# Magneto-Fluid Dynamics Seminar

#### Implicit energy- and charge-conserving particle in cell methods on sparse grids

**Speaker:**
Lee Ricketson, Lawrence Livermore National Laboratory

**Location:**
Warren Weaver Hall 905

**Date:**
Tuesday, February 25, 2020, 11 a.m.

**Synopsis:**

The particle-in-cell (PIC) method has been widely used for half a century in the simulation of kinetic plasmas. The last decade has seen two new versions of the method that move toward overcoming long-standing challenges. First, the fully implicit, energy-conserving PIC scheme mitigates the so-called finite grid instability, allowing larger time-steps and, in many cases, coarser spatial resolution while retaining stability. Second, a sparse grid version of PIC was recently introduced that shows the potential to mitigate the curse of dimensionality, thereby dramatically reducing the number of simulated particles needed to achieve satisfactory statistical resolution. In this talk, we present a scheme that marries these two advances. We prove that the energy- and charge-conservation properties of implicit PIC can be carried over to sparse grids. Key here is the appropriate definition of the electrostatic potential. In so doing, we also generalize previous conservation results for implicit PIC to more general classes of field solvers and discuss potential applications of this generalization. Theoretical results are confirmed via numerical examples using a 2D electrostatic PIC code.

This is joint work with Guangye Chen (LANL).

*Work performed under the auspices of the U.S. Department of Energy by LLNL and LANL under contracts DE-AC52-07NA27344 and DE-AC52-06NA25396 and supported by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration.