A finite volume method for the approximation of Maxwell’s equations in two space dimensions on arbitrary meshes

Hermeline, F.; Layouni, S.; Omnes, Pascal

doi:10.1016/j.jcp.2008.05.013

Cited by 21 publications

(12 citation statements)

References 57 publications

(99 reference statements)

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“…The indirect dual mesh lends itself better to the 3D framework and it provides a more accurate approximation of the gradient of the solution. Since then this type of method has been called discrete duality finite volume (DDFV) method in order to emphasize that it satisfies a discrete integration par parts (see [6]) and it proved to be efficient for dealing with several problems arising in various areas of computational physics (see [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]). Convergence analysis have been carried out in [5,12,18], for the linear case, and in [11] for the broad class of non-linear Leray-Lions type diffusion operators.…”

Section: Introductionmentioning

confidence: 99%

A finite volume method for approximating 3D diffusion operators on general meshes

Hermeline

2009

Journal of Computational Physics

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Section: Introductionmentioning

confidence: 99%

A finite volume method for approximating 3D diffusion operators on general meshes

Hermeline

2009

Journal of Computational Physics

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“…and C i is the set ofw i satisfying the constraints (16)(17)(18)(19)(20)(21). Notice that with a quadratic objective function (22) and linear equality constraints inw i j (16)(17)(18)(19)(20)(21), this becomes a straight-forward quadratic programming optimization problem.…”

Section: The Resampling Algorithmmentioning

confidence: 99%

Moment preserving constrained resampling with applications to particle-in-cell methods

Faghihi

Carey

Michoski

et al. 2020

Journal of Computational Physics

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In simulations of partial differential equations using particle-in-cell (PIC) methods, it is often advantageous to resample the particle distribution function to increase simulation accuracy, reduce compute cost, and/or avoid numerical instabilities. We introduce an algorithm for particle resampling called Moment Preserving Contrained Resampling (MPCR). The general algorithm partitions the system space into smaller subsets and is designed to conserve any number of particle and grid quantities with a high degree of accuracy (i.e. machine accuracy). The resampling scheme can be integrated into any PIC code. The advantages of MPCR, including performance, accuracy, and stability, are presented by examining several numerical tests, including a use-case study in gyrokinetic fusion plasma simulations. The tests demonstrate that while the computational cost of MPCR is negligible compared to the nascent particle evolution in PIC methods, periodic particle resampling yields a significant improvement in the accuracy and stability of the results.

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“…The first methods to calculate the electromagnetic fields were based on Yee's finite difference method [7] using structured grids. Later, finite volume (FV) [8] and finite element (FE) [9] methods were applied. Due to their excellent approximation of wave propagation and the flexible grid requirements, discontinuous Galerkin (DG) schemes have also been investigated in recent times.…”

Section: Introductionmentioning

confidence: 99%

Coupled Particle-In-Cell and Direct Simulation Monte Carlo method for simulating reactive plasma flows

Munz

Auweter‐Kurtz²,

Fasoulas

et al. 2014

Comptes Rendus. Mécanique

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Plasma flows with high Knudsen numbers cannot be treated with classic continuum methods, as represented for example by the Navier-Stokes or the magnetohydrodynamic equations. Instead, the more fundamental Boltzmann equation has to be solved, which is done here approximately by particle based methods that also allow for thermal and chemical non-equilibrium. The Particle-In-Cell method is used to treat the collisionless Vlasov-Maxwell system, while neutral reactive flows are treated by the Direct Simulation Monte Carlo method. In this article, a combined approach is presented that allows the simulation of reactive, partially or fully ionized plasma flows. Both particle methods are briefly outlined and the coupling and parallelization strategies are described. As an example, the results of a streamer discharge simulation are presented and discussed in order to demonstrate the capabilities of the coupled method.

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A finite volume method for the approximation of Maxwell’s equations in two space dimensions on arbitrary meshes

Cited by 21 publications

References 57 publications

A finite volume method for approximating 3D diffusion operators on general meshes

A finite volume method for approximating 3D diffusion operators on general meshes

Moment preserving constrained resampling with applications to particle-in-cell methods

Coupled Particle-In-Cell and Direct Simulation Monte Carlo method for simulating reactive plasma flows

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