High-order nodal discontinuous Galerkin particle-in-cell method on unstructured grids

Jacobs, Gustaaf; Hesthaven, Jan S.

doi:10.1016/j.jcp.2005.09.008

Cited by 146 publications

(99 citation statements)

References 22 publications

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“…Originally, DG-FEM has been developed for the neutron transport equation (Reed & Hill, 1973). It has been applied to a wide range of applications such as electromagnetics (Cockburn et al, 2004), aeroacoustics (Toulopoulos & Ekaterinaris, 2006) and plasma physics (Jacobs & Hesthaven, 2006), just to cite a few examples. This method relies on the exchange of numerical fluxes between adjacent elements.…”

Section: Finite-elements Discontinuous Galerkin Methods: a Weak Formumentioning

confidence: 99%

Seismic Waves - Research and Analysis

Kanao¹

2012

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Section: Finite-elements Discontinuous Galerkin Methods: a Weak Formumentioning

confidence: 99%

Seismic Waves - Research and Analysis

Kanao¹

2012

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“…As for S we choose a tensor-product shape function with univariate degree 2a, a ∈ N, and radius > 0, derived from the one proposed by Jacobs and Hesthaven in [6], i.e.,…”

Section: Smooth Particle Current Deposition With Numerical Quadraturesmentioning

confidence: 99%

Electromagnetic PIC simulations with smooth particles: a numerical study

Pinto

Lutz

Mounier³

2016

ESAIM: Proc.

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Abstract. In this article we study a charge-conserving finite-element particle scheme for the Maxwell-Vlasov system that is based on a div-conforming representation of the electric field and we propose a high-order deposition algorithm for smooth particles with piecewise polynomial shape. The numerical performances of the method are assessed with an academic beam test-case, and it is shown that for an appropriate choice of the particle parameters the efficiency of the resulting method overcomes that of similar finite-element schemes using point particles.Résumé. Cet article présente un schémaéléments-finis conservant la charge pour le système de Vlasov-Maxwell basé sur une représentation div-conforme du champélectrique, ainsi qu'un algorithme d'ordreélevé pour déposer le courant porté par des particules régulières polynômiales par morceaux. Les performances numériques du schéma couplé sontévaluéesà l'aide d'un cas test académique de faisceau, et nous montrons que pour un choix approprié des paramètres des particules, cette méthode se révèle plus efficace que d'autres schémas similaires couplés avec des particules ponctuelles.

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“…There are a lot of numerical methods for hyperbolic PDEs; we mention the papers [2,7,8,10,11,12,15,16,18,20,22,23], which are not exhaustive. Numerical methods for the simulation of hyperbolic PDEs range from Lagrangian type such as the particle in cell (PIC) method to an Eulerian type based on a fixed grid system such as the finite volume method, the finite difference method, etc.…”

Section: ϕ(T X) = ρ(T X)mentioning

confidence: 99%

An Iteration Free Backward Semi-Lagrangian Scheme for Guiding Center Problems

Piao¹,

Kim²,

Kim³

et al. 2015

SIAM J. Numer. Anal.

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Abstract. In this paper, we develop an iteration free backward semi-Lagrangian method for nonlinear guiding center models. We apply the fourth-order central difference scheme for the Poisson equation and employ the local cubic interpolation for the spatial discretization. A key problem in the time discretization is to find the characteristic curve arriving at each grid point which is the solution of a system of highly nonlinear ODEs with a self-consistency imposed by the Poisson equation. The proposed method is based on the error correction method recently developed by the authors. For the error correction method, we introduce a modified Euler's polygon and solve the induced asymptotically linear differential equation with the midpoint quadrature rule to get the error correction term. We prove that the proposed iteration free method has convergence order at least 3 in space and 2 in time in the sense of the L 2 -norm. In particular, it is shown that the proposed method has a good performance in computational cost together with better conservation properties in mass, the total kinetic energy, and the enstrophy compared to the conventional second-order methods. Numerical test results are presented to support the theoretical analysis and discuss the properties of the newly proposed scheme. 1. Introduction. The model problem we are concerned with is the guiding center model, which was developed for an efficient description of low-frequency turbulence and resulting transport phenomena in strongly magnetized plasmas. Instead of tracing the fast gyro-motions of charged particles under strong external magnetic fields, the guiding center model follows the evolution of the center of the fast gyro-motions, which allows an efficient description of charged particle dynamics under relatively slow electrostatic fluctuations ω e ω. Here, ω denotes the gyro-frequency of a charged particle. If we suppose a uniform external magnetic field and the plane perpendicular to the magnetic field, the density of the guiding centers of charged particles, which are interacting with each other through self-consistent electrostatic potential, satisfies the following form of nonlinear hyperbolic equation in the plane with a proper normalization:

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High-order nodal discontinuous Galerkin particle-in-cell method on unstructured grids

Cited by 146 publications

References 22 publications

Seismic Waves - Research and Analysis

Seismic Waves - Research and Analysis

Electromagnetic PIC simulations with smooth particles: a numerical study

An Iteration Free Backward Semi-Lagrangian Scheme for Guiding Center Problems

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