Novel Multiscale Algorithms for Molecular Dynamics

Thesis or Dissertation


In post-genomic computational biology and bioinformatics, longsimulations of the dynamics of molecular systems, particularlybiological molecules such as proteins and DNA, requireadvances in time stepping computational methods. The most severeproblem of these algorithms is instability. The objective of thisdissertation is to present original work in constructing multiscalemultiple time stepping (MTS) algorithms for molecular dynamics (MD)that allow large time steps. First, through nonlinear stability analysis and numericalexperiments, we reveal that MTS integrators such as Impulse suffernonlinear 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 ™, a newmultiscale integrator for MD simulations. TM combines an efficient implementation of B-spline MOLLY exploitinganalytical Hessians of energies and a self–consistent dissipative leapfrogintegrator. Results show that TM allows very large time steps forslow forces (and thus multiscale) for the numerically challengingflexible TIP3P water systems (Jorgensen, {it et al.} J. Chem. Phys.,vol 79, pp 926–935, 1983) while still computing the dynamical andstructural properties accurately. Finally, we show yet another new MOLLY integrator, the Backward Euler (BE) MOLLY in which hydrogen bondforces can easily be included in the averaging and thus stabilitymight be further improved.


Attribute NameValues
  • etd-07032003-150352

Author Qun Ma
Advisor Jesus A Izaguirre
Contributor Jesus A Izaguirre, Committee Chair
Contributor Menelaos I Karavelas, Committee Member
Contributor Ryan K Roeder, Committee Member
Contributor Gregory Madey, Committee Member
Contributor J Daniel Gezelter, Committee Member
Degree Level 2
Degree Discipline Computer Science and Engineering
Degree Name Doctor of Philosophy
Defense Date
  • 2003-06-26

Submission Date 2003-07-03
  • United States of America

  • KAM theory

  • mollified Impulse method

  • nonlinear instability

  • targeted Langevin stabilization

  • long molecular dynamics simulations

  • multiple time stepping

  • Verlet-I/r-RESPA/Impulse

  • University of Notre Dame

  • English

Access Rights Open Access
Content License
  • All rights reserved