Fast algorithms for large dense matrices with applications to biofluids
Fast algorithms for large dense matrices with applications to biofluids
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DOI：
10.1016/j.jcp.2019.05.042
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发表时间：
2019-10-01
影响因子：
4.1
通讯作者：
Olson, Sarah D.
中科院分区：
文献类型：
--
作者：
Rostami, Minghao W.;Olson, Sarah D.
生物流体的数值模拟需要求解流体-结构相互作用方程。在零雷诺数，求解器，如正则化Stokeslets（MRS）的方法，在实际应用中，沉浸在流体中的结构的数量是大的，会产生大而密集的矩阵。建立在以前的工作为一个无界的流体域，我们首先扩展核独立快速多极子方法（KIFMM）MRS计算矩阵矢量积的流体流动引起的点力以上的固定壁。在这种情况下，正则化图像系统的使用将额外的项引入到解中，这使得矩阵-向量乘法非常具有挑战性。此外，我们研究的情况下，一个线性系统需要解决的未知的力量，结构与已知的速度施加在流体上。我们的主要贡献是提出了几个预处理技术与MRS的几个变种，包括强制执行的情况下，无力，无扭矩的条件下的矩阵。它们利用FMM矩阵的数据稀疏性以及Krylov子空间的性质。我们的方法是内存有效的，能够处理非均匀分布的结构和适用于所有的FMM矩阵。它可以有效地计算周围的一大群动态微观结构的流场;特别是，我们研究了由肺纤毛的密集地毯的周期性跳动引起的流体混合的影响。(C)2019爱思唯尔公司All rights reserved.
Numerical simulation of biofluids entails solving equations of fluid-structure interactions. At zero Reynolds number, solvers such as the Method of Regularized Stokeslets (MRS) give rise to large and dense matrices in practical applications where the number of structures immersed in the fluid is large. Building on previous work for an unbounded fluid domain, we first extend the Kernel-Independent Fast Multipole Method (KIFMM) for MRS to compute the matrix-vector products for the fluid flow induced by point forces above a stationary wall. In this case, the use of a regularized image system introduces additional terms to the solution which cause the matrix-vector multiplication to be quite challenging. In addition, we study the case where a linear system needs to be solved for the unknown forces that structures with known velocities exert on the fluid. Our main contribution is proposing several preconditioning techniques for the matrices associated with a few variants of MRS, including the case where a force-free, torque-free condition is imposed. They take advantage of the data-sparsity of FMM matrices as well as properties of Krylov subspaces. Our approach is memory efficient, capable of handling non-uniformly distributed structures and applicable to all FMM matrices. It enables efficient computation of the flow field surrounding a large group of dynamic micro-structures; in particular, we study the effects of fluid mixing caused by the periodic beating of a dense carpet of lung cilia. (C) 2019 Elsevier Inc. All rights reserved.