In order to solve the classical equations of motion numerically,
and, thus,
to obtain the motion of all atoms the
forces acting on every atom have to be computed at each integration
step. The forces are
derived from an energy function which defines the molecular
model [1,2,3]. Besides other
important contributions (which we shall not discuss here) this
function contains the Coulomb sum

over all pairs of atoms (

A very simple -- and in fact quite widely used -- approximation
completely neglects long range electrostatic interactions beyond
a certain cut-off distance [43] of typically
8-15Å. For systems which are significantly larger than
this cut-off distance the computation of the remaining Coulomb
interactions then scales with *N* instead of *N ^{2}*. However,
such truncation leads to serious artifacts concerning the
description of the structure and
dynamics of proteins [44,24,45],
and more accurate methods which include the long range
interactions should be preferred.
Multipole methods and multiple-time-step methods
are well established and widely used for this purpose.
We briefly sketch both methods and subsequently show how their
combination allows highly efficient simulations.