COMSOL 6.3 - POD Reduction

) node to perform a model order reduction using a proper orthogonal decomposition algorithm.

Use the list to specify if the settings are synchronized with the corresponding study step, or select to specify all settings locally.

Use the list to select the basic study type. Select:

•

to perform a frequency-domain simulation using a reduced model. Then continue defining the settings For Frequency Domain.

•

to perform time stepping using a reduced model. Then continue defining the settings For Time Dependent.

From the list, choose a unit (default: Hz).

Specify the frequencies to use in the field. Click the button (

) to define frequency values, if desired.

Use the list to specify the type of linear behavior. Select:

•

(the default setting) to use a linear solver with the same linearization point for both residual and Jacobian computation, which corresponds to one step in Newton’s method.

•

to use a linear solver that computes the Jacobian in the same way as the option but uses a zero solution when computing the residual. It is useful for small-signal analysis and similar applications where the variations around a linearization point are of interest.

The values in the field is used to determine the number of POD modes so that the relative error of approximating training solution with POD modes is within the specified threshold (default: 0.01).

From the list, choose a unit (default: s).

Then use the field to enter a vector of times that define the time span for the simulation. Click the button (

) to define time values, if desired. Output from a simulation includes the times given in this field and the corresponding solutions. In addition, for a time-dependent study type, the following settings are available:

Use the field to enter a positive number (default value: 0.01). The relative tolerance is used by the solver in each time step to control the relative error. The absolute tolerance settings below work in the same way as for the time-dependent solver, but internally the full length absolute tolerance vector is transferred to the modes by the same transformation (projection) as is used to transform the problem to reduced form (the eigenmodes).

From the list choose , , or . If it is , it means that initial data will be considered in the base extension. You can use for rare cases where the automatic method does not add the initial values to the basis but it makes sense to do so. If it is , then initial data will no be considered. The default is , which means that the initial data will be considered in the base extension only if it is large enough to make a difference.

The values in the field is used to determine the number of POD modes so that the relative error of approximating a training solution with POD modes is within the specified threshold (default: 0.01).

From the list, choose a solution for POD modes training, which is synchronized from the setting in the study step.

Use the list to specify how to group variables for POD modes construction. Select:

•

to customize the grouping of dependent variables. A group can be added or removed by clicking buttons under the table. If you would just to modify the list of dependent variables in a group, click in the column and edit the content through the list below.

Once the grouping of dependent variables is determined, a reduced-order basis is constructed by concatenating POD modes computed for each group.

Use the list to specify which solution to be used when constructing the reduced model.

Use the list to specify which of the constraint modes present in the solution to include when constructing the reduced model. The default setting is , and the solver then uses all available constraint modes. Select to enter a space-separated list of constraint modes numbers in the field.

From the list, choose to create a new reduced-order model, or choose any existing reduced-order model.

From the list, if you chose from the list, choose (the default) or . In the former case, the reduced-order model acts as a black box that uses an internal solver and does not expose its state. In the latter case, the reduced-order model exposes a set of reduced-order equations and state DOFs to the solver used for the calling model, and you can choose whether to solve for the reduced-order model in the same way as for a physics interface.

The checkbox is selected by default to enable reconstruction of the unreduced solution vector. Clear it if you need to save memory; for the ROM to be capable of reconstruction, the modal basis must be stored.

In this section you can define constants that can be used as temporary constants in the solver. You can use the constants in the model or to define values for internal solver parameters. These constants overrule any previous definition (for example, from Global Definitions). The constant values are expressions and can, for example, include the range() operator, units, and global expressions. The constant name can be a new or an existing global parameter. The constant is temporary in the sense that it is only defined during the solver run. You cannot override parameters used in the following parts of the model:

Also, the Parametric and Time Dependent solvers overrule any definition of solver constants.

Constants settings for a solver node do not carry over to postprocessing.

Some examples of when it can be useful to define constants for a solver:

Click the button (

) to add a constant and then define its name in the column and its value (a numerical value or parameter expression) in the column. By default, any defined parameters are first added as the constant names, but you can change the names to define other constants. Click (

) to remove the selected constant from the list.

Select the checkbox if you want the warnings to remain in the log for troubleshooting or other use.