A hierarchical matrix approach for computing hydrodynamic interactions
A hierarchical matrix approach for computing hydrodynamic interactions
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DOI：
10.1016/j.jcp.2021.110761
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发表时间：
2021-10-14
影响因子：
4.1
通讯作者：
Chow，Edmond
中科院分区：
文献类型：
--
作者：
Xing，Xin;Huang，Hua;Chow，Edmond
对于斯托克斯流中大量小的球形颗粒的模拟，可以使用快速多极方法（FMM）或粒子网格Ewald方法（PME）快速求和Rotne-Prager-Yamakawa （RPY）核近似的远程流体动力相互作用。在本文中，我们开发了新的快速计算这些和的方法，使用h2层次矩阵表示，对于开放和周期边界条件。据我们所知，无限周期和的方法使用h2层次矩阵表示是第一个这样的方法发展。我们还考虑了处理多分散粒子半径的更一般的RPY核，并通过分析和实验表明，在这种情况下，代理表面方法有效地构建h2层次矩阵表示仍然有效。数值试验结果表明，该方法具有良好的控制精度和线性缩放计算量及存储成本。我们发现h2矩阵方法与FMM和PME相比具有较低的求和计算成本，但较高的预计算成本（每个粒子配置所需）。在具有大量粒子的布朗和斯托克动力学模拟中，当计算布朗位移或力时，这种预计算成本可以平摊在几个求和上。
For simulations of large numbers of small, spherical particles in a Stokes flow, the long-range hydrodynamic interactions approximated by the Rotne–Prager–Yamakawa (RPY) kernel can be summed rapidly using, for example, the fast multipole method (FMM) or the particle-mesh Ewald (PME) method. In this paper, we develop new fast methods for computing these sums using the H 2 hierarchical matrix representation, for open and for periodic boundary conditions. To the best of our knowledge, the method for infinite periodic sums using the H 2 hierarchical matrix representation is the first such method developed. We also consider a more general RPY kernel that handles polydisperse particle radii, and show analytically and experimentally that the proxy surface method for efficiently constructing the H 2 hierarchical matrix representation remains effective in this case. Numerical tests demonstrate the well-controlled accuracy of the H 2 summation methods and their linear-scaling computation and storage cost. We find that the H 2 matrix approach has lower cost for computing the summations compared to FMM and PME, but higher precomputation cost (required for each particle configuration). This precomputation cost can be amortized over several summations when computing Brownian displacements or forces in Brownian and Stokesian dynamics simulations with very large numbers of particles.