A FULLY DISCRETE CALDERON CALCULUS FOR TWO DIMENSIONAL TIME HARMONIC WAVES

In this paper, we present a fully discretized Calderon 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.