Recursive Tree Algorithms for Orthogonal Matrix Generation and Matrix-Vector Multiplications in Rigid Body Simulations Public Deposited

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Last Modified
  • February 26, 2019
Creator
  • Fang, Fuhui
    • Affiliation: College of Arts and Sciences, Department of Mathematics
Abstract
  • In this paper, we study a numerical linear algebra problem arising from the efficient simulation of Brownian dynamics with hydrodynamics interactions where molecules are modeled as ensembles of rigid bodies. Given the first 6 rows of a matrix Q of size 3n x 3n describing how the force on each of the n particles in a rigid body P can be mapped to the 6 entries in P’s resultant force and torque, we show how the remaining 3n − 6 rows of vectors can be constructed explicitly using O(nlog(n)) operations and storage, so that (1) they form an orthonormal basis and (2) they are orthogonal to each of the first 6 vectors. For applications where only the matrix-vector multiplications are needed, without forming Q, we introduce O(n) recursive tree algorithms for computing both Q · v and QT · v for an arbitrary vector v. Preliminary numerical results are presented to demonstrate the performance and accuracy of the numerical algorithms.
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Rights statement
  • In Copyright
Note
  • Funding: Michael P. and Jean W. Carter Research Fund
Advisor
  • Huang, Jingfang
Degree
  • Bachelor of Science
Honors level
  • Highest Honors
Degree granting institution
  • University of North Carolina at Chapel Hill
Extent
  • 20
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