Field propagator

PoissonSolve

Advances phi.

What it solves

Weak discretization of the (stabilized) Poisson equation: find

ϕ \in H^{1}

such that

ϵ \int_{Ω} ψ ϕ d x + \int_{Ω} \nabla ψ^{⊤} \nabla ϕ d x = i \sum \int_{Ω} ψ ρ_{i} (x) d x \forall ψ \in H^{1},

where $ϵ \in R$ is a stabilization parameter. Boundary terms from integration by parts are assumed to vanish. The equation is discretized as

(ϵ S + G^{⊤} M^{1} G) ϕ = i \sum (Λ^{0}, ρ_{i})_{L^{2}},

where $M^{1}$ is the $H (curl)$ -mass matrix and $S$ is a stabilization matrix.

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

Name	Kind	Accepted spaces
`phi`	FEECVariable	`H1`

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

Option	Default	Choices	Description
`stab_eps`	`0`	float	Stabilization weight used for the mass-like term in the Poisson operator. Internally mapped to `sigma_1 = stab_eps` in the parent `ImplicitDiffusion` formulation.
`stab_mat`	`Id`	`M0M0adId`	Stabilization matrix multiplied by `stab_eps`.
`diffusion_mat`	`M1`	`M1M1perpM1paraM1gyro`	Diffusion matrix.
`x0`	`None`	StencilVector	Initial guess for the iterative linear solver.
`solver`	`pcg`	`pcgcg`	Name of the symmetric iterative solver passed to `inverse`.
`precond`	`MassMatrixPreconditioner`	`MassMatrixPreconditionerMassMatrixDiagonalPreconditionerNone`	Name of the preconditioner configuration. Currently this class inherits the same behavior as `ImplicitDiffusion`, where `pc=None` is used internally.
`solver_params`	`None`	SolverParameters	Iterative-solver controls (for example `tol`, `maxiter`, `verbose`, `info`, `recycle`). If `None`, defaults to `SolverParameters()`.
`filter_params`	`None`	dict	If not None, specifies a filter to the accumulation of a specific variable.

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