The multigrid method solves the finite element equations in optimal order, i.e., solving a linear system of O(N) equations in O(N) arithmetic operations. Based on low level solutions,
we can use finite element extrapolation to obtain the high-level finite element solution on some
coarse-level element boundary, at an higher accuracy O(h^4_i). Thus, we can solve higher level
(h_j, j\lesssim2i) finite element problems locally on each such coarse-level element. That is, we can skip
the finite element problem on middle levels, h_{i+1}, h{_i+2},..., h_{j-1}. Loosely speaking, this jumping
multigrid method solves a linear system of O(N) equations by a memory of O(p\sqrt{N}), and by a
parallel computation of O(p\sqrt{N}).