A split control variate scheme for PIC simulations with collisions

When the distribution function of plasma particles stays close to some analytically known function, statistical noise inherent to Monte Carlo simulations can be greatly reduced by introducing this function as a control variate in the computation of the velocity moments. Such a method, even though it...

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Bibliographic Details
Published in:Journal of computational physics 2015-08, Vol.295, p.402-419
Main Authors: Sonnendrücker, Eric, Wacher, Abigail, Hatzky, Roman, Kleiber, Ralf
Format: Article
Language:English
Subjects:
Algorithms
Collisions
Computation
Computer simulation
Control variate
Fokker–Planck
Mathematical analysis
Mathematical models
Monte Carlo
Nonlinearity
Particle in cell
PIC
Vlasov–Poisson system
Weight reduction
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Summary:When the distribution function of plasma particles stays close to some analytically known function, statistical noise inherent to Monte Carlo simulations can be greatly reduced by introducing this function as a control variate in the computation of the velocity moments. Such a method, even though it can be naturally applied to nonlinear simulations, has originally emerged from linearised simulations and is usually called the δf particle-in-cell (PIC) method. In the past, the method has been extended to also handle collisions. This resulted in a two weight scheme which is known to produce a pronounced weight growth problem which rapidly makes it inefficient as a control variate method for variance reduction. In this work we analyse the weight growth problem within a simple example, which allows us to overcome its pathological behaviour. We also introduce a new split algorithm based on switching the control variate for PIC simulations with collisions. A key element of our algorithm is a new weight smoothing operator which enables us to obtain a significant noise reduction both in the presence of collisions and in the deep nonlinear phase of PIC simulations.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2015.04.004