Year: 2014
Author: V. Dominguez, S. Lu, F.-J. Sayas
International Journal of Numerical Analysis and Modeling, Vol. 11 (2014), Iss. 2 : pp. 332–345
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2014-IJNAM-529
International Journal of Numerical Analysis and Modeling, Vol. 11 (2014), Iss. 2 : pp. 332–345
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Calderόn calculus Boundary Element Methods Dirac deltas distributions Nyström methods.