Field propagator

CurlCurlSolve

Advances e.

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What it solves

Weak discretization of the curl-curl problem.

Find $E \in H (curl)$ such that

\int_{Ω} \nabla \times F \cdot \nabla \times E d x - σ \int_{Ω} F \cdot E d x = i \sum \int_{Ω} F \cdot J_{i} d x \forall F \in H (curl),

where $J_{i} : Ω \to R^{3}$ are real-valued and $σ \in R / {0}$ is a scalar. Boundary terms from integration by parts are assumed to vanish. The equation is discretized as

(C^{⊤} \cdot M^{2} \cdot C - σ M^{1}) e^{n + 1} = i \sum j_{i},

where $M^{1}$ and $M^{2}$ are WeightedMassOperators and $j_{i}$ is the vector of coefficients of the projection of $J_{i}$ into the discrete space $V_{h}^{1} \subset H (curl)$ .

Variables it advances

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

Name	Kind	Accepted spaces
`e`	FEECVariable	`Hcurl`

Options

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

Option	Default	Choices	Description
`sigma`	`1`	float	Coefficient multiplying the stabilization/mass contribution on the left-hand side.
`stab_mat`	`M1`	`M1Id`	Stabilization operator used in the term weighted by `sigma`.
`diffusion_mat`	`M2`	`M2`	Diffusion metric in the bilinear form `curl.T @ diffusion_mat @ curl`. You can pass the name of a pre-built operator in `mass_ops` or a custom `WeightedMassOperator` compatible with the codomain of `curl`.
`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 sets `pc=None` internally, so this option is reserved for compatibility and future extensions.
`solver_params`	`None`	SolverParameters	Iterative-solver controls (for example `tol`, `maxiter`, `verbose`, `info`, `recycle`). If `None`, defaults to `SolverParameters()`.

Used by

No model in the catalogue currently composes this propagator — it is available for building new models.