Common Settings for Nonlocal Couplings
The following sections in the Settings windows for the nonlocal coupling nodes are similar or the same for some of the nonlocal coupling nodes and are described in this section.
Operator Name
Enter a name for the operator in the Operator name field or use the default name. This is the name that is used to access the operator in the model, so use a name that describes it well. For example, genext1 is the default name for the first General Extrusion coupling operator, and you can use it to evaluate a temperature T in the destination using genext1(T), for example.
Source Selection
The source selection defines the source for the nonlocal coupling — the part of the geometry where the coupling operator evaluates the supplied expressions.
From the Geometric entity level list, select Domain, Boundary, Edge (3D only), or Point. Select Manual or All domains, All boundaries, All edges, or All points from the Selection list. If Manual is selected, select geometric entities in the Graphics window. Select All domains, for example, to add all applicable geometry to the Selection list.
Source Vertices and Destination Vertices
The selection of Source Vertices and Destination Vertices define the linear mapping from the destination to the source.
Click the Active button to activate one of the vertex selections. You can toggle between turning ON and OFF selections.
Select a single source vertex for each of Source vertex 1, Source vertex 2, Source vertex 3, and Source vertex 4. Then select a single destination vertex for each of Destination vertex 1, Destination vertex 2, Destination vertex 3, and Destination vertex 4 (vertex 4 is available for Linear Extrusion only).
For Linear Extrusion: The number of source vertices must be at least one and not more than 1+min(srcsdim,dstsdim), where srcsdim and dstsdim are the dimensions of the source and destination geometries, respectively. The number of destination vertices entered should be the same as the number of source vertices. If not all destination vertex selections are used, the empty selections must be last.
For Linear Projection, select srcedim+1 source vertices where srcedim is the dimension of the source selection. Depending on the dimension of the source selection, it can be that some of the last source vertex selections should be left empty. The number of destination vertices should be one less than the number of source vertices. If not all destination vertex selections are used, the empty selections must be last. Select srcedim destination vertices where srcedim is the dimension of the source selection. Depending on the dimension of the source selection, it can be that some of the last destination vertex selections should be left empty.
An evaluation point in the destination geometry is first orthogonally projected onto the linear space spanned by the destination vertices (unless they span the entire space). The projected point is then mapped to the source geometry by a linear mapping taking each destination vertex to the corresponding source vertex. Let L be the line through this point, which is parallel to a line through the first and last source vertices. If the source selection lies in the linear space spanned by the source vertices, the Linear Projection operator is evaluated by integrating along L. In general the operator is evaluated by integrating along the line or curve in the source selection, which is mapped to L under orthogonal projection onto the linear space spanned by the source vertices.
Source Boundaries and Destination Boundary
Select Manual or All boundaries from the Selection list to define the source selection. If Manual is selected, select boundaries in the Graphics window. Select All boundaries to add all boundaries to the Selection list.
There can only be one destination boundary. Click the Active button to enable or disable the Destination Boundary selection. Then choose the boundary in the Graphics window.
Source Frame and Source Map
Select a Source frame to use in the source. In most cases the Source section default settings can be used. Optionally, select the Use source map check box and enter expressions in the x-expression, y-expression, and z-expression fields (in 3D) for the source map from the source to the intermediate mesh.
For the General Extrusion nonlocal coupling, the number of source map expressions is the same as the number of destination map expressions. With the default source map expressions, the intermediate mesh can be considered identical to the source.
The dimensionality idim of the intermediate space is determined by the number of nonempty source and destination map expressions, which must be the same, and must also satisfy srcedim ≤ idim ≤ srcsdim, where srcedim is the dimension of the source selection, and srcsdim is the dimension of the source geometry.
Advanced Settings for Nonlocal Couplings
For the General Extrusion, Linear Extrusion, Boundary Similarity and Identity Mapping nonlocal couplings, select an option from the Mesh search method list to specify what should happen if an evaluation point in the destination is mapped to a point outside the source:
If Use tolerance is selected (the default) the result depends on the other field definitions in this section.
If Closest point is selected, the closest point in the source selection is used.
Enter a scalar positive value in the Extrapolation tolerance field. If the mapped point is within a distance of the extrapolation tolerance times the mesh element size, the point is considered to be in the source. Otherwise, the mapping fails.
Select the Use NaN when mapping fails check box to evaluate the operator to NaN (Not-a-Number) if the mapping fails. Otherwise an error occurs.
For the Integration and Average couplings, select Integration or Summation over nodes from the Method list. In most cases use integration. Summation over nodes is useful, for example, for calculating reaction forces.
You can only use the Summation over nodes option for expressions that have uniquely defined values in the nodal points.
If Integration is selected, enter a value in the Integration order field (see integration order in the Glossary). Also, when working with multiple frames, select a Frame from the list for the volume element to be used in the integration.
For axisymmetric geometries, the Compute integral in revolved geometry check box is selected by default to perform the integration in 3D (for a 2D axisymmetric model) or in 2D (for a 1D axisymmetric model).