Equation View
Equation View () is a subnode available for all physics feature nodes. To display these subnodes, click the Show More Options button () and select Equation View from the Show More Options dialog box.
The Settings window for Equation View contains detailed information about the implementation of each physics feature: variables, shape functions, weak-form equation expressions, and constraints.
To update the values in the Settings window for Equation View to reflect the latest changes in a physics feature, click the Refresh Equations button () in the Settings window’s toolbar.
Editing the predefined expressions for variables, equations, and constraints means that the equations are altered and that COMSOL Multiphysics solves the model using the new expressions.
You can edit the expressions or values of variables, weak-form expressions, and constraints in the corresponding tables under Variables, Weak Expressions, and Constraints, respectively. This makes it possible to introduce custom changes to the equations and variable definitions. If the expression that defines a variable, for example, does not fit inside of the text field, a tooltip displays the entire expression. Press Ctrl+Space or use the Insert Expression button () below the tables to choose from a number of applicable variables, parameters, functions, operators, and constants that you can insert into the expression at the position of the cursor. In the table of variables under Variables, you can click any of the column headers to sort the table contents alphabetically based on the contents of that column (in ascending order; click again for descending order; click yet again to restore the original order).
For a changed definition of a variable or a change to a weak-form expression or constraint, a warning icon () appears in the leftmost column, and a small padlock is added to the lower-right corner of the icon for the physics node where you have made modifications in its equation view. To restore only the change in the selected variable, weak-form expression, or constraint, click the Reset Selected button () under the table in the Variables, Weak Expression, or Constraints section. To reset all changes in the equation view, click the Reset All button () in the Settings window’s toolbar. If no changes remain, the padlock disappears from the corresponding physics node. An orange color for the expression that defines the variable is a warning that the unit of the expression does not match the expected unit for the variable that it defines. To store all information in the tables under Variables, Shape Functions, Weak Expressions, or Constraints to a text file, click the corresponding Save to File button ().
For information about the Equation displays available, see Physics Nodes — Equation Section.
Study
From the Show equation view assuming list, choose No study or any of the available studies. The equation view of the parent feature is then recomputed with the assumption that the selected study step was solved. This operation also updates all children to the parent feature, so the lists in their equation views are also updated. When solving a study (or study step), the list also changes to represent the last computed study step. The default is No study and represents a default behavior, which computes the equations without any study type information. The equation form used is then undefined and depends on the physics that the parent feature belongs to. The equation view reverts to No study if you change some setting in the parent feature to indicate that the equation view no longer represent a specific study step.
Variables
This section has a table with the variables that the physics node defines. The table includes these columns:
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Name: the name of the variable.
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Expression: the expression, using COMSOL syntax, that defines the variable.
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Unit: the unit for the variable (in the active unit system). If the unit of the expression does not match the unit of the variable, the expression is displayed in orange.
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Description: a description of the variable.
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Selection: the geometric entities (domains, boundaries, edges, or points) where the variable is defined (Domain 1, for example).
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Details: this column contains some details about the variable’s behavior. See About the Details Column below.
If you click a single variable, its selection, as indicated in the Selection column, appears in the Graphics window.
Shape Functions
This section has a table with the dependent variables that the physics node defines and their shape functions. This is primarily applicable to equation model nodes; for most physics nodes such as boundary conditions, the table is empty. The table has these columns:
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Name: the name of the variable.
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Shape function: the type of shape function (element) for the variable (for example, Lagrange for Lagrange elements, which are the most common elements).
Selecting an Element Type
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Unit: the unit for the variable (in the active unit system).
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Description: a description of the variable.
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Shape frame: the frame type (typically either a spatial or a material frame) for the shape function.
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Selection: the geometric entities (domains, boundaries, edges, or points) where the shape function is defined (Domain 1, for example).
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Details: This column contains some details about the shape function’s behavior. See About the Details Column below.
Weak Expressions
This section has a table with the weak-formulation equation contributions that the physics node generates. The table consist of the following columns:
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Weak expression, the equation expressed in a weak formulation. It is possible to modify these expressions, but you then override the equation as specified by the physics interface, and a warning appears in the leftmost column of the table.
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Integration order, the order for the integration of the weak expression (see integration order in the Glossary). Polynomials of at most the given integration order are integrated without systematic errors. For smooth expressions, a sufficient integration order is typically twice the order of the shape function. For example, the default integration order for second-order Lagrange elements is 4. You can modify the integration order if desired. A warning then appears in the leftmost column of the table to indicate that the predefined order has been changed.
See the following blog post for information about modifying the integration order: https://www.comsol.com/blogs/introduction-to-numerical-integration-and-gauss-points/
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Frame, the frame type (typically either a spatial or a material frame) used when integrating the expression.
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Selection: the geometric entities (domains, boundaries, edges, or points) where the weak expression is defined (Domain 1, for example).
Each equation contribution appears on its own row under Weak expression, but the order is not significant.
The PDE interfaces and the ODEs and DAEs interfaces do not display any weak expressions. They are either implemented using strong formulations, directly display the weak formulation, or define equations discretized in the time domain only.
Constraints
This section has a table with the constraints that the physics node generates. This is typically the case for boundary conditions of constraint types, such as prescribed displacements, temperature, or velocities. Many other physics nodes do not generate any constraints, and the table is then empty. The table consists of the following columns:
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Constraint: the expression for the constraint.
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Constraint force: the expression that defines the associated constraint force, which is typically the test function of the constraint.
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Shape function: the type of shape function (element) for the constraint (for example, Lagrange for Lagrange elements).
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Selection: the geometric entities (domains, boundaries, edges, or points) where the constraint is defined (Boundaries 1–5, for example).
About the Details Column
The Details column shows some information about the behavior of variables and shape functions. For variables:
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An empty cell indicates that overlapping contributions are overridden.
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+ operation indicates that overlapping contributions are added.
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For some variables, Meta indicates that the variable definitions are not fully updated until you solve the model. It is therefore not possible to edit the expressions for such variables.
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In rare cases, other operations (* operation, for example) can occur.
For shape functions:
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Slit means that the shape function creates a slit for the degree of freedom.