  In this paper, we present a fully discretized Calder\'{o}n Calculus for the
two dimensional Helmholtz equation. This full discretization can be understood
as highly non-conforming Petrov-Galerkin methods, based on two staggered grids
of mesh size $h$, Dirac delta distributions substituting acoustic charge
densities and piecewise constant functions for approximating acoustic dipole
densities. The resulting numerical schemes from this calculus are all of order
$h^2$ provided that the continuous equations are well posed. We finish by
presenting some numerical experiments illustrating the performance of this
discrete calculus.
