Field propagator

Magnetosonic

Advances n, u and p.

What it solves

FEEC discretization of the following equations:

find $ρ ~ \in L^{2}, U ~ \in {H (curl), H (div), (H^{1})^{3}}, p ~ \in L^{2}$ such that

\frac{\partial ρ ~}{\partial t} + \nabla \cdot (ρ_{0} U ~) \int_{Ω} ρ_{0} \frac{\partial U ~}{\partial t} \cdot V d x - \int_{Ω} p ~ \nabla \cdot V d x \frac{\partial p ~}{\partial t} + \nabla \cdot (p_{0} U ~) + \frac{2}{3} p_{0} \nabla \cdot U ~ = 0 = \int_{Ω} (\nabla \times B_{0}) \times B ~ \cdot V d x \forall V \in {H (curl), H (div), (H^{1})^{3}} = 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.

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

Option	Default	Choices	Description
`u_space`	`Hdiv`	`HcurlHdivH1vec`	FEEC space used for the velocity variable `u`.
`solver`	`pbicgstab`	`pbicgstabbicgstabgmres`	Iterative solver used by `SchurSolver`.
`precond`	`MassMatrixPreconditioner`	`MassMatrixPreconditionerMassMatrixDiagonalPreconditionerNone`	Preconditioner applied to the mass matrix block associated with `u_space`.
`solver_params`	`None`	SolverParameters	Iterative-solver controls. If `None`, defaults to `SolverParameters()`.

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