Mesh Smoothing

Related Topics

After generating the mesh, it is sometimes necessary to modify that mesh, either by changing the positions of the nodes or by removing the mesh altogether. Trelis contains a variety of mesh smoothing algorithms for this purpose. Node positions can also be fixed, either by specific node or by geometry entity, to restrict the application of smoothing to non-fixed nodes.

Mesh smoothing in Trelis operates in a similar fashion to mesh generation, i.e. it is a process whereby a smooth scheme is chosen and set, then a smooth command performs the actual smoothing. Like meshing algorithms, there is a variety of smoothing algorithms available, some of which apply to multiple geometry entity types and some which only apply to one specific type (these algorithms are described below.)

To smooth the mesh on a geometry entity

  1. On the Command Panel, click on Mesh.
  2. Click on Volume, Surface or Curve.
  3. Click on the Smoothing action button.
  4. Select the desired scheme from the drop-down menu.
  5. Enter the appropriate values for Volume ID(s), Surface ID(s) or Curve ID(s). This can also be done using the Pick Widget function.
  6. Depending on the scheme selected, optionally specify the Tolerance.
  7. Enter any other appropriate settings.
  8. Click Apply.

{Curve|Surface|Volume} <range> Smooth Scheme <scheme>

where <scheme> is any acceptable smooth scheme described in this section. Also set any scheme-specific information, using the smooth scheme setting commands described below.

Smooth Curve <range>

Smooth Surface <range> [Global]

Smooth {Body|Volume|Group} <range>

Groups of entities may be smoothed, by smoothing a group or a body.

If a Body is specified, the volumes in that Body are smoothed. If a Group is specified, only the volume meshes within these groups are smoothed - no smoothing of the surface meshes is performed.

Global Smoothing

When smoothing a set of surfaces, the keyword global can be added to the smooth command such as

Smooth Surface <range> [Global]

If the smoothing algorithm for two neighboring surfaces are both allowed to move boundary nodes, then appending the "global" keyword will often result in a higher quality mesh near the curve(s) shared by those two surfaces.

Focused Smoothing on Groups of Mesh Entities

Meshed entities such as hexes or tris can be smoothed individually or in groups by specifying the entities in a list.

To smooth hexes and tets

  1. On the Command Panel, click on Mesh.
  2. Click on Hex or Tet.
  3. Click on the Smooth action button.
  4. Enter the appropriate value for Hex ID(s) or Tet ID(s). This can also be done using the Pick Widget function.
  5. Optionally, specify the scheme.
  6. Click Apply.

To smooth quads, tris and edges

  1. On the Command Panel, click on Mesh.
  2. Click on Quad, Tri or Edge.
  3. Click on the Smooth action button.
  4. Enter the appropriate value for Quad ID(s), Tri ID(s) or Edge ID(s). This can also be done using the Pick Widget function.
  5. Optionally, specify the scheme.
  6. Enter the appropriate value for Target Surface ID or Target Curve ID. This can also be done using the Pick Widget function.
  7. Click Apply.

Smooth {Hex|Tet} <range>[Scheme {Equipotential|Laplacian|Random}]

Smooth {Face|Tri} <range>[Scheme {Laplacian|Centroid|Winslow}] [Target Surface <id>]

Smooth Edge <id_range> [Scheme Laplacian] [Target Surface <id>]

The Smooth Edge command allows the user to smooth individual edges owned by a curve. Specifying a target curve allows the user to move the edges on a meshed curve to a different curve. The target curve or surface does not necessarily need to be the owning curve or surface of the nodes. For example, if given two curves (A and B) and curve A was meshed, the target smoothing could be used to move all of the edges of curve A onto curve B. The smooth scheme option for the edge smoothing is currently limited only to the laplacian scheme.

The Smooth Face|Tri command is used to smooth individual faces or triangles. The target option is similar to the curve target option above. Faces or Tris can be smoothed to a surface that is not necessarily the owning surface; in fact, the faces or tris do not even have to be attached to any surface. This makes this option especially helpful for smoothing free meshes. Specifying a smooth scheme allows for relaxation based surface smoothers (i.e. centroid area pull, laplacian, winslow) to be utilized during targeted smoothing. It is not currently enabled for optimization based smoothing schemes.

Smooth Tolerance

Smoothing algorithms move nodes in an attempt to improve the quality of the mesh elements. Most of these algorithms are iterative, and the algorithm terminates when some criterion is met. Specifically, for the Laplacian and Equipotential style smoothers, smoothing is terminated either by satisfying a smoothing tolerance or by performing the maximum number of smoothing iterations. For these smoothers, the smooth tolerance may be set by the user:

[Set] Smooth Tolerance <tol>

The value <tol> tells the smoother to stop when node movement is less than tol * local_minimum_edge_length.

The default value for tol is 0.05. The maximum number of iterations may be set by the user. For volumes, the smooth tolerance and iterations may also be set by

(Note: The above command affects all smoother that respect tolerance.)

Volume Smooth Tolerance <tol>

Volume Smooth Iterations <iters>

(Note: The above two commands only affect the volume smoothers.)

Boundary Mesh Smoothing

Where used in the smooth schemes below, the Free keyword permits the nodes lying on the bounding entities to "float" along those entities; without this keyword, boundary nodes remain fixed.

Nodal positions may be fixed so that no smoothing scheme, either implicit or explicit, will move them, with the following command:

{Curve|Surface|Volume} <range> Node Position {Fixed|Free}

Node <range> Position {Fixed|Free}

The following command does not fix nodal positions, but does fix the connectivity of the mesh, preventing certain volume schemes from changing the bounding mesh:

{Curve|Surface|Volume} Mesh {Fixed|Free}

The additional following scheme is available for research purposes and can be used only after issuing a 'set developer on' command.