  Recently, nonlocal models attract the wide interests of scientist. They
mainly come from two applied scientific fields: peridyanmics and anomalous
diffusion. Even though the matrices of the algebraic equation corresponding the
nonlocal models are usually Toeplitz (denote a0 as the principal diagonal
element, a1 as the trailing diagonal element, etc). There are still some
differences for the models in these two fields. For the model of anomalous
diffusion, a0/a1 is uniformly bounded; most of the time, a0/a1 of the model for
peridyanmics is unbounded as the stepsize h tends to zero. Based on the uniform
boundedness of a0/a1, the convergence of the two-grid method is well
established [Chan, Chang, and Sun, SIAM J. Sci. Comput., 19 (1998), pp.
516--529; Pang and Sun, J. Comput. Phys., 231 (2012), pp. 693--703; Chen, Wang,
Cheng, and Deng, BIT, 54 (2014), pp. 623--647]. This paper provides the
detailed proof of the convergence of the two-grid method for the nonlocal model
of peridynamics. Some special cases of the full multigrid and the V-cycle
multigrid are also discussed. The numerical experiments are performed to verify
the convergence.
