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Title page for ETD etd-07032003-150352

Type of Document Dissertation
Author Ma, Qun
URN etd-07032003-150352
Title Novel Multiscale Algorithms for Molecular Dynamics
Degree Doctor of Philosophy
Department Computer Science and Engineering
Advisory Committee
Advisor Name Title
Jesus A Izaguirre Committee Chair
Gregory Madey Committee Member
J Daniel Gezelter Committee Member
Menelaos I Karavelas Committee Member
Ryan K Roeder Committee Member
  • KAM theory
  • mollified Impulse method
  • nonlinear instability
  • targeted Langevin stabilization
  • long molecular dynamics simulations
  • multiple time stepping
  • Verlet-I/r-RESPA/Impulse
Date of Defense 2003-06-26
Availability unrestricted
In post-genomic computational biology and bioinformatics, long

simulations of the dynamics of molecular systems, particularly

biological molecules such as proteins and DNA, require

advances in time stepping computational methods. The most severe

problem of these algorithms is instability. The objective of this

dissertation is to present original work in constructing multiscale

multiple time stepping (MTS) algorithms for molecular dynamics (MD)

that allow large time steps.

First, through nonlinear stability analysis and numerical

experiments, we reveal that MTS integrators such as Impulse suffer

nonlinear overheating when $Delta t = T/3$ or possibly $Delta t =

T/4$ when constant--energy MD simulations are attempted, where $Delta t$

is the longest step size and $T$ is the shortest period of the modes

in the system. Second, we present Targeted MOLLY (TM), a new

multiscale integrator for MD simulations. TM

combines an efficient implementation of B-spline MOLLY exploiting

analytical Hessians of energies and a self--consistent dissipative leapfrog

integrator. Results show that TM allows very large time steps for

slow forces (and thus multiscale) for the numerically challenging

flexible TIP3P water systems (Jorgensen, {it et al.} J. Chem. Phys.,

vol 79, pp 926--935, 1983) while still computing the dynamical and

structural properties accurately. Finally, we show yet another new

MOLLY integrator, the Backward Euler (BE) MOLLY in which hydrogen bond

forces can easily be included in the averaging and thus stability

might be further improved.

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