The Reduced Cell Multipole method [19], RCMM, attempts to reduce the cost of the Ewald sum by utilizing the hierarchical approach of [27] and [18]. The main difference is that interactions between the unit cell and near neighbors image of the unit cell (26 cells) are computed using the cell multipole method of [18], which is very similar to FMA, while interactions with the distant cells are calculated using the Ewald sum.
To compute the distant interactions efficiently, each distant unit cell is replaced by
a reduced cell. The reduced cell consists of 35 randomly placed charged-particles.
Each of the 35 charges is assumed
to be a point charge whose strength 
is calculated such that the first five moments of the
reduced cell equal those of the original cell.
The authors claim that this method is highly accurate
and that it scales linearly with the number of atoms in the unit cell.
It should be pointed out that the 35-particle reduced cell approximates the moments of a
particle system only up to the 5th-order, hence for simulations that require accuracy beyond
the 5th-order, RCMM may be limited to an average accuracy.