A fully discrete Calderon Calculus for two dimensional time harmonic waves
Numerical Analysis
2012-10-30 v2
Abstract
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 , 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 provided that the continuous equations are well posed. We finish by presenting some numerical experiments illustrating the performance of this discrete calculus.
Cite
@article{arxiv.1210.7017,
title = {A fully discrete Calderon Calculus for two dimensional time harmonic waves},
author = {Victor Dominguez and Sijiang L. Lu and Francisco-Javier Sayas},
journal= {arXiv preprint arXiv:1210.7017},
year = {2012}
}