Periodic Condition

The node adds a periodic boundary condition that can be used to reduce the model size by using symmetries and periodicities in the geometry and physics interfaces being modeled. This feature works well for cases like opposing parallel boundaries. In other cases, use the section to control the destination. By default, it contains the source and destination selection that COMSOL Multiphysics identifies. The periodic condition automatically defines a mapping between the source xs and the destination xd points on the boundaries.

Boundary Selection


	The software usually automatically identifies the boundaries as either source boundaries or destination boundaries, as indicated in the selection list. This works fine for cases like opposing parallel boundaries. In other cases, right-click Periodic Condition and select Manual Destination Selection to control the destination. By default it contains the selection that COMSOL Multiphysics identifies.

Destination Selection

This section is available for specifying the destination boundaries, if needed, when the option is selected in the context menu for the node. You can only select destination boundaries from the union of all source and destination boundaries.

Periodicity Settings

Select a : (the default), , (Bloch periodicity), , or .

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For the values of the field variables at destination are set equal to the source: p(xd) = p(xs), u(xd) = u(xs), and T(xd) = T(xs). If the source and destination boundaries are rotated with respect to each other, a transformation is automatically performed, so that corresponding velocity components are connected.

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For Antiperiodicity the values of the field variables on the destination are set equal to the values on the source with the sign reversed: p(xd) = −p(xs), u(xd) = −u(xs), and T(xd) = −T(xs). If the source and destination boundaries are rotated with respect to each other, a transformation is automatically performed, so that corresponding velocity components are connected.

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For , also known as Bloch periodicity, enter a kF (SI unit: rad/m) for the , , and coordinates (3D components), the and coordinates (2D axisymmetric components), or and coordinates (2D components). This is the wave number of the excitation.

This condition is used to model infinite periodic structures with nonnormal incident pressure fields or excitations. Use it to model, for example, a large perforated plate with an oblique incident wave with wave vector k (and set kF = k) by only analyzing one hole or one subset of holes that is periodic.

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For select a : (the default) or . For enter a value for θS (SI unit: rad). Enter an m (dimensionless).

This condition is used to model any geometry that has a cyclic periodic structure such as a microphone or a loudspeaker driver. Setting the azimuthal mode number determines what mode is analyzed. The response of the full system to an external excitation is in general a linear combination of many different modes.

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For select the check box for any of the field variables as needed. Then for each selection, choose the — or . If the source and destination boundaries are rotated with respect to each other, a transformation is automatically performed, so that corresponding velocity components are connected.

In the time domain, both the and the boundary conditions reduce to the continuity condition.


	To get correct behavior of the Periodic Condition, in particular the Floquet periodicity and the Cyclic symmetry conditions, it is recommended that the source and destination meshes are identical. This can be achieved using the Identical Mesh mesh feature. When the Periodic Condition stretches across regions with a mix of default material models, PMLs, background pressure fields, or background acoustic fields, it is recommended to add one Periodic Condition for each set of such boundaries.

Constraint Settings

To display this section, click the button (

) and select in the dialog box. For information about the section, see Constraint Settings in the COMSOL Multiphysics Reference Manual.

Excluded Edges/Points

To display this section, click the button (

) and select in the dialog box. See Suppressing Constraints on Lower Dimensions for details.

Orientation of Source

To display this section, click the button (

) and select in the dialog box. For information about the section, see Orientation of Source and Destination in the COMSOL Multiphysics Reference Manual.

Orientation of Destination

This section appears if the setting for in the section is changed from the default value, , and is selected in the dialog box. For information about the section, see Orientation of Source and Destination in the COMSOL Multiphysics Reference Manual.

Mapping Between Source and Destination

To display this section, click the button (

) and select in the dialog box. For information about the section, see Mapping Between Source and Destination in the COMSOL Multiphysics Reference Manual.