Exact charge-conserving scatter–gather algorithm for particle-in-cell simulations on unstructured grids: A geometric perspective

Moon, Haksu; Teixeira, Fernando L.; Omelchenko, Y. A.

doi:10.1016/j.cpc.2015.04.014

Cited by 79 publications

(65 citation statements)

References 40 publications

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“…14. The proposed FETD-BOR solver is incorporated into a PIC algorithm [66,67,68] to simulate the wave-plasma interaction in the device [9]. The PIC algorithm is based on an unstructured grid and explained in detail in [9,24,25]. For this problem it suffices to consider the TE φ polarized field with m = 0.…”

Section: Backward-wave Oscillator (Bwo) In the Relativistic Regimementioning

confidence: 99%

Finite element time-domain body-of-revolution Maxwell solver based on discrete exterior calculus

Borges

Teixeira

2019

Journal of Computational Physics

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We present a finite-element time-domain (FETD) Maxwell solver for the analysis of body-of-revolution (BOR) geometries based on discrete exterior calculus (DEC) of differential forms and transformation optics (TO) concepts. We explore TO principles to map the original 3-D BOR problem to a 2-D one in the meridian ρz-plane based on a Cartesian coordinate system where the cylindrical metric is fully embedded into the constitutive properties of an effective inhomogeneous and anisotropic medium that fills the domain. The proposed solver uses a (TE φ , TM φ ) field decomposition and an appropriate set of DEC-based basis functions on an irregular grid discretizing the meridian plane. A symplectic time discretization based on a leap-frog scheme is applied to obtain the full-discrete marching-on-time algorithm. We validate the algorithm by comparing the numerical results against analytical solutions for resonant fields in cylindrical cavities and against pseudo-analytical solutions for fields radiated by cylindrically symmetric antennas in layered media. We also illustrate the application of the algorithm for a particlein-cell (PIC) simulation of beam-wave interactions inside a high-power backward-wave oscillator.

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Section: Backward-wave Oscillator (Bwo) In the Relativistic Regimementioning

confidence: 99%

Finite element time-domain body-of-revolution Maxwell solver based on discrete exterior calculus

Borges

Teixeira

2019

Journal of Computational Physics

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“…The fundamentals of present finite element time-domain (FETD) Maxwell field solver are briefly summarized in this appendix. A more comprehensive discussion of the Maxwell field solver, together with various details on the scatter, gather, and pusher steps of the EM-PIC algorithm can be found in [16,17,18].…”

Section: Appendix a Fetd Maxwell Field Solvermentioning

confidence: 99%

“…In this work, we employ Whitney-form-based gather/scatter algorithms [16] which guarantee the exact charge conservation on irregular grids, from the first principle, within the limit of the machine precision. Note that each superparticle is modeled as being point-like, implying that the shape function of superparticles is assumed to be a delta function.…”

Section: Appendix C Particle and Grid Interactionsmentioning

confidence: 99%

“…Grid currents and charges are evaluated based on Whitney 1-and 0-forms, as where e is electron charge [C] and j i and q i are DoFs of electric current and charge for i th edge and i th node, respectively. Plugging the above grid charges and currents to the discrete counterpart of continuity equation, one can prove the charge conservation [16].…”

Section: Appendix C Particle and Grid Interactionsmentioning

confidence: 99%

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Diagnosing numerical Cherenkov instabilities in relativistic plasma simulations based on general meshes

Nicolini

Lee

et al. 2020

Journal of Computational Physics

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Numerical Cherenkov radiation (NCR) or instability is a detrimental effect frequently found in electromagnetic particle-in-cell (EM-PIC) simulations involving relativistic plasma beams. NCR is caused by spurious coupling between electromagnetic-field modes and multiple beam resonances. This coupling may result from the slow down of poorlyresolved waves due to numerical (grid) dispersion and from aliasing mechanisms. NCR has been studied in the past for finite-difference-based EM-PIC algorithms on regular (structured) meshes with rectangular elements. In this work, we extend the analysis of NCR to finite-element-based EM-PIC algorithms implemented on unstructured meshes. The influence of different mesh element shapes and mesh layouts on NCR is studied. Analytic predictions are compared against results from finite-element-based EM-PIC simulations of relativistic plasma beams on various mesh types.

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“…The first remedies have been to correct the electric field by solving exact [9] or approximate [51,47] Poisson equations, until Eastwood, Villasenor and Buneman [30,70] noticed that stable solvers could be obtained by an adequate computation of the current from the particles which would preserve a discrete Gauss law. In the framework of curl-conforming finite element method, we have described a generic algorithm in [17], revisited in a geometric perspective in [66,57]. More recently it was noticed that this algorithm fits in a semi-discrete Hamiltonian structure, where the divergence constraints are identified as Casimirs and thus are automatically conserved [46].…”

Section: Compatible Maxwell Solvers With Particles Imentioning

confidence: 99%

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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Exact charge-conserving scatter–gather algorithm for particle-in-cell simulations on unstructured grids: A geometric perspective

Cited by 79 publications

References 40 publications

Finite element time-domain body-of-revolution Maxwell solver based on discrete exterior calculus

Finite element time-domain body-of-revolution Maxwell solver based on discrete exterior calculus

Diagnosing numerical Cherenkov instabilities in relativistic plasma simulations based on general meshes

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

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