The Magnetic Field Formulation (mfh) interface (), found under the AC/DC>Electromagnetic Fields>Vector Formulations branch when adding a physics interface, is used to compute magnetic fields and induced current distributions. It is especially suitable for time-domain magnetic modeling of materials with a strongly nonlinear E-J characteristic such as superconductors. Stationary, frequency-domain, small-signal analysis and time-domain modeling are supported in 2D and 3D. Note that the formulation requires a nonzero conductivity everywhere.

The main node is Faraday’s Law, which adds the equation for the magnetic field and provides an interface for defining the constitutive relations and its associated properties such as the relative permeability.

When this physics interface is added, these default nodes are also added to the Model Builder — Magnetic Field Formulation, Faraday’s Law, Magnetic Insulation (the default boundary condition), Initial Values, and Magnetic Gauss’ Law. Then, from the Physics toolbar, add other nodes that implement, for example, boundary conditions and external currents. You can also right-click Magnetic Field Formulation to select physics features from the context menu.

The physics-controlled mesh is controlled from the Mesh node’s Settings window (if the Sequence type is Physics-controlled mesh). There, in the table in the Physics-Controlled Mesh section, find the physics interface in the Contributor column and select or clear the check box in the Use column on the same table row for enabling (the default) or disabling contributions from the physics interface to the physics-controlled mesh.

The Label is the default physics interface name.

The Name is used primarily as a scope prefix for variables defined by the physics interface. Refer to such physics interface variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different physics interfaces, the name string must be unique. Only letters, numbers, and underscores (_) are permitted in the Name field. The first character must be a letter.

The default Name (for the first physics interface in the model) is mfh.

The dependent variable is the Magnetic field H. You can change both its field name and the individual component variable names. If the new field name coincides with the name of another magnetic vector potential field in the model, the interfaces share degrees of freedom and component names. The new field name must not coincide with the name of a field of another type or with a component name belonging to some other field. Component names must be unique within a model, except for fields of the same type sharing a common field name.

To display this section, click the Show More Options button () and select Advanced Physics Options.

The Activate divergence constraint check box is selected by default, which enables the default Magnetic Gauss’ Law node. Click to clear the check box to disable the Magnetic Gauss’s Law node and remove it from the physics interface.

To display this section, click the Show More Options button () and select Advanced Physics Options.

When the Check applicability of features in study check box is selected, any features that are incompatible with the study will generate an error message when trying to solve or show the default solver. No solver will be generated. Deselect it and you will be able to run the model, possibly with runtime errors instead. It is available to allow the advanced user to tweak any feature and use it outside of its intended study scope.

Select the shape order for the Magnetic field dependent variable — Linear, Linear type 2, Quadratic (the default), Quadratic type 2, Cubic, or Cubic type 2. For more information about the Discretization section, see Settings for the Discretization Sections in the COMSOL Multiphysics Reference Manual.