  We extend the simplex-in-cell (SIC) technique recently introduced in the
context of collisionless dark matter fluids (Abel et al. 2012; Hahn et al.
2012) to the case of collisionless plasmas. The six-dimensional phase space
distribution function $f(\mathbf x,\mathbf v)$ is represented by an ensemble of
three-dimensional manifolds, which we refer to as sheets. The electric
potential field is obtained by solving the Poisson equation on a uniform mesh,
where the charge density is evaluated by a spatial projection of the phase
space sheets. The SIC representation of phase space density facilitates robust,
high accuracy numerical evolution of the Vlasov-Poisson system using
significantly fewer tracer particles than comparable particle-in-cell (PIC)
approaches by reducing the numerical shot-noise associated with the latter. We
introduce the SIC formulation and describe its implementation in a new code,
which we validate using standard test problems including plasma oscillations,
Landau damping, and two stream instabilities in one dimension. Merits of the
new scheme are shown to include higher accuracy and faster convergence rates in
the number of particles. We finally motivate and outline the efficient
application of SIC to higher dimensional problems.
