the basic problem when dealing with vortex rings is to find out the circulation associated to the rings where the non-penetration boundary condition has to be imposed (the bounded lattices). because the velocity associated to a vortex ring at a given point depends linearly on the circulation of that ring, a system of linear equations can be written, so that when solved, it will provide the value of the local circulations that will cancel the normal velocity at each control point. the matrix problem for this situation can be found in the article about the vortex lattice method.