A: Pseudo-Code of FAMUSAMM

 

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:

                  	If H>M:

				Extrapolate LTE of hierarchy level H.

			Else:

           			Sum up contributions to LTE at level H according to interaction list

			If H>1:

				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.

		Else:

			Add extrapolated forces from distance class j=1.

		Perform Verlet integration step.