We present scalable algorithms to simulate large-scale stochastic particle systems amenable for modeling dense colloidal suspensions, glasses and gels. To handle the large number of particles and consequent many-body interactions present in such systems, we leverage an Accelerated Stokesian Dynamics (ASD) approach, for which we developed parallel algorithms in a distributed memory architecture. We present parallelization of the sparse near-field (including singular lubrication) interactions, and of the matrix-free many-body far-field interactions, along with a strategy for communicating and mapping the distributed data structures between the near- and far field. Scaling to up to tens of thousands of processors for a million particles is demonstrated. In addition, we propose a novel algorithm to efficiently simulate correlated Brownian motion with hydrodynamic interactions. The original Accelerated Stokesian Dynamics approach requires the separate computation of far-field and near-field Brownian forces. Recent advancements propose computation of a far-field velocity using positive spectral Ewald decomposition. We present an alternative approach for calculating the far-field Brownian velocity by implementing the fluctuating force coupling method and embedding it using a nested scheme into ASD. This straightforward and flexible approach reduces the computational time of the Brownian far-field force construction from $O{(NlogN)}^{1+|\alpha |}$ to $O(NlogN)$.

我们提出了可扩展的算法来模拟适合于模拟稠密的胶体悬浮液，玻璃和凝胶的大规模随机粒子系统。为了处理此类系统中存在的大量粒子以及随之而来的多体交互作用，我们利用了加速斯托克斯动力学（ASD）方法，为此我们在分布式内存体系结构中开发了并行算法。我们提出了稀疏近场（包括奇异润滑）相互作用和无基质多体远场相互作用的并行化，以及在近场和远场之间通信和映射分布式数据结构的策略。演示了针对一百万个粒子最多可扩展到成千上万个处理器。此外，我们提出了一种新颖的算法，可以有效地模拟与水动力相互作用的相关布朗运动。原始的加速斯托克斯动力学方法需要分别计算远场和近场布朗力。最近的进展提出了使用正谱埃瓦尔德分解来计算远场速度。我们提出一种替代方法，通过实施波动力耦合方法并将其使用嵌套方案嵌入到ASD中来计算远场布朗速度。这种简单而灵活的方法减少了布朗远场力构造的计算时间，从 最近的进展提出了使用正谱埃瓦尔德分解来计算远场速度。我们提出一种替代方法，通过实施波动力耦合方法并将其使用嵌套方案嵌入到ASD中来计算远场布朗速度。这种简单而灵活的方法减少了布朗远场力构造的计算时间，从 最近的进展提出了使用正谱埃瓦尔德分解来计算远场速度。我们提出一种替代方法，通过实施波动力耦合方法并将其使用嵌套方案嵌入到ASD中来计算远场布朗速度。这种简单而灵活的方法减少了布朗远场力构造的计算时间，从$Ø{（ñ升ØGñ）}^{\mathrm{1个}+|\alpha |}$ 至 $Ø（ñ升ØGñ）$。