Optimizations for a semi-implicit, energy- and charge-conserving particle-in-cell algorithm with iVPIC
Abstract
A semi-implicit, energy- and charge-conserving PIC algorithm has recently been developed for solving the relativistic Vlasov-Maxwell system. The algorithm employs the leap-frog scheme for Maxwell's equations, and a Crank-Nicolson scheme for the particle equations. The implicit field-particle integration ensures exact accounting of energy transfer between the field and particles. A new particle pusher is used to be exactly energy- and charge-conserving. We have designed a simple and effective Picard iteration algorithm that only requires a single orbit computation per outer iteration, thereby minimizing wall-clock time impact vs. the explicit VPIC algorithm. The Picard algorithm requires only a few iterations (3-5) to converge to single precision round-off levels. With further code optimizations we have obtained speedups of a factor of 3 vs. a naive implementation, resulting in a cost per implicit iteration comparable to a single explicit update of the baseline VPIC implementation. As a result, the semi-implicit algorithm is only a few times slower than the explicit baseline. We present numerical results that demonstrate the speedups of the algorithmic and code optimizations with sample test problems.
Work performed under the auspices of the U.S. DOE by the Triad National Security, LLC, LANL and was supported by the U.S. DOE SC FES.- Publication:
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APS Division of Plasma Physics Meeting Abstracts
- Pub Date:
- 2019
- Bibcode:
- 2019APS..DPPT10035C