A COMSOL Multiphysics® simulation typically includes one or more field quantities in its output. Depending on the number of field quantities, the geometry’s complexity, and the mesh density required for valid results, simulations can include millions of degrees of freedom (DOFs). Oftentimes, storing one or more scalar quantities or the results on a small geometry part is sufficient. Here, we explore tools for storing selected output quantities and minimizing model file sizes and the time required to display this data.

### Two Options for Storing Relevant Simulation Output

COMSOL Multiphysics provides two ways for you to include only selected parts of a solution in your output. The first option is to define one or more selections, including the points, boundaries, or domains of interest, so you can restrict the output from the study to only include the fields in the parts of the geometry that those selections define. This method is straightforward and suitable if you are only interested in the simulation output within a certain part of the geometry, where you can perform postprocessing and access the fields and derived quantities as usual.

Note that if you store the solution for some boundaries or points, only the solution fields (the dependent variables) are available using this method. This means that derivatives and quantities that include derivatives, such as stresses and fluxes, are not available as they require that the solution is also available in the domain. If you are interested in storing some derived values such as stresses on just a few boundaries or points of interest, you will want to use our second option.

The second option is to add an *ODE and DAE* interface to define a new dependent variable, to which you can transfer the quantity of interest. The quantity of interest could be a global scalar quantity, such as the average or maximum of some field, or it could be the field value along some boundary. (In the latter case, using a selection provides an easier way of achieving the same result.) This method is useful in situations where the output of interest is a global scalar value that you transfer to a single degree of freedom as a variable within a simple algebraic equation. As mentioned above, it is also useful if the quantity of interest is a derived value based on derivatives, such as stresses and fluxes.

### Creating a Selection to Store Selected Parts of a Solution

To only store the solution in a selected part of a geometry, create a named selection in the model component. To do so, right-click *Definitions* and choose a selection from the *Selections* submenu. An *Explicit* selection is simple to use if you want the selection to include some specific geometric entities — for example, domains, boundaries, or points. You can give the selection node a descriptive label like *Surrounding Air* or *Substrate Contact*. You can use several selection nodes to represent different parts of the geometry and combine them, either when determining what to store in the output or by creating another selection node that implements a Boolean operation, such as a *Union* or an *Intersection* selection node. Use one or more of these created selections in the study step settings to define the parts of the geometry for which the solution will be stored.

#### Example: A Selection for Storing the Deflection on the Top Surfaces of a Mechanical Design

In a solid mechanics simulation, the value of the deflection (displacement) on one or more specific surfaces or points of interest can provide valuable information, which may be sufficient for you as the output from a simulation. The following plot, for instance, indicates the selected top surfaces on the model geometry for a feeder clamp within the Graphics window.

*Selected surfaces for a solid mechanics simulation.*

To store only the solution on those surfaces (boundaries), create an *Explicit* selection with the input entities set to the four top surfaces within the geometry where you want to store the solution. If a surface or point is not part of the created geometry, you can add extra *Curve* or *Point* nodes in the geometry sequence to divide a boundary or add a point (and a mesh node) at the desired location. The settings for the *Explicit* selection node appear as shown below.

Explicit *selection node settings.*

Here, the label has been changed to *Deflection Surfaces* to reflect what the selection contains.

You can now modify what to store in the output. In the Settings window of the *Study* step node, locate and expand the *Values of Dependent Variables* section. This section contains *Store fields in output* settings, where you can choose *For selections* from the drop-down menu. You can then click the *Add* button to open a list with available selections. In this case, choose the *Deflection Surface* selection and click *OK*.

*Settings for storing the deflection for the selected surfaces in the geometry.*

Now you can run your simulation. The only output will be the solution on the top surfaces, which you can visualize using a *Surface* plot.

*The displacement in the* y* direction on the selected surfaces in the geometry. For the rest of the geometry, there is no solution output.*

For the solution at points, you can postprocess the output using a *Point Evaluation* node under *Derived Values* and display the total displacement, for example. You can also use a *Point Graph* node in a *1D Plot Group* to plot the displacement versus time in a time-dependent simulation or a parameter value in a parametric sweep.

### Creating a Variable of Interest to Store in the Output

If you are interested in a scalar quantity, you only need a single degree of freedom (variable) that represents that quantity in the output. You can create such a variable as a simple algebraic equation using a global equation defined via the *Global ODEs and DAEs* interface. This interface and similar physics interfaces for defining ODEs and DAEs on domains or at points, for instance, are available under *Mathematics > ODE and DAE Interfaces* in the *Add Physics* window and in the Model Wizard. In the Settings window for the *Global Equations* node, define the name of the variable and the simple equation that sets it to the scalar quantity that you want to include in your simulation output.

Scalar coupling operators are important features in COMSOL Multiphysics to utilize for this purpose as well. With these powerful tools, you have the ability to create scalar quantities that are made globally available within the model.

#### Example: A Variable that Represents the Average Temperature

Say that you are primarily interested in the average temperature within the model geometry. To extract its value, add an *Average Coupling Operator* (`aveop1`

, for example), defining it to be valid in the entire geometry (all domains) or in the domains of interest. You can then use this operator in a global algebraic equation to make it available in the simulation output as a scalar variable. If you want to store the maximum temperature instead, you can use a *Maximum Coupling Operator*.

The equation that the *Global ODEs and DAEs* interface solves for is

In this case, however, the equation should only set the variable equal to the average temperature. As such, it is sufficient to enter `aveop1(T)-avtemp`

if you have called the variable in the algebraic equation `avtemp`

. Remember that the *Global ODEs and DAEs* interface sets the expression to zero to form the equation, thus solving the simple equation ` avtemp = aveop1(T)`

. Here, *T* represents the temperature field in the geometry, which is the dependent variable that you solve for but don’t want to include in the output. The following screenshot shows the Settings window for a *Global Equations* node in the *Global ODEs and DAEs* interface for this case.

Global Equations *node settings for creating a variable to store.*

Notice the *Units* section within the Settings window shown above. To avoid unit inconsistencies and to evaluate the created variable with the correct units, you should adjust the respective units for the dependent variable and for the source term.

Your final step is to set up the simulation so just the new scalar variable that you have defined is stored in the output. The following plot shows the average temperature in a geometry for a time-dependent simulation as a *Global* plot defined in a *1D Plot Group*.

*The mean (average) temperature versus time, computed as a single scalar output from a time-dependent simulation.*

### Controlling What Is Stored in the Output

In the study that you want to perform, first make sure that you have access to the solver configurations by right-clicking the main *Study* node and choosing *Show Default Solver*. Select *Solver Configurations > Solution > Dependent Variable* to access the settings for the dependent variables. In the cases above, there will be two nodes: a *Field* node (temperature) and a *State* node (average temperature). The first node represents the full temperature field in the geometry, while the second node represents the variable for the average temperature.

Click the *Temperature* node to display its Settings window. At the bottom of the *General* section, clear the *Store in output* check box so that the solver no longer stores the temperature field in the output.

*Clearing the* Store in output *check box within the* Temperature *node settings.*

When you have computed the solution, the scalar quantity will be available as a variable that you can display in a table using a *Global Evaluation* node. You can also plot a *Global* graph plot to show the deflection versus time or the mean temperature versus some parametric solutions. Since there are no field solutions, any plots that show such variables, or quantities using such variables, will appear with values of zero.

#### Example: An Algebraic Equation for the Equivalent Stress on the Top Surfaces

Let’s revisit our feeder clamp model to show how to use an algebraic equation to store the equivalent stress (von Mises stress) values on the top surfaces. To do so, add a *Boundary ODEs and DAEs* interface, available under *Mathematics > ODE and DAE Interfaces* in the *Add Physics* window and in the Model Wizard.

In the Settings window for the main *Boundary ODEs and DAEs* interface, use the same *Deflection Boundaries* selection for the top surfaces. Make sure to specify the units so that they are compatible with a stress quantity. You can do so by choosing *Stress tensor* as the quantity for the new dependent variable and for the source, which is the von Mises stress from the main *Solid Mechanics* interface.

*The settings for the* Boundary ODEs and DAEs *interface, set up for a mechanical stress quantity.*

In the *Distributed ODE* subnode, you define the algebraic equation that sets the new dependent variable *bndstress* (defined on the top surfaces only) equal to the predefined variable for the von Mises stress, *solid.mises*, from the *Solid Mechanics* interface: `bndstress-nojac(solid.mises)`

.

The `nojac()`

operator is required, since we do not want this equation to contribute to the Jacobian (the system matrix) for the full model. You enter this expression in the source term and set all other coefficients to zero to solve the equation `0 = bndstress-nojac(solid.mises)`

(that is, ` bndstress = nojac(solid.mises)`

).

*The settings in the* Distributed ODE *node for defining an algebraic equation for the boundary stress.*

Before solving, you have to clear the *Store in output* check box in the *Displacement field* node under *Dependent Variables* in the solver sequence. You can then compute the solution and only store the stress values on the top surfaces, which you can plot using a *Surface* plot.

*A plot of the von Mises stress, stored only for the top surfaces.*

### Optimize Your Simulations with Storing Solution Techniques

As we have shown here today, with just a few simple steps, you can set up a simulation where only part of the fields computed for, or even just one or a few scalar quantities of interest, can be stored in the output. These modeling techniques can significantly reduce your model file size and the time it takes to calculate and display these scalar quantities of interest. This is especially true if you plan to make simulations that include large parametric sweeps or long, detailed time-dependent studies.

To learn about other tools in COMSOL Multiphysics that are designed to optimize your simulation workflow, browse other posts within our Core Functionality category on the COMSOL Blog. If you have further questions relating to the modeling techniques presented here, please feel free to contact us.

## Comments (6)

## Andrii Lesiuk

September 3, 2016Hi. Is this option available only in version 5.2 or in earlier version 5.1 as well? I mean the method with Selections.

## Magnus Ringh

September 5, 2016Hi Andrii, yes, the method with Selections in available from version 5.2. If you want to upgrade to the latest version of COMSOL Multiphysics (version 5.2a), please contact your local COMSOL representative.

## Zhichao Jia

September 5, 2016Good work!!!

## Tarkes Dora

March 12, 2017Can anyone suggest how to store all the eigenfrequencies/values ?

## Magnus Ringh

March 13, 2017Hi Tarkes, to store all eigenfrequencies or eigenvalues but not the corresponding field solutions, solve the eigenmode problem but clear the “Store in output” check box for the dependent values. You can then export the eigenfrequencies or eigenvalues (stored in the built-in variables “freq” and “lambda”, respectively).

## Mahmoud Elzouka

May 29, 2017Thank you for the article,

I have a quite relevant question:

How can I remove the solutions corresponding to certain eigenvalues?

Thanks