Mean Ratio

Applies to: Triangular or Quadrilateral Surface Meshes, Tetrahedral or Hexahedral Volume Meshes. Does not apply to Mixed Element Meshes.

Summary: Moves interior mesh nodes to optimize the average mean ratio metric value of the mesh.

To use mean ratio smoothing

  1. On the Command Panel, click on Mesh.
  2. Click on Volume or Surface.
  3. Click on the Smoothing action button.
  4. Select Mean Ratio from the drop-down menu.
  5. Enter in the appropriate values for Volume ID(s) or Surface ID(s). This can also be done using the Pick Widget function.
  6. Enter the appropriate value for Time (minutes).
  7. Click Apply.

Surface <surface_id_range> Smooth Scheme Mean Ratio [cpu <double=10>]

Volume <volume_id_range> Smooth Scheme Mean Ratio [cpu <double=10>]

Discussion:

Trelis includes a mean ratio smoother provided by MESQUITE, a mesh optimization toolkit by Argonne National Laboratory and Sandia National Laboratories. (See Brewer, et al. 2003 for more details on the MESQUITE toolkit.) This smoother is similar in purpose to the Condition Number smoother. However, the Mean Ratio smoother uses a second order optimization method, and therefore it will often reach a near-optimal mesh more quickly than the Condition Number smoother. The Mean Ratio smoother requires the initial mesh to be untangled, but the smoother is guaranteed to not tangle the mesh. If the user attempts to call the Mean Ratio smoother on a tangled mesh, an untangler will first attempt to untangle the mesh before calling the Mean Ratio smoother.

The Mean Ratio smoother's optimization process terminates when one of the following three criteria is met:

  1. The mesh is "close" to an optimal mesh configuration.
  2. The maximum allotted time has been exceeded.
  3. The user interrupts the smoothing process.

The user has control over the second and the third criteria only. For criterion 2, the default is for the smoother to terminate after ten minutes even if a near-optimal mesh has not been reached. The user can change this time bound by specifying the optional "cpu" argument in the command listed above. This argument takes a single, positive number that represents the time (in minutes) that will be used as a time bound. If the user wishes to terminate the process early, criteria three allows the user to "interrupt" (for example, on some platforms, by pressing CTRL-C) the process. If the process is terminated early, the mesh will not revert to the original node positions; Trelis will instead keep the partially optimized mesh.