The Coefficient Form PDE (c) interface (), found under the Mathematics>PDE Interfaces branch () when adding an interface, covers many well-known PDEs.

When this interface is added, these default nodes are also added to the Model Builder: Coefficient Form PDE, Zero Flux, and Initial Values. Then, from the Physics toolbar, add other nodes that implement, for example, boundary conditions. You can also right-click Coefficient Form PDE to select features from the context menu.

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 Coefficient Form PDE interface in the model) is c (in domains), cb (on boundaries), ce (on edges), or cp (at points).

From the Equation form list, choose Study controlled (the default when working in the user interface), Time domain (default when working in the API), or Frequency domain. This setting controls the interpretation of time derivatives of the interface’s dependent variables. See Interpretation of Time Derivatives for details.

When the setting is Study controlled, the study decides the equation form for the physics interface. It then appears as Automatic (Stationary), for example, in the Physics and Variables Selection section in the study step’s Settings window.

If Frequency domain has been selected a frequency-domain interpretation of time derivatives will be used irrespective of study step type. By default the Frequency to be used when interpreting time derivatives is taken From solver. If the solver does not define a frequency, or you want to solve the Coefficient Form PDE interface for a frequency other than the one supplied by the solver, select User defined and specify the desired frequency f (SI unit: Hz).

Also, if applicable, choose which equation to display by selecting a study from the Show equation assuming list. The corresponding equation, which this interface will solve, appears below.

Select the Dependent variable quantity that defines the unit for the dependent variable u. The default is Dimensionless (with 1 in the Unit column). Click the Select Dependent Variable Quantity button () to open the Physical Quantity dialog box to browse to find a physical quantity to use. You can also type a search string in the text field at the top of the dialog box and then click the Filter button () to filter the list of physical quantities. For example, type potential and click the Filter button to only list physical quantities that represent some kind of potential. Alternatively, click the Define Dependent Variable Unit button () to edit the unit directly in the Unit column, typing a unit to define the dependent variable quantity. The quantity column then contains Custom unit.

Select the Source term quantity that defines the unit for the source term f (the unit for the right — and left — side of the PDE). Custom unit is the default quantity (with m^-2 in the Unit column). Click the Select Source Term Quantity button () to open the Physical Quantity dialog box to browse to find a physical quantity to use. You can also type a search string in the text field at the top of the dialog box and then click the Filter button () to filter the list of physical quantities. For example, type potential and click the Filter button to only list physical quantities that represent some kind of potential. Alternatively, click the Define Source Term Unit button () to edit the unit directly in the Unit column, typing a unit (for example, W/m^3 or A/m^3) to define the dependent variable quantity. The quantity column then contains Custom unit.

Enter the Number of dependent variables (the default is 1) and set the field and dependent variable names. The default Field name and Dependent variables name for a single scalar PDE variable is u. If the Field name coincides with the name of another field of the same unit and number of components, the two fields (and the interfaces which define them) share degrees of freedom and dependent variable names.

Select a Shape function type (finite element type): Lagrange (the default), Hermite, Discontinuous Lagrange, Nodal discontinuous Lagrange, Discontinuous scalar density, Bubble, or Gauss point data.

To display additional settings in this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box.

If you have added a Deformed Geometry or Moving Mesh interface, there is also a Frame list for specifying the frame for differentiation and quadrature. Choosing the frame can be needed if you want to write your own mesh smoothing or regularization equations when working with a deformed geometry. Select Geometry, Mesh, Spatial (the default), or Material from the Frame list.