Fast numerical methods for molecular dynamics simulations.

Michael Griebel

Universit\"at Bohn
Institut f\"ur Angewandte Mathematik
Germany  


A major difficulty in MD-simulation methods is the complexity of the long range
force evaluation in each time step. To cope with this
problem, there exists various multiscale type methods, i.e. treecodes,
multipole approaches or multigrid techniques, which
reduces the $O(N^2)$ complexity of the naive approach to $O(N \log N)$ or
even $O(N)$.

Our approach make use of a variant of the adaptive Barnes-Hut/Multipole method.
For dealing with the adaptivity of the method, we use a hash-technique.
A further reduction on execution time is possible by parallelization. Here,
however - especially for adaptive tree-type methods - the
implementation is quite difficult and cumbersome.
We present a parallel method with space-filling Hilbert-curves by assigning
segments of the increasingly ordered hashtable-key list to each processor.
Particularly to mention are special concepts to reduce the communication
between the processors and the complexity of the force-evaluation and
tree-building.
Altogether this results in an efficient long-range (e.g. Coulomb-Forces)
force evaluation without potential cut-off and a simple
incorporation of short-range forces, which we have tested on several
MIMD-platforms up to $512$ processors (Cray T3E).

We will present various MD-simulations with long-range interactions, as for
example the melting-process of NaCl, simulations with the protein BPTI etc.