Electromagnetic PIC simulations with smooth particles: a numerical study

Pinto, Martin Campos; Lutz, Mathieu; Mounier, Marie

doi:10.1051/proc/201653009

Cited by 6 publications

(6 citation statements)

References 7 publications

(9 reference statements)

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“…where the last equality is a structural property of the Whitney forms [18,29,30,31] with C ij being the elements of the so called incidence matrix with entries {−1, 0, +1} [18]. The incidence matrix encodes the discrete (primed) curl operator distilled from the metric (or more precisely, the coboundary operator on the mesh [32]).…”

Section: Te ϕ Field Solvermentioning

confidence: 99%

“…In typical mixed finite-element time-domain schemes, E and B fields are assumed to be primal quantities [21,35,33,34,47,37,1,2]. However, this is not strictly necessarily and one can choose for D and H instead to be discretized on the primal mesh [48,49,31,50]. For example, for TE ϕ polarized fields in zρ plane, the D field is represented as a (twisted) 2-form with dergees of freedom associated with the area elements of the primal mesh and expanded using Whitney 2-forms.…”

Section: Te ϕ Field Solvermentioning

confidence: 99%

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Local, Explicit, and Charge-Conserving Electromagnetic Particle-In-Cell Algorithm on Unstructured Grids

Moon

Omelchenko³

et al. 2016

IEEE Trans. Plasma Sci.

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A novel electromagnetic particle-in-cell algorithm has been developed for fully kinetic plasma simulations on unstructured (irregular) meshes in complex body-of-revolution geometries. The algorithm, implemented in the BORPIC++ code, utilizes a set of field scalings and a coordinate mapping, reducing the Maxwell field problem in a cylindrical system to a Cartesian finite element Maxwell solver in the meridian plane. The latter obviates the cylindrical coordinate singularity in the symmetry axis. The choice of an unstructured finite element discretization enhances the geometrical flexibility of the BORPIC++ solver compared to the more traditional finite difference solvers. Symmetries in Maxwell's equations are explored to decompose the problem into two dual polarization states with isomorphic representations that enable code reuse. The particle-in-cell scatter and gather steps preserve charge-conservation at the discrete level. Our previous algorithm (BORPIC+) discretized the E and B field components of TE ϕ and TM ϕ polarizations on the finite element (primal) mesh [1,2]. Here, we employ a new field-update scheme. Using the same finite element (primal) mesh, this scheme advances two sets of field components independently: (1) E and B of TE ϕ polarized fields, (E z , E ρ , B ϕ ) and (2) D and H of TM ϕ polarized fields, (D ϕ , H z , H ρ ). Since these field updates are not explicitly coupled, the new field solver obviates the coordinate singularity, which otherwise arises at the cylindrical symmetric axis, ρ = 0 when defining the discrete Hodge matrices (generalized finite element mass matrices). A cylindrical perfectly matched layer is implemented as a boundary condition in the radial direction to simulate open space problems, with periodic boundary conditions in the axial direction. We investigate effects of charged particles moving next to the cylindrical perfectly matched layer. We model azimuthal currents arising from rotational motion of charged rings, which produce TM ϕ polarized fields. Several numerical examples are provided to illustrate the first application of the algorithm.

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Section: Te ϕ Field Solvermentioning

confidence: 99%

Section: Te ϕ Field Solvermentioning

confidence: 99%

Local, Explicit, and Charge-Conserving Electromagnetic Particle-In-Cell Algorithm on Unstructured Grids

Moon

Omelchenko³

et al. 2016

IEEE Trans. Plasma Sci.

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“…Because the longterm charge conservation properties of the scheme require an accurate time-average of the particle current in the deposition method as demonstrated in [30,17], this feature actually simplifies the involved algorithms. For more details on these algorithms we refer to [18]. To assess the numerical stability properties of the proposed FEM and Conga methods over long time ranges we plot in Figure 6.4 the profiles of some fields computed with the Conga-PIC scheme, using a final time chosen such that the particles have travelled approximatively five diode lengths.…”

Section: Compatible Maxwell Solvers With Particles Imentioning

confidence: 99%

“…Equation (4.12) is obtained by applying again the standard commuting diagram recalled in Lemma 3.4 and using the fact that P 1 h = I on V 1 h . To show next that (4.13) holds as stated, i.e., ( 18) we observe that both sides belong toṼ 1 h by construction, so that we can test this equality against an arbitrary v ∈Ṽ 1 h and use the definition of the various operators to compute …”

Section: Gauss-compatibility Of the Non-conforming Maxwell Solvermentioning

confidence: 99%

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Compatible Maxwell solvers with particles I: conforming and non-conforming 2D schemes with a strong Ampere law

Pinto¹,

Sonnendrücker²

2017

The SMAI Journal of Computational Mathematics

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Abstract. This article is the first of a series where we develop and analyze structure-preserving finite element discretizations for the time-dependent 2D Maxwell system with long-time stability properties, and propose a charge-conserving deposition scheme to extend the stability properties in the case where the current source is provided by a particle method. The schemes proposed here derive from a previous study where a generalized commuting diagram was identified as an abstract compatibility criterion in the design of stable schemes for the Maxwell system alone, and applied to build a series of conforming and non-conforming schemes in the 3D case. Here the theory is extended to account for approximate sources, and specific chargeconserving schemes are provided for the 2D case. In this article we study two schemes which include a strong discretization of the Ampere law. The first one is based on a standard conforming mixed finite element discretization and the long-time stability is ensured by a Raviart-Thomas finite element interpolation for the current source, thanks to its commuting diagram properties. The second one is a new non-conforming variant where the numerical fields are sought in fully discontinuous spaces. Numerical experiments involving Maxwell and Maxwell-Vlasov problems are then provided to validate the stability of the proposed methods.Math. classification. 35Q61, 65M12, 65M60, 65M75.

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An unstructured body-of-revolution electromagnetic particle-in-cell algorithm with radial perfectly matched layers and dual polarizations

Na,

Teixeira,

Omelchenko

2024

Computer Physics Communications

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Electromagnetic PIC simulations with smooth particles: a numerical study

Cited by 6 publications

References 7 publications

Local, Explicit, and Charge-Conserving Electromagnetic Particle-In-Cell Algorithm on Unstructured Grids

Local, Explicit, and Charge-Conserving Electromagnetic Particle-In-Cell Algorithm on Unstructured Grids

Compatible Maxwell solvers with particles I: conforming and non-conforming 2D schemes with a strong Ampere law

An unstructured body-of-revolution electromagnetic particle-in-cell algorithm with radial perfectly matched layers and dual polarizations

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