  We present a linear scaling formulation for the solution of the all-electron
Coulomb problem in crystalline solids. The resulting method is systematically
improvable and well suited to large-scale quantum mechanical calculations in
which the Coulomb potential and energy of a continuous electronic density and
singular nuclear density are required. Linear scaling is achieved by
introducing smooth, strictly local neutralizing densities to render nuclear
interactions strictly local, and solving the remaining neutral Poisson problem
for the electrons in real space. While the formulation includes singular
nuclear potentials without smearing approximations, the required Poisson
solution is in Sobolev space $H^1$, as required for convergence in the energy
norm. We employ enriched finite elements, with enrichments from isolated atom
solutions, for an efficient solution of the resulting Poisson problem in the
interacting solid. We demonstrate the accuracy and convergence of the approach
by direct comparison to standard Ewald sums for a lattice of point charges, and
demonstrate the accuracy in all-electron quantum mechanical calculations with
an application to crystalline diamond.
