An adaptive Particle-In-Cell method using multi-resolution analysis

Chehab, J.-P.; Cohen, Albert; Jennequin, D.; Nieto, Juan J.; Roland, Ch.; Roche, J. R.

doi:10.4171/012-1/2

Cited by 4 publications

(5 citation statements)

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“…Notably, methods based on δf or re-mapping of the distribution function have been successful to reduce particle noise, and hence enhance the accuracy of PIC simulations (see, e.g. [17,78,26]). Of course, this aspect lies in the realm of algorithm optimization.…”

Section: Discussionmentioning

confidence: 99%

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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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Section: Discussionmentioning

confidence: 99%

“…We note that methods based on δf or re-mapping of the distribution function have been developed in the PIC community to reduce particle noise. This has led to some very interesting work (see for instance [17,78,26]), but has not yet resulted in a commonly accepted denoising technique adopted by the PIC community.…”

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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“…Equipped with the LTP transport operator T h [F ] defined in (13) for a generic flow F , and with the field solver described in Section 2.4, we are now in position to specify the numerical transport involved in the scheme (8), namely the operator…”

Section: Time Marching Schemementioning

confidence: 99%

“…Resulting numerical diffusion from the remappings can be reduced by use of high order adaptive schemes; see, e.g., [11,12]. Other methods to reduce the noise have also been studied, such as wavelet-based denoising techniques; see e.g., [13,14,15].…”

Section: Introductionmentioning

confidence: 99%

Noiseless Vlasov–Poisson simulations with linearly transformed particles

Pinto

Sonnendrücker

Friedman

et al. 2014

Journal of Computational Physics

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We introduce a deterministic discrete-particle simulation approach, the Linearly-Transformed Particle-In-Cell (LTPIC) method, that employs linear deformations of the particles to reduce the noise traditionally associated with particle schemes. Formally, transforming the particles is justified by local first order expansions of the characteristic flow in phase space. In practice the method amounts to using deformation matrices within the particle shape functions; these matrices are updated via local evaluations of the forward numerical flow. Because it is necessary to periodically remap the particles on a regular grid to avoid excessively deforming their shapes, the method can be seen as a development of Denavit's Forward Semi-Lagrangian (FSL) scheme [J. Denavit, J. Comp. Physics 9, 75 (1972)]. However, it has recently been established [M. Campos Pinto, "Smooth particle methods without smoothing", arXiv:1112.1859 (2012)] that the underlying Linearly-Transformed Particle scheme converges for abstract transport problems, with no need to remap the particles; deforming the particles can thus be seen as a way to significantly lower the remapping frequency needed in the FSL schemes, and hence the associated numerical diffusion. To couple the method with electrostatic field solvers, two specific charge deposition schemes are examined, and their performance compared with that of the standard deposition method. Finally, numerical 1d1v simulations involving benchmark test cases and halo formation in an initially mismatched thermal sheet beam demonstrate some advantages of our LTPIC scheme over the classical PIC and FSL methods. Benchmarked test cases also indicate that, for numerical choices involving similar computational effort, the LTPIC method is capable of accuracy comparable to or exceeding that of state-of-the-art, high-resolution Vlasov schemes.

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“…Afterwards one would perform a fast wavelet transform on the regularized particle field and filter out high-oscillatory components with large wavelet coefficients by a thresholding procedure. Such an approach has been used successfully before in the whole-space case [5] and might be able combine the best of both approaches.…”

Section: Discussion and Outlookmentioning

confidence: 99%

On particles and splines in bounded domains

Kirchhart

2021

ESAIM: M2AN

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We propose numerical schemes that enable the application of particle methods for advection problems in general bounded domains. These schemes combine particle fields with Cartesian tensor product splines and a fictitious domain approach. Their implementation only requires a fitted mesh of the domain's boundary, and not the domain itself, where an unfitted Cartesian grid is used. We establish the stability and consistency of these schemes in $W^{s,p}$-norms, $s\in\mathbb{R}$, $1\leq p\leq\infty$.

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An adaptive Particle-In-Cell method using multi-resolution analysis

Cited by 4 publications

References 0 publications

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

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

Noiseless Vlasov–Poisson simulations with linearly transformed particles

On particles and splines in bounded domains

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