Next Article in Journal
Special Issue on Plasma Medicine
Next Article in Special Issue
Development of a Gyrokinetic Particle-in-Cell Code for Whole-Volume Modeling of Stellarators
Previous Article in Journal
Temperature and Lifetime Measurements in the SSX Wind Tunnel
Previous Article in Special Issue
Investigation of a Multiple-Timescale Turbulence-Transport Coupling Method in the Presence of Random Fluctuations
Open AccessArticle

Implicit Temporal Discretization and Exact Energy Conservation for Particle Methods Applied to the Poisson–Boltzmann Equation

1
Departement Wiskunde, University of Leuven, KU Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium
2
School of Physics, Huazhong University of Science and Technology, Wuhan 430007, China
*
Author to whom correspondence should be addressed.
Plasma 2018, 1(2), 242-258; https://doi.org/10.3390/plasma1020021
Received: 14 September 2018 / Revised: 4 October 2018 / Accepted: 5 October 2018 / Published: 9 October 2018
(This article belongs to the Special Issue Multiscale Methods in Plasma Physics)
We report on a new multiscale method approach for the study of systems with wide separation of short-range forces acting on short time scales and long-range forces acting on much slower scales. We consider the case of the Poisson–Boltzmann equation that describes the long-range forces using the Boltzmann formula (i.e., we assume the medium to be in quasi local thermal equilibrium). We develop a new approach where fields and particle information (mediated by the equations for their moments) are solved self-consistently. The new approach is implicit and numerically stable, providing exact energy conservation. We test different implementations that all lead to exact energy conservation. The new method requires the solution of a large set of non-linear equations. We consider three solution strategies: Jacobian Free Newton Krylov, an alternative, called field hiding which is based on hiding part of the residual calculation and replacing them with direct solutions and a Direct Newton Schwarz solver that considers a simplified, single, particle-based Jacobian. The field hiding strategy proves to be the most efficient approach. View Full-Text
Keywords: particle-in-cell; Poisson–Boltzmann; multiscale material modeling particle-in-cell; Poisson–Boltzmann; multiscale material modeling
Show Figures

Graphical abstract

MDPI and ACS Style

Lapenta, G.; Jiang, W. Implicit Temporal Discretization and Exact Energy Conservation for Particle Methods Applied to the Poisson–Boltzmann Equation. Plasma 2018, 1, 242-258.

Show more citation formats Show less citations formats

Article Access Map by Country/Region

1
Back to TopTop