Conservative Projection Between Finite Element and Particle Bases

@article{Pusztay2022ConservativePB,
  title={Conservative Projection Between Finite Element and Particle Bases},
  author={Joseph V. Pusztay and Matthew G. Knepley and Mark F. Adams},
  journal={SIAM J. Sci. Comput.},
  year={2022},
  volume={44},
  pages={310-}
}
. Particle-in-Cell (PIC) methods employ particle representations of unknown fields, but also employ continuum fields for other parts of the problem. Thus projection between particle and continuum bases is required. Moreover, we often need to enforce conservation constraints on this projection. We derive a mechanism for enforcement based on weak equality, and implement it in the PETSc libraries. Scalability is demonstrated to more than 1B particles. the field in the particle synthesis step with a… 
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