Geodesic
From particle methods to forward-backward Lagrangian schemes
Campos Pinto, Martin1 ; Charles, Frédérique1
1Sorbonne Université, Université Paris-Diderot SPC, CNRS, Laboratoire Jacques-Louis Lions, LJLL, F-75005 Paris
The SMAI Journal of computational mathematics, Tome 4 (2018), pp. 121-150
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In this article we study a novel method for improving the accuracy of density reconstructions based on markers pushed forward by some available particle code. The method relies on the backward Lagrangian representation of the transported density, and it evaluates the backward flow using the current position of point particles seen as flow markers. Compared to existing smooth particle methods with either fixed or transformed shapes, the proposed reconstruction achieves higher locality and accuracy. This is confirmed by our error analysis which shows a theoretical gain of one convergence order compared to the LTP/QTP methods introduced in [8], and by numerical experiments that demonstrate significant CPU gains and an improved robustness relative to the remapping period.

Publié le :
DOI : 10.5802/smai-jcm.31

Campos Pinto, Martin  1   ; Charles, Frédérique  1

1 Sorbonne Université, Université Paris-Diderot SPC, CNRS, Laboratoire Jacques-Louis Lions, LJLL, F-75005 Paris 
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     title = {From particle methods to forward-backward {Lagrangian} schemes},
     journal = {The SMAI Journal of computational mathematics},
     pages = {121--150},
     year = {2018},
     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
     volume = {4},
     doi = {10.5802/smai-jcm.31},
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Campos Pinto, Martin; Charles, Frédérique. From particle methods to forward-backward Lagrangian schemes. The SMAI Journal of computational mathematics, Tome 4 (2018), pp. 121-150. doi: 10.5802/smai-jcm.31

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