The Coefficient Form PDE Interfaces
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 Coefficient Form PDE interface is also available in other forms from the PDE interfaces>Lower Dimensions submenu: Coefficient Form Boundary PDE, Coefficient Form Edge PDE, and Coefficient Form Point PDE. Also see Modeling with PDEs on Boundaries, Edges, and Points.
The Coefficient Form PDE discusses the formulation and settings pertaining to the coefficient form, as well as the general PDE terminology used in COMSOL Multiphysics.
Settings
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).
Units
By default, the PDE interfaces are dimensionless, but units can be defined for the dependent variable and the source term (that is, the overall left and right side of the equation). The units for these quantities — in combination with the units for length and time — fully define the units for all other terms in the equations. Select the units from a list of physical quantities or enter the unit directly.
From the list, select the Dependent variable quantity that defines the unit for the dependent variable u. The default is Dimensionless [1]. Select None to enter a unit (for example, K, m/s, or mol/m^3) in the Unit field.
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). None is the default quantity, and m^-2 is the default Unit, which is consistent with a dimensionless dependent variable. Enter another unit (for example, W/m^3 or A/m^3) in the Unit field as needed.
For the Classical PDE>Heat Equation interface, the Dependent variable quantity defaults to Temperature (K) and the Source term quantity defaults to Heat source (W/m^3).
Dependent Variables
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.
A 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 when two interfaces share a common field name.
Discretization
To display this section, click the Show button () and select Discretization.
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.
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.
For an example of the use of units in a PDE interface, see Shell Diffusion in a Tank: Application Library path COMSOL_Multiphysics/Equation_Based/shell_diffusion.