Coupling propagator

VlasovAmpereCoupling

Advances e and ions.

What it solves

PIC-FEEC discretization of the following equations:

find $E \in H (curl)$ and $f$ such that

- \int_{Ω} \frac{\partial E}{\partial t} \cdot F d x \frac{\partial f}{\partial t} + \frac{1}{ε} E \cdot \frac{\partial f}{\partial v} = \frac{α ^{2}}{ε} \int_{Ω} \int_{R^{3}} f v \cdot F d^{3} v d x \forall F \in H (curl) = 0.

Time discretization: Crank-Nicolson (implicit mid-point).

System size reduction via struphy.linear_algebra.schur_solver.SchurSolver.

The variables this step updates over a time step dt, and the discrete spaces each one accepts.

Name	Kind	Accepted spaces
`e`	FEECVariable	`Hcurl`
`ions`	PICVariable	`Particles6D`

Set these on the propagator in a parameter file, for example VlasovAmpereCoupling.Options(solver=...).

Option	Default	Choices	Description
`solver`	`pcg`	`pcgcg`	Symmetric iterative solver used by `SchurSolver`.
`precond`	`MassMatrixPreconditioner`	`MassMatrixPreconditionerMassMatrixDiagonalPreconditionerNone`	Preconditioner for electric-field mass matrix block.
`solver_params`	`None`	SolverParameters	Solver controls.

Each model splits its time step into a sequence of propagators. This one appears in 3 models, at the position shown.