Gauge Fixing for A-Field


	For 2D and 2D axisymmetric components. Gauge fixing is available when vector (curl) shape functions are used, that is, when having in-plane dependent variables. The node is made available when In-plane vector potential or Three-component vector potential is selected from the Components section on the Settings window for The Magnetic Fields Interface.

The 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.


	Explicit Gauge Fixing/Divergence Constraint

Domain Selection

From the 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 , ensuring that the gauge fixing is applied to all the valid domains in the model.

Gauge Fixing for A-Field

The is set to by default. For Time Dependent and Frequency Domain studies, set to can be efficient to handle regions without conductivity.

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 ψ 0 (SI unit: A/m). The default value is 1 A/m, which is appropriate for most models.

Advanced Settings

To display this section, click the button (

) and select in the dialog box.

This section allows a more fine control on the boundary conditions for ψ applied by the 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 nonsingular model. The check box (selected by default) imposes a constant value on the conductive boundaries in the model, such as Magnetic Insulation. Select the to enforce this condition: (the default) or .

If there are no such boundaries, select the to ensure that there is always a constraint set (at least in one point) on the value of the divergence condition variable ψ.


	If you apply Gauge Fixing across pair boundaries, the internal logic for constraining ψ in at least one point does not work. The problem is most likely to appear in gauge fixing for rotating machinery. Assume you have one gauge fixed Ampère's Law domain in the stator and one in the rotor, then one must use separate Gauge Fixing features for these as the geometry analysis for setting up point constraints on ψ does not work across pairs. It can also be handled by adding manual constraints on ψ.


	Applying Gauge Fixing to nonlinear models, for example with materials involving magnetic saturation has the known side-effect that the nonlinear solver fails to converge for models with zero or numerically small excitation. Thus, starting for example parametric sweeps from exactly zero applied source currents should be avoided.