比,其迭代次数最大可减少1686倍,最大的迭代时间可节省1003倍;同时探讨了加速比与线程数和节点个数之间的关系,当线程数为64时其加速比可达到最大,且预处理共轭梯度法的加速比与共轭梯度法相比可增大4.5倍,预处理共轭梯度法的加速比最大达到了88.5倍。
[Abstract]:To solve the problem of slow convergence of linear equations in meshless Galerkin method by iterative method. A parallel meshless Galerkin algorithm coupled with GPU and preconditioned conjugate gradient method is proposed in this paper. When the total penalty stiffness matrix is assembled in parallel, the diagonal preprocessing conjugate matrix can be obtained at the same time, which saves the storage space and computation time of GPU effectively. By using the tetrahedron integral background grid, the adaptability of the proposed algorithm to the three-dimensional complex geometric shape problem is improved, and the feasibility of the proposed algorithm is verified by two three-dimensional numerical examples. Compared with the conjugate gradient method, the maximum number of iterations can be reduced by 1686 times and the maximum iteration time can be saved by 1003 times. At the same time, the relationship between the speedup ratio and the number of threads and nodes is discussed. When the number of threads is 64, the speedup can reach the maximum, and the speedup of the pretreatment conjugate gradient method can be increased by 4.5 times compared with the conjugate gradient method. The maximum speedup of the pretreatment conjugate gradient method is 88.5 times.
【作者单位】：湘潭大学机械工程学院;
【基金】：国家自然科学基金(51375417;51405415)
【分类号】：TP338.6
【正文快照】： 无网格Galerkin(Element-Free Galerkin,EFG)法仅需要节点信息,可适用于网格划分困难或需要网格重构的问题[1],且因其具有较高的计算精度,现已在塑性变形[2]、裂纹扩展[3]、结构优化[4]等领域得到了广泛应用。但其与传统算法如有限元相比,则存在计算量大、计算效率低等问题。

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