中文摘要：

针对进行大规模拓扑优化问题计算量庞大且计算效率低的问题,设计并实现了一种基于图形处理器（GPU）的并行拓扑优化方法。采用双向渐进结构拓扑优化（BESO）为基础优化算法,采用一种基于节点计算的共轭梯度求解方法用于有限元方程组求解。通过对原串行算法的研究,并结合GPU的计算特点,实现了迭代过程全流程的并行计算。上述方法的程序设计和编写采用统一计算架构（CUDA）,提出了基于单元和基于节点的两种并行策略。编写程序时充分使用CUDA自带的各种数学运算库,保证了程序的稳定性和易用性。数值算例证明,并行计算方法稳定并且高效,在优化结果一致的前提下,采用GTX580显卡可以取得巨大的计算加速比。

英文摘要：

In this paper, a parallel topology optimization method is proposed to calculate large -scale structural design problems based on GPU. The parallel algorithms presented here are based on the Bi - directional Evolutionary Structural Optimization （BESO） formulation with soft - kill technology. Considering the characteristic of GPU computation, the conjugate gradient iterative solver with a nodal based visual finite element assembly scheme is introduced for the finite method problem. Compute Unified Device Architecture （CUDA） is employed to design and code program, including several high API offered by CUDA for free. Two parallel computing strategies include nodal - based and element -based mapping strategies. Finally, a total parallel optimization program is realized. Several numerical examples are considered, more than 100 times speedup can be obtained in handling large -scale design problems on a personal computing with a NVIDIA GTX 580 GPU. It shows the scalability and effectiveness of the present parallel approach.