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Martin Campos Pinto; Frédérique Charles
From particle methods to forward-backward Lagrangian schemes
SMAI-Journal of computational mathematics, 4 (2018), p. 121-150, doi: 10.5802/smai-jcm.31
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Abstract

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.

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