  Large molecular dynamics simulations (millions of atoms, tens of
microseconds, thousands of processors) hit the strong scalability wall:
simulation on twice as many processors does not take half the time. Inspired by
large N-body space simulations, we suggest to calculate the bottleneck---the
long-range interactions---parallel in time. This technical report aims to
present the combination of parareal method and multilevel summation method. We
thoroughly describe both methods and reasons for their particular combination.
We also propose several optimizations that should provide the acceleration by
an order of magnitude.
