TY - JOUR
T1 - A Fully Discrete Calderόn Calculus for Two Dimensional Time Harmonic Waves
AU - Dominguez , V.
AU - Lu , S.
AU - Sayas , F.-J.
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 332
EP - 345
PY - 2014
DA - 2014/11
SN - 11
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/529.html
KW - Calderόn calculus, Boundary Element Methods, Dirac deltas distributions, Nyström methods.
AB - <p style="text-align: justify;">In this paper, we present a fully discretized Calderόn 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.</p>