Fang Fuhui, Huang Jingfang, Huber Gary, McCammon J Andrew, Zhang B O
Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3250.
Howard Hughes Medical Institute, University of California at San Diego, La Jolla, CA 92093-0365.
SIAM J Sci Comput. 2018;40(3):A1345-A1361. doi: 10.1137/17M1117744. Epub 2018 May 10.
In this paper, we apply the hierarchical modeling technique and study some numerical linear algebra problems arising from the Brownian dynamics simulations of biomolecular systems where molecules are modeled as ensembles of rigid bodies. Given a rigid body consisting of beads, the 6×3 transformation matrix that maps the force on each bead to 's translational and rotational forces (a 6 × 1 vector), and the row space of , we show how to explicitly construct the (3 - 6) × 3 matrix consisting of (3 - 6) orthonormal basis vectors of (orthogonal complement of ) using only operations and storage. For applications where only the matrix-vector multiplications and are needed, we introduce asymptotically optimal hierarchical algorithms without explicitly forming . Preliminary numerical results are presented to demonstrate the performance and accuracy of the numerical algorithms.
在本文中，我们应用分层建模技术并研究一些数值线性代数问题，这些问题源于生物分子系统的布朗动力学模拟，其中分子被建模为刚体集合。给定一个由珠子组成的刚体、将每个珠子上的力映射到其平移和旋转力（一个6×1向量）的6×3变换矩阵以及的行空间，我们展示了如何仅使用操作和存储来显式构造由的（3 - 6）个正交基向量组成的（3 - 6）×3矩阵（的正交补）。对于仅需要矩阵 - 向量乘法和的应用，我们引入了渐近最优的分层算法，而无需显式形成。给出了初步数值结果以证明数值算法的性能和准确性。
