Direct implicit large time-step particle simulation of plasmas

Langdon, A. B.; Cohen, B. I.; Friedman, A.

doi:10.1016/0021-9991(83)90083-9

Cited by 163 publications

(130 citation statements)

References 23 publications

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“…A limit on the time step imposed by the number of simulation particles is discussed in Ref. [34]. Denoting with N pc the number of simulation particles per cell, the time step must satisfy the inequality…”

Section: The Numerical Algorithmmentioning

confidence: 99%

“…(Direct implicit methods, which replace the fluid moment equations by an expansion about the unperturbed particle orbits are described for electrostatic plasmas in Ref. [34], magnetized plasma in Ref. [3], and electromagnetic plasmas in Ref.…”

Section: The Numerical Algorithmmentioning

confidence: 99%

“…(40) is troublesome for two reasons. (Essentially the same equation appears in the direct implicit formulation [22,34], so the problem is not unique to the implicit moment method.) First, Eq.…”

Section: Temporal Discretizationmentioning

confidence: 99%

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A Simplified Implicit Maxwell Solver

Ricci

Lapenta

Brackbill

2002

Journal of Computational Physics

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We apply the second-order formulation of Maxwell's equations proposed by Jiang et al. (1996, J. Comput. Phys. 125, 104) to the solution of the implicit formulation of the three-dimensional, time-dependent Vlasov-Maxwell's system. An implicit finite difference algorithm is developed to solve the Maxwell's equations in a bounded domain with physical boundary conditions comprising electrically conducting walls (perfect conductors) and constant magnetic flux walls. We formulate the boundary conditions for Maxwell's equations to satisfy Poisson's equation throughout the domain by solving it only on the boundary. This eliminates the need for a separate projection step. We compare numerical results with analytical solutions for electromagnetic waves in vacuo, and using the implicit particle-in-cell code CELESTE3D, we test the new solver on the geospace environment modeling magnetic reconnection challenge problem. c 2002 Elsevier Science (USA)

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Section: The Numerical Algorithmmentioning

confidence: 99%

Section: The Numerical Algorithmmentioning

confidence: 99%

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A Simplified Implicit Maxwell Solver

Ricci

Lapenta

Brackbill

2002

Journal of Computational Physics

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“…Of course, this generally translates into the requirement for large computational resources. Historically, the search for more efficient PIC schemes based on implicit time discretization dates back to the 1980s, when the implicit moment [55][56][57] and the direct implicit [58,59] methods were introduced. Both methods rely on a linearization of the equations for the electromagnetic fields, and, thus, they should be more properly regarded as semi-implicit methods.…”

Section: Introductionmentioning

confidence: 99%

On the velocity space discretization for the Vlasov–Poisson system: Comparison between implicit Hermite spectral and Particle-in-Cell methods

Camporeale

Delzanno

Bergen

et al. 2016

Computer Physics Communications

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a b s t r a c tWe describe a spectral method for the numerical solution of the Vlasov-Poisson system where the velocity space is decomposed by means of an Hermite basis, and the configuration space is discretized via a Fourier decomposition. The novelty of our approach is an implicit time discretization that allows exact conservation of charge, momentum and energy. The computational efficiency and the cost-effectiveness of this method are compared to the fully-implicit PIC method recently introduced by Lapenta (2011) andChen et al. (2011). The following examples are discussed: Langmuir wave, Landau damping, ion-acoustic wave, two-stream instability. The Fourier-Hermite spectral method can achieve solutions that are several orders of magnitude more accurate at a fraction of the cost with respect to PIC.

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“…11 The implicit PIC method has been developed for a number of years since its original introduction. Two main approaches have emerged: the direct implicit method 12 and the implicit moment method. 11 Here we consider the implicit moment method.…”

Section: Introductionmentioning

confidence: 99%

Kinetic approach to microscopic-macroscopic coupling in space and laboratory plasmas

Brackbill²,

2006

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Kinetic plasma simulation typically requires to handle a multiplicity of space and time scales. The implicit moment particle in cell (PIC) method provides a possible route to address the presence of multiple scales effectively. Here, a new implementation of the implicit moment method is described. The present paper has two goals. First, the most modern implementation of the implicit moment method is described. While many of the algorithms involved have been developed in the past, the present paper reports for the first time how the implicit moment method is currently implemented and what specific algorithms have been found to work best. Second, we present the CELESTE3D code, a fully electromagnetic and fully kinetic PIC code, based on the implicit moment method. The code has been in use for a number of years but no previous complete description of its implementation has been provided. The present work fills this gap and introduces a number of new methods not previously presented: a new implementation of the Maxwell solver and a new particle mover based on a Newton-Krylov nonlinear solver for the discretized Newton’s equations. A number of benchmarks of CELESTE3D are presented to shown the typical application and to investigate the improvements introduced by the new solver and the new mover.

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Direct implicit large time-step particle simulation of plasmas

Cited by 163 publications

References 23 publications

A Simplified Implicit Maxwell Solver

A Simplified Implicit Maxwell Solver

On the velocity space discretization for the Vlasov–Poisson system: Comparison between implicit Hermite spectral and Particle-in-Cell methods

Kinetic approach to microscopic-macroscopic coupling in space and laboratory plasmas

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