Geodesic
Wavelet denoising for postprocessing of a 2D Particle - In - Cell code
Salimou Gassama1 ; Éric Sonnendrücker1 ; Kai Schneider2 ; Marie Farge3 ; Margarete O. Domingues4
1 Institut de Recherche Mathématique Avancée, UMR CNRS 7501 Université Louis Pasteur, Strasbourg, France.
2 MSNM–CNRS & CMI, Université de Provence, 39 rue Joliot–Curie, 13453 Marseille cedex 13, France.
3 LMD–CNRS, Ecole Normale Supérieure, 24 rue Lhomond,75231 Paris cedex 05, France.
4 Laboratório Associado de Computação e Matemática Aplicada (LAC), Instituto Nacional de Pesquisas Espaciais (INPE), Av. dos Astronautas, 1758, 12227-010 São José dos Campos, Brasil.
ESAIM. Proceedings, Tome 16 (2007), pp. 195-210.

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In this paper, we aim at improving the accuracy of a Vlasov-Poisson solver using a 2D Particle-In-Cell (PIC) scheme, by denoising its charge density field. To this end, we have used an improvement of Donoho and Johnstone's wavelet denoising technique. To some extent, our work is a continuation of that performed by Chehab et al. [Chehab, Cohen, Roche, Jennequin, Nieto and Roland, CEMRACS 2003, IRMA Lectures in Mathematics and Theoretical Physics, EMS, pp. 29-42]. Indeed, they made such a study in the one dimensional case and validated their analysis by considering the simulation of the Landau damping phenomenon. They concluded on the efficiency of the method in reducing the number of particles. However, our approach is quite different, since we do not use wavelets to directly interpolate the charge density, but we smooth the density field calculated by the PIC code. This is carried out via an iterative wavelet denoising technique introduced by Azzalini et al. [Azzalini, Farge and Schneider, Appl. Comput. Harm. Anal. 18 (2005), no. 2, 177185]. Our work consists in studying the application of the method as a post-processing tool, in view of a future embedding into the PIC code. The results are the following: first, we showed that the hypotheses underlying the application of this method are valid. Secondly, we can infer from this study that it is possible to significantly reduce the amount of data needed for a simulation.
DOI : 10.1051/proc:2007013

Salimou Gassama 1 ; Éric Sonnendrücker 1 ; Kai Schneider 2 ; Marie Farge 3 ; Margarete O. Domingues 4

1 Institut de Recherche Mathématique Avancée, UMR CNRS 7501 Université Louis Pasteur, Strasbourg, France.
2 MSNM–CNRS & CMI, Université de Provence, 39 rue Joliot–Curie, 13453 Marseille cedex 13, France.
3 LMD–CNRS, Ecole Normale Supérieure, 24 rue Lhomond,75231 Paris cedex 05, France.
4 Laboratório Associado de Computação e Matemática Aplicada (LAC), Instituto Nacional de Pesquisas Espaciais (INPE), Av. dos Astronautas, 1758, 12227-010 São José dos Campos, Brasil. 
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     author = {Salimou Gassama and \'Eric Sonnendr\"ucker and Kai Schneider and Marie Farge and Margarete O. Domingues},
     title = {Wavelet denoising for postprocessing of a {2D} {Particle~-~In~-~Cell} code},
     journal = {ESAIM. Proceedings},
     pages = {195--210},
     publisher = {mathdoc},
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     year = {2007},
     doi = {10.1051/proc:2007013},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc:2007013/}
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Salimou Gassama; Éric Sonnendrücker; Kai Schneider; Marie Farge; Margarete O. Domingues. Wavelet denoising for postprocessing of a 2D Particle - In - Cell code. ESAIM. Proceedings, Tome 16 (2007), pp. 195-210. doi : 10.1051/proc:2007013. http://geodesic.mathdoc.fr/articles/10.1051/proc:2007013/

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