coefficients are computed for each of the boxes box 22 through box 85 in the level 3 array 23 shown in fig3 d to obtain coefficients about the center of the box for a truncated multipole expansion of the vortex segments that reside in this box once this is accomplished the coefficients for the truncated multipole expansion for the vortex segments in a box at the next highest level are computed about the center of this box for example box 9 in fig3 c corresponds to boxes 28 29 36 and 37 in fig3 d and the coefficients generated with respect to those boxes in fig3 d are then used to provide a set of coefficients for box 9 in fig3 c this step can be accomplished by simple summation and translation operations when this procedure has been completed truncated multipole expansions are obtained for all boxes at all levels once this procedure is completed velocities for each vortex segment are determined beginning at the second level below the largest box to define an interaction list for each box this list identifies the boxes for which the interaction must be computed directly for each of these boxes the coefficients of a taylor series expansion are obtained about the center and are computed from the coefficients of the multipole expansions and are taken with respect to the center of a smaller box using recursion relationships the process continues until the taylor series expansions have been computed for all boxes at all levels once the computation of the taylor series coefficients is complete the computation for the interactions begins this proceeds by computing the direct interaction for all vortex segments in the same box as a field point and for all vortex segments in the boxes on the interaction list of that.