Built-in Operators for Evaluation in the Layered Material
Evaluation Along the Layered Material
The extra dimension temperature T can be evaluated along the layered material by using the atxd1 operator on the extra dimension, with the expression xdimTag.atxd1(xd, expr), where:
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xdimTag is the extra dimension tag. For example, it may be slmat1_xdim, when a single layer material (slmat1) is selected in the Layered material list of the Thin Layer node. This tag can be deduced from the Selection column of the Equation View subnode of the node applied on the thin layer, by clicking the Show More Options button () on the Model Builder tool bar and selecting Equation View.
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xd is the coordinate in the extra dimension. It varies from 0 to slmat1.th, which is the total thickness of the layered material. By convention, xd=0 corresponds to the downside of the boundary where the thin layer is defined, whereas xd=slmat1.th corresponds to its upside. Upside and downside settings can be visualized by plotting the global normal vector (nx, ny, nz), that always points from downside to upside. See Tangent and Normal Variables in the COMSOL Multiphysics Reference Manual. Note that the normal vector (ht.nx, ht.ny, ht.nz) may be oriented differently.
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expr is the quantity to be evaluated at the point xd. For example, it can be set to T to evaluate the temperature. There are others postprocessing variables defined on the extra dimension that can be found in the Equation View subnode of the node applied on the thin layer.
Figure 3-2: Schematic representation of a 2D geometry with a thin layer composed of three layers, with an evaluation of the results along the layer at the coordinate xd.
This operator can be used to define manually a slice plot in the layered material. In 2D and 2D axisymmetric geometries, the slice is represented in a line graph under a 1D plot group, whereas it is a surface plot for 3D geometries.
Evaluation Through the Layered Material
The extra dimension temperature T can be evaluated through the layered material, at a specific point (x0, y0) or (x0, y0,z0), by using the operators atxd1 in 2D and 2D axisymmetric geometries, and atxd2 in 3D geometries. Note that this time the operators are used on the component and not on the extra dimension.
In 2D and 2D axisymmetric geometries, use compTag.atxd1(x0, y0, expr), where:
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 compTag is the component tag. In most cases, this tag is comp1. It is possible to check it in the Properties window of the component node (display it by right-clicking on the node and selecting Properties).
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 x0 and y0 are the coordinates of the point in the base geometry that belongs to the boundary linked with the extra dimension. Note that these are 2D coordinates from the global coordinate system and not curvilinear coordinates.
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 expr is the quantity to be evaluated at the point (x0, y0). For example, it can be set to T to evaluate the temperature.
In 3D geometries, use compTag.atxd2(x0, y0, z0, expr), where:
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 compTag is the component tag. For example, it can be comp1.
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 x0, y0, and z0 are the coordinates of the point in the base geometry that belongs to the boundary linked with the extra dimension.
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 expr is the quantity to be evaluated at the point (x0, y0, z0). For example, it can be set to T to plot the temperature. Note that here too, these are 3D coordinates from the global coordinate system and not curvilinear coordinates.
Figure 3-3: Schematic representation of a 2D geometry with a thin layer composed of three layers, with an evaluation of the results through the layer at the point (x0,y0).
This operator can be used to define manually a through thickness plot in the layered material. For all dimensions, the section is represented in a line graph under a 1D plot group. In order to use this, the Dataset selected in the Data section of the 1D plot group has to select the extra dimension as component. One method is to duplicate the default Solution node under the Datasets node, set the Component of the new node to the extra dimension, and use this new dataset into the 1D plot group, with the domains of the extra dimension selected.
Integration in the Layered Material
The integral of a variable in the layered material defined on a thin layer boundary can be evaluated by using the xdintopall operator, with the following expression: featTag.xdintopall(expr), where:
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featTag is the tag of the physics node defining the operator xdintopall. For example, for a Thin Layer node in the Heat Transfer interface, it may be ht.sls1.
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expr is the quantity to be integrated. For example, it can be set to T to evaluate the temperature.
Localization of the Evaluation in the Thin Layer
For a layerwise computation, the atonly operator should be used to multiply the expression to be evaluated. This operator, applied to the extra dimension with the following expression, xdimTag.atonly(dom==i), returns 1 on the i th layer of the layered material, 0 on the other layers.
Here, xdimTag is the tag of the extra dimension. For example, it may be llmat1_xdim when a layered material link (llmat1) is selected in the Layered material list of the Thin Layer node. This tag can be deduced from the Selection column of the Equation View subnode of the node applied on the thin layer, by clicking the Show More Options button () on the Model Builder tool bar and selecting Equation View.
Therefore, by using featTag.xdintopall(xdimTag.atonly(dom==i)*expr), you evaluate the integral of expr on the i th layer of the layered material.
See atxd, atonly, and noxd in the COMSOL Multiphysics Reference Manual for details about the operators.