0000000000682568

AUTHOR

Francesco Vecil

showing 4 related works from this author

A numerical study of attraction/repulsion collective behavior models: 3D particle analyses and 1D kinetic simulations

2013

39p; International audience; We study at particle and kinetic level a collective behavior model based on three phenomena: self-propulsion, friction (Rayleigh effect) and an attractive/repulsive (Morse) potential rescaled so that the total mass of the system remains constant independently of the number of particles N . In the first part of the paper, we introduce the particle model: the agents are numbered and described by their position and velocity. We iden- tify five parameters that govern the possible asymptotic states for this system (clumps, spheres, dispersion, mills, rigid-body rotation, flocks) and perform a numerical analysis on the 3D setting. Then, in the second part of the paper…

Collective behaviorParticle numberKinetic energy01 natural sciencesMSC 92B05 70F99 65P40 35L50symbols.namesakecollective behavior0103 physical sciences[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]Statistical physics0101 mathematicsRayleigh scattering010306 general physicsParticle systemSelf-organizationPhysicsNumerical analysisStatistical and Nonlinear Physicsattractive/repulsive potentialCondensed Matter Physicsself-organizationswarming010101 applied mathematicsClassical mechanicssymbolsSPHERES[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
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Discontinuous Galerkin semi-Lagrangian method for Vlasov-Poisson

2011

We present a discontinuous Galerkin scheme for the numerical approximation of the one-dimensional periodic Vlasov-Poisson equation. The scheme is based on a Galerkin-characteristics method in which the distribution function is projected onto a space of discontinuous functions. We present comparisons with a semi-Lagrangian method to emphasize the good behavior of this scheme when applied to Vlasov-Poisson test cases. Une méthode de Galerkin discontinu est proposée pour l’approximation numérique de l’équation de Vlasov-Poisson 1D. L’approche est basée sur une méthode Galerkin-caractéristiques où la fonction de distribution est projetée sur un espace de fonctions discontinues. En particulier, …

T57-57.97Applied mathematics. Quantitative methods[SPI.PLASMA]Engineering Sciences [physics]/Plasmas010103 numerical & computational mathematicsSpace (mathematics)Poisson distribution01 natural sciences010101 applied mathematicssymbols.namesakeTest caseDistribution functionNumerical approximationDiscontinuous Galerkin methodScheme (mathematics)QA1-939symbolsApplied mathematics0101 mathematicsAlgorithmMathematicsLagrangian[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]Mathematics
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WENO schemes applied to the quasi-relativistic Vlasov-Maxwell model for laser-plasma interaction

2014

Abstract In this paper we focus on WENO-based methods for the simulation of the 1D Quasi-Relativistic Vlasov–Maxwell (QRVM) model used to describe how a laser wave interacts with and heats a plasma by penetrating into it. We propose several non-oscillatory methods based on either Runge–Kutta (explicit) or Time-Splitting (implicit) time discretizations. We then show preliminary numerical experiments.

Strategy and ManagementFOS: Physical sciences010103 numerical & computational mathematics01 natural scienceslaw.inventionMathematics::Numerical Analysislaser-plasma interactionMathematics - Analysis of PDEslawMedia TechnologyFOS: MathematicsVlasov--Maxwell[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]General Materials ScienceMathematics - Numerical Analysis0101 mathematicsMarketingPhysicsPhysics::Computational PhysicsWENOPlasmaNumerical Analysis (math.NA)Computational Physics (physics.comp-ph)LaserRunge--Kutta schemes010101 applied mathematicsClassical mechanicsStrang splittingFocus (optics)Physics - Computational PhysicsAnalysis of PDEs (math.AP)Strang splitting
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A semi-Lagrangian AMR scheme for 2D transport problems in conservation form

2013

In this paper, we construct a semi-Lagrangian (SL) Adaptive-Mesh-Refinement (AMR) solver for 1D and 2D transport problems in conservation form. First, we describe the a-la-Harten AMR framework: the adaptation process selects a hierarchical set of grids with different resolutions depending on the features of the integrand function, using as criteria the point value prediction via interpolation from coarser meshes, and the appearance of large gradients. We integrate in time by reconstructing at the feet of the characteristics through the Point-Value Weighted Essentially Non-Oscillatory (PV-WENO) interpolator. We propose, then, an extension to the 2D setting by making the time integration dime…

Numerical AnalysisMathematical optimizationSpeedupPhysics and Astronomy (miscellaneous)Adaptive mesh refinementApplied MathematicsFunction (mathematics)SolverComputer Science ApplicationsComputational MathematicsStrang splittingModeling and SimulationApplied mathematicsPolygon meshConservation formMathematicsInterpolationJournal of Computational Physics
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