This work presents a parallel implementation of density-based topology optimization using distributed GPU computing systems. The use of multiple GPU devices allows us accelerating the computing process and increasing the device memory available for GPU computing. This increment of device memory enables us to address large models that commonly do not fit into one GPU device. The most modern scientific computers incorporate these devices to design energy-efficient, low-cost, and high-computing power systems. However, we should adopt the proper techniques to take advantage of the computational resources of such high-performance many-core computing systems. It is well-known that the bottleneck of density-based topology optimization is the solving of the linear elasticity problem using Finite Element Analysis (FEA) during the topology optimization iterations. We solve the linear system of equations obtained from FEA using a distributed conjugate gradient solver preconditioned by a smooth aggregation-based algebraic multigrid (AMG) using GPU computing with multiple devices. The use of aggregation-based AMG reduces memory requirements and improves the efficiency of the interpolation operation. This fact is rewarding for GPU computing. We evaluate the performance and scalability of the distributed GPU system using structured and unstructured meshes. We also test the performance using different 3D finite elements and relaxing operators. Besides, we evaluate the use of numerical approaches to increase the topology optimization performance. Finally, we present a comparison between the many-core computing instance and one efficient multi-core implementation to highlight the advantages of using GPU computing in large-scale density-based topology optimization problems.

这项工作提出了使用分布式GPU计算系统的基于密度的拓扑优化的并行实现。使用多个GPU设备使我们能够加快计算过程并增加可用于GPU计算的设备内存。设备内存的增加使我们能够处理通常不适合一个GPU设备的大型模型。最先进的科学计算机结合了这些设备，以设计节能，低成本和高计算能力的电源系统。但是，我们应该采用适当的技术来利用此类高性能多核计算系统的计算资源。众所周知，基于密度的拓扑优化的瓶颈是在拓扑优化迭代过程中使用有限元分析（FEA）解决线性弹性问题。我们使用分布式共轭梯度求解器求解从FEA获得的线性方程组，该共轭梯度求解器通过使用多个设备进行GPU计算的基于平滑聚集的代数多重网格（AMG）进行预处理。基于聚合的AMG的使用减少了内存需求，并提高了插值操作的效率。这个事实对于GPU计算是有益的。我们使用结构化和非结构化网格来评估分布式GPU系统的性能和可伸缩性。我们还使用不同的3D有限元素和松弛运算符来测试性能。除了，我们评估使用数值方法来提高拓扑优化性能。最后，我们在多核计算实例与一种有效的多核实现之间进行了比较，以突出显示在大规模基于密度的拓扑优化问题中使用GPU计算的优势。