Periodic Condition

he 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 a subnode 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.

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 non-normal 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).

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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 optimize the performance of the Floquet periodicity and the Cyclic symmetry conditions, it is recommended that the source and destination meshes are identical. This can be achieved by first meshing the source boundary or edge and then copying the mesh to the destination boundary or edge. 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.