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##

Fast Multiple Time Step Structure Adapted Multipole Method

A closer look at the algorithm reveals that the computational
effort for the evaluation of local expansions is of the same magnitude as
for the forces from the IIZ.
It is possible to use the Multiple Time Step Method described in
Section 6.2.2
to avoid unnecessarily frequent computations of the local expansions
and of forces from the IIZ.
In our approach we divided the IIZ in two distance classes. The forces between
all atoms which are closer then 5Å are calculated exactly in every
integration step. The sum of forces from atoms of the second distance class
(5 - 10Å) however is calculated exactly only every other integration step.
The values of two previously calculated integration steps are used to
extrapolate the forces for the steps between two exact integration steps.
As a result of this the computational effort for the IIZ is reduced by a
factor of almost two.

As explained above, the influence of atoms separated by more then 10Å is
represented through the local expansions. Analogous to the time development of
forces the time development
of the coefficients of local expansions varies slowly and can be
extrapolated for a certain number of integration steps without risking
too large errors. Thus the time consuming calculation of
local expansions is avoided periodically.

The combination of the Multiple Time Step Method and the Structure
Adapted Fast Multipole Method is called
*FAst MUltiple time step Structure Adapted Multipole Method*
[9] (FAMUSAMM).
The computational effort of this method scales with *O*(*N*).

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**Up:** Methods to Increase Efficiency
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*Helmut Heller *

2000-04-19