**Steps 1-2.**Same as the steps 1-2 in the algorithm described in chapter 2.**Step 3.**Computation of the multipole moments:In this step we use (3.23) [resp. (3.40)] for the computation of the multipole moments associated with leaves. Also, we use (3.24) [(3.32)] for M2M translations tracing the tree structure of cells upward (decreasing ).

**Step 4.**Computation of the local expansion: In this step we use (3.27) [(3.35)] for M2L translations and (3.29) [(3.37)] for L2L translations tracing the tree structure of cells downward (increasing ).**Step 5.**Evaluation of the integral in (3.15): In this step we use (3.38) [(3.38)] for the direct computation and use (3.26) [(3.34)] for the evaluation of contributions with the local expansion.