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Volume 11, Issue 2
A Fully Discrete Calderόn Calculus for Two Dimensional Time Harmonic Waves

V. Dominguez, S. Lu & F.-J. Sayas

Int. J. Numer. Anal. Mod., 11 (2014), pp. 332-345.

Published online: 2014-11

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  • 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.

  • Keywords

Calderόn calculus, Boundary Element Methods, Dirac deltas distributions, Nyström methods.

  • AMS Subject Headings

65N38, 65N35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-11-332, author = {Dominguez , V.Lu , S. and Sayas , F.-J.}, title = {A Fully Discrete Calderόn Calculus for Two Dimensional Time Harmonic Waves}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2014}, volume = {11}, number = {2}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/529.html} }
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 -

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.

Dominguez , V.Lu , S. and Sayas , F.-J.. (2014). A Fully Discrete Calderόn Calculus for Two Dimensional Time Harmonic Waves. International Journal of Numerical Analysis and Modeling. 11 (2). 332-345. doi:
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