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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 Keywords
- 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 Abstract In post-genomic computational biology and bioinformatics, longsimulations 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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