Phone: (505) 284-9915
Fax: (505) 845-7442
Sandia National Laboratories
P.O. Box 5800, MS 1318
Albuquerque, NM 87185-1318
Stephen D. Bond
Stephen D. Bond
Geometric integration, backward error analysis, and molecular dynamics
Biomolecular simulation serves as an interesting paradigm for the difficulties in effectively modeling multiscale behavior. On the shortest classical scale, the motion is governed by the vibrations of bonded atoms which occur on a time scale of 10-14 seconds, and a length scale of 10-10 meters. In contrast, larger scale conformational (e.g. allosteric and denaturing) changes occur on a time scale of 10-5 to 101 seconds, and often involve the collective motion of hundreds of thousands (to millions) of atoms. It is for this reason that a typical molecular dynamics simulation can take months of supercomputer time, only to capture a very small segment (in space and time) of a larger biochemical process.
Unfortunately, classical "forward" error analysis is not useful in the context of molecular dynamics, due to the extremely long simulation time, large time step size, and quasiergodic nature of the underlying system. Efficiency of a numerical method must be measured with respect to averages (from Statistical Mechanics), since there is no meaningful concept of an exact trajectory in these systems. My research in this field has been centered around "geometric integrators" and "backward" error analysis, which has proved useful in designing numerical methods which preserve important statistical properties over long time intervals.
Finite elements, multilevel preconditioning, and coarse-grain continuum models