A Can0nical Integrati0n Technique

Ruth, Ronald D.

doi:10.1109/tns.1983.4332919

Cited by 679 publications

(463 citation statements)

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“…. 4, that generalize the leap-frog method and are known to be stable and nondissipative [12], [23], [24]. Applied to the time-dependent system (13)-(14), they compute auxiliary solutions by first letting E n,0 := E n , B n,0 := B n , then for j = 0, .…”

Section: Consistency Criteria For Time-domain Fem Schemesmentioning

confidence: 99%

Charge-conserving FEM–PIC schemes on general grids

Pinto

Jund

Salmon

et al. 2014

Comptes Rendus. Mécanique

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In this article we aim at proposing a general mathematical formulation for charge conserving finite element Maxwell solvers coupled with particle schemes. In particular, we identify the finite element continuity equations that must be satisfied by the discrete current sources for several classes of time domain Vlasov-Maxwell simulations to preserve the Gauss law at each time step, and propose a generic algorithm for computing such consistent sources. Since our results cover a wide range of schemes (namely curl-conforming finite element methods of arbitrary degree, general meshes in 2 or 3 dimensions, several classes of time discretization schemes, particles with arbitrary shape factors and piecewise polynomial trajectories of arbitrary degree), we believe that they provide a useful roadmap in the design of high order charge conserving FEM-PIC numerical schemes.

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Section: Consistency Criteria For Time-domain Fem Schemesmentioning

confidence: 99%

Charge-conserving FEM–PIC schemes on general grids

Pinto

Jund

Salmon

et al. 2014

Comptes Rendus. Mécanique

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show abstract

“…The strong proton beam in another ring and the electron beam are considered rigid and will not be affected by the test particles in the simulation. The particle motion in the magnetic elements is tracked with the 4th order symplectic integration by R. Ruth [5]. To save the time involved in the numeric tracking, we treat the multipoles as thin lenses.…”

Section: Tracking Setupmentioning

confidence: 99%

Simulation study of dynamic aperture with head-on beam-beam compensation in the RHIC

Luo¹,

Fischer²

2010

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“…A symplectic integration method explicitly preserves the Hamiltonian nature of the system during numerical integration. There has been a lot of activity recently in formulating symplectic integration algorithms [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. In this paper, we consider an application of our symplectic integration method to the nonlinear pendulum Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%