Frequency Domain, Modal Reduced-Order Model
A Frequency Domain, Modal Reduced-Order Model node () contains settings for a reduced-order model that uses a frequency domain modal method. See Modal Reduced-Order Models.
Click Export Reduced Model () to save the reduced-order model to file as COMSOL Reduced Model file (MPHROM-file). Note that export is only possible if all defined outputs are linear quantities.
The Settings window for a Frequency Domain, Modal, Reduced-Order Model node contains the following sections:
Usage
Here you specify whether the reduced-order model should have stateless or stateful interface. Choose Stateless (the default) or Stateful from the Interface list. 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.
Parameters
Here you specify the Frequency value to be used when evaluating outputs (when using the stateless interface) or generating reduced-order equations (in the stateful case). It is by default set to freq, which means that the reduced-order model will use the same frequency as the calling model in which it is used.
Model Control Inputs
The list in this section contains the reduced-order model input quantities that were set as active in the corresponding Model Reduction node’s Model Control Inputs section when the reduced-order model was created. For each model control input in the Variable column, specify a corresponding Expression to be used when evaluating outputs from the reduced-order model, or when using the stateful interface, when solving reduced-order equations. The default expression is the name of the corresponding reduced-order model input variable. The effect of this is that the reduced-order model will be evaluated for the same value of the input as is seen by the calling model in which it is used. This is usually the desired behavior.
Constraint Modes
The Constraint Modes section is only available when you have selected Stateful from the Interface list in the Usage section. The table in this section specifies constraints for the modal reduced-order model. Each row corresponds to a constraint mode in the basis, and also to a potential constraint on the reduced-order model.
The Modal Reduction solver classifies constraints in the unreduced model when training the reduced-order model according to whether they depend on a reduced-order model input or not. Constraints depending on more than one reduced-order model input are considered an error. Input-dependent constraints are then compared to the constraint modes. If a constraint can be satisfied by a single constraint mode, then that mode is considered to be input-controlled. Constraints that can be satisfied by more than one constraint mode are considered an error during training. Input-controlled modes are treated differently from other modes. There are four columns in the table: Constrained, Variable, Expression, and Description.
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The Variable column contains a variable name identifying the reduced-order model state associated with each constraint mode. The variable is defined as <rom>.state(<index>) for some index corresponding to the constraint mode’s position in the basis.
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The Expression column is the value to which the constraint mode state will be constrained, if the constraint is active. If the mode is input-controlled, then the Expression field will contain the name of the variable representing the expression specified for this input in the Model Control Inputs section, and the field will not be editable. Otherwise, its default value is 0.
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The Description column allows specifying the description to be used for the variable in postprocessing and menus. By default it will be ModeX, where X is the number of the constraint mode.
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The Constrained column determines whether the corresponding constraint mode will be constrained. When the constraint mode is input-controlled, the check box is selected by default; otherwise, it is unchecked.
The constraints defined by the settings in the Constraint Modes table are applied in a symmetric way directly on the constraint mode states. This has a few important implications:
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Since the constraint mode states multiply the constraint mode base vectors directly, their values depend on the scaling of the constraint modes. A given Expression will have different effect depending on the scaling of the corresponding constraint mode.
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Inhomogeneous constraints on the unreduced model that do not depend on any reduced-order model input are handled using a particular solution which is part of the basis but whose corresponding state is not solved for. If the particular solution is not orthogonal to the constraint modes, it will change the effect of enabling a constraint on the affected modes.
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Constraints on constraint modes added using this table will only force solutions reconstructed from the reduced-order model to respect the corresponding constraint if the constraint mode is orthogonal to all other modes. This is often the case, but it is not enforced.
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The symmetric application of constraints means that the equations of any dependent variables used in the Expression column of an active constraint will get a reaction term contribution. This may or may not be desired behavior.
Outputs
This section provides an overview of output quantities that the reduced-order model makes available for evaluation, both during solution and in postprocessing. These outputs are defined in the corresponding Model Reduction node’s Outputs section. The Variable column shows the variable names defined by the reduced-order model.
When Use output dependent variables is selected, the reduced-order model also declares the dependent variable names entered in the Dependent variable column. When the reduced-order model is part of another model, these dependent variables can be assigned the value of the corresponding output variable each time a solution is stored. If the reduced-order model has a stateless interface, this behavior is controlled by the Store output dependent variables setting in the Physics and Variables Selection section of each study step where the reduced-order model is used. If the reduced-order model has a stateful interface, this behavior is controlled by whether the reduced-order model is solved for in a given study step. Apart from the setting to solve for a reduced-order model with a stateful interface, these settings are only available for reduced-order models that have outputs.
Online Settings
This section displays a list of dependent variable fields that this reduced-order model can reconstruct. When the reduced-order model is used in a calling model, it defines an operator <rom_name>.eval(<expr>), where <rom_name> is the Name of the reduced-order model and <expr> is an arbitrary expression.
Field reconstruction is not possible in a Reduced Model node that uses reduced-order model data saved in a COMSOL Reduced Model file and then imported. The original model data needed is then not available.
Use the Load factor to scale the constant part of the right-hand side of the frequency-domain model. This scaling in practice scales all loads, source terms, and constraint right-hand sides with the specified factor.
Information
This section contains information about the reduced-order model: Which study it was created from, which solution data that contains the reduced model data, the model reduction type, the unreduced study type, and some general information about the model reduction.
Under Matrices, all matrices that the reduced model solution includes are listed. The listed vectors and matrices can be accessed using the COMSOL API.
Build Log
The build log contains output from the reduced-order model solution process, similar to other solver logs.