Dependent Variable Declaration
A Dependent Variable Declaration node () declares a dependent variable (field variable) used by the physics interface. This node does not make the interface add any shape functions for this variable, it just declares that a dependent variable exists. All dependent variables in a physics interface must have a unique identifier (or reference tag) within an interface. In most cases, you only solve for one type of physical quantity per interface, so the physical quantity works fine as a reference tag. If you need two or more dependent variables for the same physical quantity, it is necessary to append a unique tag to the reference tag.
You must use this reference tag when defining the actual shape functions for the variable, which you do under a feature or a property; see Dependent Variable Definition.
You can also use the same shapes as a dependent variable for constraints, and then you need the reference tag to point to the correct variable. The reason for using a reference tag instead of a variable name is that the dependent variable name can be changed in the Model Builder. In the Physics Builder, you can only declare a default name.
Add these subnodes: Dependent Variable Declaration, Initial Values, Component Settings, Disable in Solvers, and Hide in GUI.
To add a Dependent Variable Declaration, first add a Physics Interface or Multiphysics Interface, then:
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On the Physics Interface toolbar, click Dependent Variable Declaration ().
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Right-click the Physics Interface or Multiphysics Interface node and select it from the Variables submenu.
To find the definitions of the variable, click the Find Declarations of this Variable button () in the Settings window, or click the node and press F7, or right-click the node and choose Search > Find Definitions.
The Settings window has the following sections:
Declaration
Select a Dependent variable reference: Use physical quantity (the default) or Use physical quantity + tag.
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Keep the default Use physical quantity if you want to use the physical quantity as the reference.
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For Use physical quantity + tag you can specify an arbitrary unique tag. Enter the tag in the Unique tag field. This tag is added to the end of the name of the Physical quantity chosen. For example, if you choose Area (m^2) from the list and enter house in the Unique tag field, the name for the node (in brackets) in the Physics Builder changes to areahouse.
The Physical quantity list defines what quantity the dependent variable represents, including the unit. As mentioned previously, the physical quantity is also used to generate the unique reference tag for the dependent variable. In addition to the predefined and built-in physical quantities you can use locally defined physical quantities or physical quantities imported from an external resource:
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Select From built-in quantities (the default) from the Physical quantity list to choose a built-in physical quantity. To specify a physical quantity, click the Select Quantity button () to open the Physical Quantity dialog 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 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 Custom Unit button () to enter a unit (for example, m/s^2) in the text field (the physical quantity then becomes a Custom unit).
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Select Locally defined from the Physical quantity list to use one of the locally defined physical quantities, which you choose from the Link list. Click the Add button () to display a quick menu where you can select a source to add in to the list and use it as the current reference. A Confirm Operation dialog will appear and ask for confirmation if there is already a reference exist in the Link list. Click the Go to Source button () to move to the Physical Quantity node for the selected local physical quantity.
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Select Imported from external resource from the Physical quantity list to use physical quantities from another imported Physics Builder file, which you choose from the Imported file list. Click the Go to Source button () to move to the Import node for the imported Physics Builder file.
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Select Any unit (only check expression) from the Physical quantity list to accept any unit and only check the expression.
It you choose None from the list it is recommended to use the option Use physical quantity + tag in the Dependent variable reference list. As None is not a physical quantity, enter an explicit unit in the SI unit field. It is possible, in some contexts, to use arguments and values of user inputs to define the SI unit; this way you can enable dynamic units from arguments or other user inputs. There is also an operator, evalUnit, that you can use to parse units of known variables, typically dependent variables (example, evalUnit(dep.u)).
The Default variable name field declares the default name for the dependent variable, and the Description field has the descriptive text for the variable shown in analysis and variable listings.
Enter a LaTeX-encoded string in the Symbol (LaTeX encoded) field to define a symbol (\mu, for example, to display the Greek letter μ).
Select a Dimension: Scalar, Vector (3x1), Matrix (3x3), and Custom. For Custom, you can specify a nonstandard dimension (for example, 3x3x3 if you need a tensor of rank 3 with indices of dimension 3).
Do not use tensors of rank higher than 4 due to the rapid increase in memory usage.
Preferences
Select or clear the Show in plot menu and Announce variable to feature inputs checkboxes and edit their additional settings if required. See Preferences described for Variable Declaration.
Discretization
This section contains settings for defining the discretization levels that control the shape-function order used in the physics interface and the Discretization section of the physics interface instance. By default the parameter for the shape order is set automatically and includes five levels for order 1–5. You can also specify a default level (set to 2 by default). Use the Parameter list to specify if the discretization parameter name and description should be defined automatically (the default) or manually. This is the list in the physics interface instance that, in its automatic configuration, has the description Element order and has valid values Linear, Quadratic, and so on. Below the Parameter setting is a table with the following columns: Level, Level description, Shape order, Geometry shape function, and Lower level. This table controls the values that can be selected in the discretization parameter. Each row in this table represents a discretization level, which corresponds to a shape order for the dependent variable and an allowed value for the discretization parameter. Enter the value in the Level column and its description in the Level description column. Each level has a shape order, which you define in the Shape order column. Select the geometric shape order from the Geometry shape function list. The Lower level column’s value should point to a discretization level that has a shape function order that is smaller than the current one, so it needs to be a value that is present in the Level column. The Lower level setting is used by the multigrid preconditioner.
To support a varying, user-defined shape order, enter -1 in the Shape order column. The Level name could then be something like expr, the level description Shape expression, and the Geometry shape function set to Automatic. When using these settings, the physics interface will then show, in the Model Builder, the Shape order expression field where users can add the order expression. Remember that the shape function that is set in the corresponding Dependent Variable Definition node has to be one of the shape functions that support this setting (an hierarchical shape function).
In the Default level list, select the default level for the discretization parameter (default value: 2, for a quadratic order of the shape functions).
From the Geometry shape function rule list, choose a rule for determining the geometry shape function for the dependent variable. The following options are available
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 Prefer maximum order (0): Only let this variable choose the geometry shape function order if no other variable requires a maximum order.
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 Require maximum order if first variable (1) (the default): Let this variable require a maximum geometry shape function order if it is the first dependent variable for a physics interface.
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 Require maximum order for all variables (2): Let this variable require a maximum geometry shape function order no matter where it is in the list of dependent variables.
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 From expression: Let an expression, which you enter in the Rule index field that appears, evaluate to an integer representing one of the above rules. The integer for a rule appears within parentheses.
Select the Enable accurate boundary flux option checkbox to make the Compute boundary fluxes checkbox visible in the Discretization section of the physics interface instance. The On by default checkbox (selected by default) controls the default value of that parameter. Note that to make the computation of accurate boundary fluxes work as well as possible, it is also necessary to add Flux Definition nodes that define the flux for the dependent variable anywhere it is defined.
Advanced
This section contains advanced options that you do not have to change in most cases. In the Base vector system list, you can override the base vector system specified by the parent (for example, a feature or property) by choosing something other than the option Same as parent.
For tensors, choose a type from the Tensor type list: Normal tensor, Tensor density, or Tensor capacity. A tensor density is a concentration, for example, where it is multiplied with the volume factor. A tensor capacity is the inverse.
Choose Real or Complex (the default) from the Default value type list. This becomes the default choice when solving with splitting of complex degrees of freedoms (DOFs) into real-valued and complex-valued DOFs.
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Using Coordinate Systems
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Transformation Between Coordinate Systems