Field propagator

CurrentCoupling5DDensity

Advances u.

What it solves

FEEC discretization of the following equations:

find $U \in {H (curl), H (div), (H^{1})^{3}}$ and $B \in H (div)$ such that

\int ρ_{0} \frac{\partial U ~}{\partial t} \cdot V d x = \frac{A _{h}}{A _{b}} \frac{1}{ϵ} ∭ f^{vol} (1 - \frac{B _{∥}}{B _{∥}^{*}}) U ~ \times B_{f} \cdot V d x d v_{∥} d μ \forall V \in {H (curl), H (div), (H^{1})^{3}},

FE coefficients update:

u^{n + 1} - u^{n} = - \frac{A _{h}}{A _{b}} \frac{1}{ϵ} L^{2} B_{f}^{\times} N (1/ g) WN (1 - \frac{B ^ _{∥}^{0}}{B ^ _{∥}^{* 0}}) (L^{2})^{⊤} \frac{Δ t}{2} \cdot (u^{n + 1} + u^{n}) .

For the detail explanation of the notations, see `2022_DriftKineticCurrentCoupling `_.

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

Name	Kind	Accepted spaces
`u`	FEECVariable	`HcurlHdivH1vec`

Set these on the propagator in a parameter file, for example CurrentCoupling5DDensity.Options(ep_scale=...).

Option	Default	Choices	Description
`ep_scale`	`1`	float	Scaling factor applied in the energetic-particle accumulation kernel.
`u_space`	`Hdiv`	`HcurlHdivH1vec`	FEEC space used for the unknown `u` variable.
`solver`	`pbicgstab`	`pbicgstabbicgstabgmres`	General iterative solver used for the linear system.
`precond`	`MassMatrixPreconditioner`	`MassMatrixPreconditionerMassMatrixDiagonalPreconditionerNone`	Preconditioner applied to the FEEC mass matrix.
`solver_params`	`None`	SolverParameters	Iterative-solver controls. If `None`, defaults to `SolverParameters()`.
`filter_params`	`None`	FilterParameters	Particle-to-grid filtering parameters used by the accumulator. If `None`, defaults to `FilterParameters()`.

Each model splits its time step into a sequence of propagators. This one appears in 1 model, at the position shown.