In this section we provide a summarizing pseudo-code description of FAMUSAMM. For clarity, we have omitted the special algorithmic steps, which are necessary during the start-up phase or are associated with hierarchical grouping and recalculation of the interaction list. As to decide, whether in a given time step forces or local Taylor expansions have to be explicitly calculated or may be extrapolated, we introduce a variable M, which denotes the highest hierarchy level H of SAMM for which an explicit calculation has to be performed (cf. Figure 4). M is called extrapolation level. The following abbreviations are used: LTE: local Taylor expansion, MM: multipole moments, SU: structural unit. Indentation defines the grouping of instructions.
For every integration step:
Set extrapolation level M.
Set all LTE coefficients to zero.
Calculate MMs of all SUs (hierarchy level H=1).
For H=2 to :
Calculate MMs for each cluster on higher hierarchy levels H.
For down to H=1:
For every object at level H:
Extrapolate LTE of hierarchy level H.
Sum up contributions to LTE at level H according to interaction list
Inherit LTE of level H to level H-1.
For every atom:
Compute non-electrostatic forces forces (van der Waals, chem. binding forces).
Add Coulomb forces from LTE of SU.
Add Coulomb forces from atoms in distance class j=0 (cf. Figure 4).
If integration step even:
Add calculated forces from distance class j=1.
Add extrapolated forces from distance class j=1.
Perform Verlet integration step.