Field propagator

ShearAlfvenPropagator

Advances u and b.

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_{Ω} ρ_{0} \frac{\partial U ~}{\partial t} \cdot V d x \frac{\partial B ~}{\partial t} = \int_{Ω} B ~ \cdot \nabla \times (B_{0} \times V) d x \forall V \in {H (curl), H (div), (H^{1})^{3}} = \nabla \times (U ~ \times B_{0})

Time discretization:

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
`u`	FEECVariable	`HcurlHdivH1vec`
`b`	FEECVariable	`Hdiv`

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

Option	Default	Choices	Description
`u_space`	`Hdiv`	`HcurlHdivH1vec`	FEEC space used for the velocity variable.
`algo`	`implicit`	`implicitexplicit`	Time stepping algorithm.
`solver`	`pcg`	`pcgcg`	Symmetric iterative solver used by implicit or explicit operators.
`precond`	`MassMatrixPreconditioner`	`MassMatrixPreconditionerMassMatrixDiagonalPreconditionerNone`	Preconditioner for the mass-matrix block.
`solver_params`	`None`	SolverParameters	Solver controls; defaults to `SolverParameters()`.
`butcher`	`None`	ButcherTableau	Explicit Runge-Kutta tableau when `algo="explicit"`.

Each model splits its time step into a sequence of propagators. This one appears in 4 models, at the position shown.