The Gauge Fixing for A-Field node enforces the gauge
∇⋅A = 0 by adding an additional potential variable,
ψ, and its associated conservation equation to the system. This is often necessary to get a unique and numerically stable solution to the equation solving for the magnetic vector potential
A.
From the Selection list, choose the domains to define the gauge-fixing potential
ψ. In most cases, the feature should be applied to all domains where the magnetic vector potential
A is solved for. By default, the selection is set to
All domains, ensuring that the gauge fixing is applied to all the valid domains in the model.
The variable ψ is used to impose a condition on the derivatives of the magnetic vector potential, so its absolute value does not have particular significance; only its gradient enters the equations (the variable
ψ acts more or less like a potential). The absolute value of the variable can be set by entering the
Divergence condition variable scaling ψ 0 (SI unit: A/m). The default value is 1 A/m, which is appropriate for most models.
This section allows a more fine control on the boundary conditions for ψ applied by the
Gauge Fixing feature. The domain equation for ψ only imposes a condition on the gradient, so it is important to constrain the absolute value of ψ to ensure a non-singular model. The
Constant value on insulation boundaries check box (selected by default) imposes a constant value on the conductive boundaries in the model, such as
Magnetic Insulation. Select the
Method to enforce this condition:
Constrain value (the default) or
Constrain tangential gradient.
If there are no such boundaries, select the Constrain variable in at least one point to ensure that there is always a constraint set on the value of the divergence condition variable
ψ.
) and select