General Projection
Use a General Projection nonlocal coupling () to define integration along curves. A projection coupling operator evaluates an expression defined on a source by integration along lines or curves depending on the evaluation point in the destination. The General Projection operator is defined by mapping the source to an abstract intermediate space of dimension srcedim, and the destination to the subspace of dimension srcedim1 obtained by setting the last coordinate to 0 (srcedim is the dimension of the source selection). To every point in the destination, there is a vertical line in the intermediate space, obtained by allowing the last coordinate to vary while the remaining coordinates are given by the destination map. The set of points in the source selection that are mapped onto this line by the source map is a line or curve, and the projection operator is evaluated by integrating along this line or curve. The default Operator name is genproj1.
See Common Settings for Nonlocal Couplings for information about the Source Selection section.
Source map
Specify the general projection source map using expressions in the x-expression, y-expression, and z-expression fields.
The dimension of the intermediate space equals the dimension srcedim of the source. If the selection has lower dimension than the source geometry, specify only the first srcedim expressions.
Use expressions containing spatial coordinates in the source geometry when defining the map. The map must be approximately linear within each mesh element. Select a Source frame from the list.
Destination Map
Enter an x-expression and, depending on the dimensions, y-expression for each coordinate except the last in the intermediate space.
The destination map has one field less than the source map. When defining the map you can use expressions containing spatial coordinates in the destination geometry. The destination mapping can be highly nonlinear or noninvertible.
If the selection has lower dimension than the source geometry, specify only the first srcedim1 expressions. A general projection operator can be evaluated at any point where its destination map is defined.
Advanced
Enter an Integration order of the numerical integration method (default: 4). See integration order in the Glossary.