# 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…

## One Citation

### Dual PIC: a structure preserving method for discretizing Lie-Poisson brackets

- Mathematics, Computer Science
- 2022

A general discretization strategy for Hamiltonian theories generated by Lie-Poisson brackets is considered which is called dual PIC (DPIC), which involves prescribing two discrete representations of the dynamical variable which are constrained as a Casimir invariant of the Hamiltonian theory to coincide with one another via an L 2 projection throughout the entire simulation.

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