Comparison of Preconditioning Strategies in Energy Conserving Implicit Particle in Cell Methods (Communications in Computational Physics, 2018)
This work presents a set of preconditioning strategies able to significantlyaccelerate the performance of fully implicit energy-conserving Particle-in-Cell methodsto a level that becomes competitive with semi-implicit methods. We comparethree different preconditioners. We consider three methods and compare them with astraight unpreconditioned Jacobian Free Newton Krylov (JFNK) implementation. Thefirst two focus, respectively, on improving the handling of particles (particle hiding)or fields (field hiding) within the JFNK iteration. The third uses the field hiding preconditionerwithin a direct Newton iteration where a Schwarz-decomposed Jacobian iscomputed analytically. Clearly, field hiding used with JFNK or with the direct Newton-Schwarz(DNS) method outperforms all method. We compare these implementationswith a recent semi-implicit energy conserving scheme. Fully implicit methods are stilllag behind in cost per cycle but not by a large margin when proper preconditioning isused. However, for exact energy conservation, preconditioned fully implicit methodsare significantly easier to implement compared with semi-implicit methods and can beextended to fully relativistic physics.
Keywords: Preconditioners in Particle-in-Cell; energy conserving Particle-in-Cell; plasma numerics.