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Particle-in-cell 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 one billion particles.
Pusztay et al. (Mon,) studied this question.
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