For modern characterizations of brain topologies with ever-increasing levels of complexity, the above system of equations for ρ ρ m is very large; it is therefore solved iteratively. An initial guess for ρ ρ m is the last term on its right-hand side while the sum is ignored. Next, the sum is computed and the initial guess is refined, etc. This solution employs the simple Jacobi iterative method. The more rigorous generalized minimum residual method (GMRES) yields a much faster convergence of the BEM-FMM. In either case, the major work is in computing the underbraced sum in the system of equations above for every m at every iteration; this operation corresponds to a repetitive matrix-vector multiplication. However, one can recognize this sum as an electric field (times 1 2 π π ϵ ϵ 0 ) of M charges to be computed at M observation points. Such a computation is exactly the task of the fast multipole method, which performs fast matrix-by-vector multiplication in O ( M log ⁡ ⁡ M ) or even O ( M ) operations instead of O ( M 2 ) . The FMM3D library realized in both Python and MATLAB can be used for this purpose. It is therefore unnecessary to form or store the dense system matrix typical for the standard BEM.