Mathematical and numerical methods for Vlasov–Maxwell equations: The contribution of data mining

Franck Assous; Joël Chaskalovic

doi:10.1016/j.crme.2014.06.010

Theoretical and numerical approaches for Vlasov–Maxwell equations

Mathematical and numerical methods for Vlasov–Maxwell equations: The contribution of data mining

Franck Assous ^1,² ; Joël Chaskalovic ³

¹ Ariel University, 40700 Ariel, Israel
² Bar-Ilan University, 52900 Ramat-Gan, Israel
³ D'Alembert, University Pierre and Marie Curie, Paris, France

Comptes Rendus. Mécanique, Volume 342 (2014) no. 10-11, pp. 560-569.

Résumé

This paper deals with the applications of data mining techniques in the evaluation of numerical solutions of Vlasov–Maxwell models. This is part of the topic of characterizing the model and approximation errors via learning techniques. We give two examples of application. The first one aims at comparing two Vlasov–Maxwell approximate models. In the second one, a scheme based on data mining techniques is proposed to characterize the errors between a $P_{1}$ and a $P_{2}$ finite element Particle-In-Cell approach. Beyond these examples, this original approach should operate in all cases where intricate numerical simulations like for the Vlasov–Maxwell equations take a central part.

Reçu le : 2014-04-01
Accepté le : 2014-06-01
Publié le : 2014-08-06

DOI : 10.1016/j.crme.2014.06.010

Mots clés : Data mining, Error estimate, Vlasov–Maxwell equations, Asymptotic analysis, Paraxial model

Affiliations des auteurs :

Franck Assous ^{1, 2} ; Joël Chaskalovic ³

¹ Ariel University, 40700 Ariel, Israel
² Bar-Ilan University, 52900 Ramat-Gan, Israel
³ D'Alembert, University Pierre and Marie Curie, Paris, France

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Franck Assous; Joël Chaskalovic. Mathematical and numerical methods for Vlasov–Maxwell equations: The contribution of data mining. Comptes Rendus. Mécanique, Volume 342 (2014) no. 10-11, pp. 560-569. doi : 10.1016/j.crme.2014.06.010. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.06.010/

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