The method based on fast Fourier transforms proposed by G. Rom\'an-P\'erez
and J. M. Soler [Phys. Rev. Lett. 103, 096102 (2009)], which allows for a
computationally fast implementation of the nonlocal van der Waals (vdW)
functionals, has significantly contributed to making the vdW functionals
popular in solid-state physics. However, the Rom\'an-P\'erez-Soler method
relies on a plane-wave expansion of the electron density; therefore it can not
be applied readily to all-electron densities for which an unaffordable number
of plane waves would be required for an accurate expansion. In this work, we
present the results for the lattice constant and binding energy of solids that
were obtained by applying a smoothing procedure to the all-electron density
calculated with the linearized augmented plane-wave method. The smoothing
procedure has the advantages of being very simple to implement, basis-set
independent, and allowing the calculation of the potential. It is also shown
that the results agree very well with those from the literature that were
obtained with the projector augmented wave method
