A fully discrete Calderon Calculus for two dimensional time harmonic waves
Provides a new numerical framework for solving time-harmonic wave problems, but the contribution is incremental as it extends existing Calderón Calculus concepts to a fully discrete setting.
The paper develops a fully discretized Calderón Calculus for the 2D Helmholtz equation, achieving second-order accuracy (h^2) with staggered grids and Dirac delta distributions. Numerical experiments confirm the performance.
In this paper, we present a fully discretized Calderón 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.