Dependent Variables

The node (

) handles initial data and scaling for the dependent variables that you solve for as well as how to compute dependent variables not solved for. The methods are applicable to the dependent variables present as Field subnodes (

) under the Dependent Variables node. The Field node name matches the name of the variable.

	The Dependent Variables node automatically updates the Field nodes. So, if the study type for the solver changes or if you use a different study type, then the Field nodes change accordingly. Also see Scaling of Variables and Equations for information.

To plot and evaluate the initial values for the dependent variables, right-click the node and choose (

) or click the button in the toolbar (this is similar to the option for the main Study nodes). Click the button (

) in the toolbar to refresh the dependent variable list, which might be useful if you need to manually edit the dependent variable settings (with manual scaling, for example).

The window has the following sections:

Use the list to specify if the settings are synchronized with the corresponding study step. Select to specify all settings locally in the node’s window. This setting relates to the Field node’s setting to .

This section is only available if you select from the list.

Use the list to specify how to compute initial values for the dependent variables that you solve for. Select:

•

to use initial values as specified by a solution object. Use the list to specify what solution object to use (directly or as part of the initial expression). Select:

Depending on the study type for the selected solution object, you can choose different solutions from a list underneath the list:

•

For a Stationary study, from the list, select (the default) to use the last (typically the only) solution, select to use the first (typically the only) solution, select to use the last (typically the only) solution, select to use all (typically just one) solutions from that study, select to use a specific solution number that you specify, or select to use the first (typically the only) solution. If you use a parametric continuation of the stationary study, there can be additional solutions to choose from.

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For a Time Dependent study, from the list, select (the default) to use the solution for the last time, select to use the first solution, select to use the last solution, select to use all solutions from that study, select to specify a time in the text field that opens and use the interpolated solution at that time, select to use a specific solution number that you specify, or select one of the output times to use the solution at that time.

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For an Eigenvalue study, from the list, select (the default) to use the first eigenvalue and its associated eigensolution, select to use the first solution, select to use the last solution, select to use all solutions from that study, select to use a specific solution number that you specify, or select one of the eigenvalues to use the corresponding eigensolution.

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For a Parametric Sweep or Frequency Domain study, from the list, select (the default) to use the first parameter value set or frequency, select to use the first solution, select to use the last solution, select to use all solutions from that study, select to use a specific solution number that you specify, or select one of the parameter value sets or frequencies to use the corresponding solution.

Use the list to specify how to scale the variables solved for. Select:

•

to get an automatically determined scaling (the default), which works well for most models. It is initially based on the magnitudes of the elements in the Jacobian and mass matrices. For nonlinear problems these scales are recomputed based on the magnitude of the solution iterate.

•

to get a scaling that is determined from the initial values. Use this if the components of the initial values give a good estimate of the order of magnitude of the solution.

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to manually enter a scaling if you know the order of magnitudes of the variables in advance. For instance, suppose that a model solves for a dependent variable u, and that the values of u are on the order of 10−4. To use this knowledge, type 1e-4 in the field. The solvers then internally use a solution vector rescaled to the order of 1 for u. If there is more than one dependent variable that the model solves, they are all rescaled with the same factor.

	The automatic scaling in COMSOL Multiphysics does not work when using the nonlinear stationary solver and a field or state has an identically zero solution (the solver does not converge). In this case use Manual or None.

The scaling method also can be specified for each dependent variable in the window for the variable’s node. For more information about scaling, see Scaling of Variables and Equations.

From the list choose (the default) or . For time-dependent problems, the Automatic residual scale is updated when a sufficiently large change in the residual is detected during time stepping. You can then enter a value in the field, so that the residual scale updates automatically when a sufficiently large change in the residual is detected. The default value is 100. For Manual, enter a scale factor in the field (default: 1). For the scaling, see Termination Criterion for the Fully Coupled and Segregated Attribute Nodes. A manual tuning of the scale factor may help convergence in some cases where the solution does not converge when using automatic scaling does not work (this could be the case for some contact problems, for example).

This section is only available if you select from the list.

These settings are only applicable if there are dependent variables in the model that you do not solve for (in the case, for example, when solving a multiphysics model using a sequential approach). Then use the list to specify how to compute the values of variables not solved for. Select:

•

to use initial values as specified by a solution object. Then use the list to specify what solution object to use if has been set to . Select:

Depending on the solution object to use, you can choose different solutions to use. If a solution has nodes for storing solutions in its sequence, you can choose which solution to use using the list. The value is the value that the solution has at the moment the value is read. The other values are the values stored in the respective nodes of the sequence. Choose to enter the index for the solution that you want to use. The index can be a global parameter that is swept in a Parametric sweep with solution number inputs to it.

	See Solution List Options by Study Type for additional choices based on study type and then available in this section.

You select whether to solve for a variable or not by left-clicking a subnode (

) and then select or clear the check box in the window.

The settings in this section makes it possible to control values of parameters in models when used as constants in initial values. By default, those values are controlled automatically by the study step, and the settings are not available unless you choose from the list in the section above. The value is updated as soon as a subsequent solver gets its times, frequencies, or parameter lists updated. The value for each parameter is the first value in each list. You can override this automatic behavior by choosing from the list. You can then add parameters as constants to the column and the corresponding initial value as a parameter expression in the column. The constants defined here must be used in an initial value expression for the dependent variables.