%0 Journal Article
%T Implicit Temporal Discretization and Exact Energy Conservation for Particle Methods Applied to the Poisson¨CBoltzmann Equation
%A Giovanni Lapenta
%A Wei Jiang
%J -
%D 2018
%R https://doi.org/10.3390/plasma1020021
%X Abstract 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¨CBoltzmann 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-Tex
%K particle-in-cell
%K Poisson¨CBoltzmann
%K multiscale material modeling
%U https://www.mdpi.com/2571-6182/1/2/21