Use Mapped () to generate a structured quadrilateral mesh on boundaries in 3D and domains in 2D, as shown in Figure 8-85. The operation can also be used to remesh imported meshes in 3D.

You can control the number, size, and distribution of elements using Size (only the Maximum element size parameter is used) and Distribution subnodes.

To create a mapped quadrilateral mesh for each domain (boundaries in 3D), the mapped mesher maps a regular grid defined on a logical unit square onto each domain. The mapping method is based on transfinite interpolation. The settings in the Size and Distribution nodes used by a Mapped node determine the density of the logical meshes. For the mapping technique to work, the opposite sides of each logical unit square must be discretized by the same number of edge elements.

By default, the relationship between the four sides of the logical unit square and the boundaries around a domain is based on a criterion related to the sharpest angle between boundaries. If you want to control this relationship, right-click the Mapped node to add an Edge Groups subnode.

For a geometry that does not initially meet these criteria, it is usually possible to modify it so that a mapped mesh is generated, for example, by partitioning it into simpler domains, as shown in Figure 8-86. Consider using Mesh Control Operations to hide the added edges and points from the physics view.

For imported meshes in 3D, use Mapped to remesh one or several faces. The operation separates the selected boundaries from the mesh, creates geometry from the separated mesh, meshes the geometry, and then copies the new generated mesh onto the original mesh. Edges adjacent to faces outside the selection are kept unchanged, while other edges are remeshed.

To add a Mapped () node, select boundaries (3D) or domains (2D) in the Graphics window, then choose one of the following:

Define the boundaries (3D) or domains (2D) where you want to create a mapped quad mesh. Choose the level of the geometry from the Geometric entity level list:

Use the Smooth across removed control entities setting to smooth the transition in element size across removed control entities. Use Automatic (default) to let the algorithm decide if to apply smoothing or not. Smoothing will be applied if, for example, 2D domains adjacent to removed edges contain triangular elements only. When set to On, the mesher adjusts the sizes of the mesh elements to get a smoother transition from large to small elements by adjusting the locations of the mesh vertices on the entity that is removed. Select Off to not adjust the mesh. When set to On, you can specify the number of smoothing iterations in the Number of iterations field. In the Maximum element depth to process field you can specify the maximum element depth for the mesh vertices to be smoothed.

Select the Adjust edge mesh checkbox (cleared by default) to allow the mapped mesher to adjust the mesh on edges that are not already meshed and where no explicit distribution is applied in order to reduce the element skewness (see Figure 8-88 below).

In this section you can choose between two different interpolation methods in the Interpolation method list. This specifies how the mapped meshing operation determines the positions of the interior mesh vertices. Select Automatic (default) to let the mapped meshing operation determine a suitable interpolation method automatically. In many cases, the interpolation methods give the same result. If you select Transfinite in 2D, the positions of the interior mesh vertices are determined by transfinite interpolation in the 2D parameter space of the corresponding surface. This method works best for faces with smooth surface parameterization. If you select Transfinite in 3D, transfinite interpolation is done in 3D to determine these positions. This method works best if the shape of the exterior edges represent the shape of the surface in a good way.

For information, see Generated and Modified Elements.