  The hybrid model of particle-ion-fluid-electron is widely utilized in
astrophysical and laser-produced plasmas due to its kinetic characteristics and
remarkable computational efficiency. However, the current numerical methods for
the hybrid model have limitations when it comes to simulating non-quasi-neutral
plasmas. To address this issue, I proposed a novel method called Convolutional
Hybrid PIC (conv-HPIC). The conv-HPIC is based on a convolution equation
derived from the Poisson's equation and the generalized Ohm's law. I performed
numerical simulations on the collisionless electrostatic shock to validate the
effectiveness of this method. The results demonstrate that the proposed method
can accurately describe and predict the behavior of non-quasi-neutral plasmas.
This method can be applied to both stationary and non-stationary electrostatic
issues. It avoids the need for iterative calculations, effectively suppresses
numerical noise, exhibits good computational efficiency, and can be easily
parallelized.
