Field propagator

OhmCold

Advances j and e.

What it solves

FEEC discretization of the following equations:

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

\int_{Ω} \frac{1}{n _{0}} \frac{\partial j}{\partial t} \cdot F d x - \frac{\partial E}{\partial t} = \frac{1}{ε} \int_{Ω} E \cdot F d x \forall F \in H (curl), = \frac{α ^{2}}{ε} j,

time_discret: Crank-Nicolson (implicit mid-point). System size reduction via struphy.linear_algebra.schur_solver.SchurSolver, such that

[j^{n + 1} - j^{n} e^{n + 1} - e^{n}] = \frac{Δ t}{2} [0 - \frac{1}{ε} M_{1/ n_{0}}^{- 1} \frac{1}{ε} M_{1/ n_{0}}^{- 1} 0] [α^{2} M_{1/ n_{0}} (j^{n + 1} + j^{n}) M_{1} (e^{n + 1} + e^{n})] .

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

Name	Kind	Accepted spaces
`j`	FEECVariable	`Hcurl`
`e`	FEECVariable	`Hcurl`

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

Option	Default	Choices	Description
`solver`	`pcg`	`pcgcg`	Symmetric iterative solver used by `SchurSolver`.
`precond`	`MassMatrixPreconditioner`	`MassMatrixPreconditionerMassMatrixDiagonalPreconditionerNone`	Preconditioner applied to the weighted mass matrix `M1ninv`.
`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 2 models, at the position shown.