What is the best (scalability and efficiency) algorithms for generating unstructured quad meshes in 2D?

Where can I find a good unstructured quad mesh-generator? (open-source preferred)

  • $\begingroup$ Tsk. A tip: when creating a multi-word tag, please use dashes to separate out the words. $\endgroup$
    – J. M.
    Dec 28, 2011 at 23:49

2 Answers 2


The are essentially two approaches to free quad meshing:

  • Direct methods generate a quad mesh directly, usually by some advancing front method. The Paving paper is a standard reference and is the method used by CUBIT, so you have seen these meshes in many publications.

  • Indirect methods generate some intermediate decomposition of the domain (e.g. triangles) and then produce an all-quad mesh through recombination and/or further decomposition. Q-Morph is an example that is used by ANSYS.

Note that smoothing is necessary for both approaches, sometimes with alternating topology fix-up and smoothing steps. Some open source tools have built-in smoothing facilities and the LGPL-licensed Mesquite package is designed as a library specifically for mesh quality improvement.

I know of two open source free-quad meshers:

  • Gmsh (GPL with linking exception) can generate quad meshes using a recombination algorithm described in this paper.
  • The Jaal component of MeshKit (LGPL) is based on recombination similar to Q-Morph above, read the IMR-2011 paper for more details. You can download the source through the link above, but it is not ready for production use yet.
  • LBIE generates quad and hex meshes from volumetric data. From what I can tell, it is an interactive environment rather than a library. The site says that the source is available under GPL upon request.
  • CUBIT is not open source (and although not expensive compared to commercial software, acquiring a license takes a long time), but produces high quality meshes and can be linked into other applications.
  • $\begingroup$ I have learned that Gmsh (geuz.org/gmsh) now also has support for unstructured 2D quad generation by some ”Blossom” recombination algorithm. $\endgroup$ Dec 29, 2011 at 9:59
  • $\begingroup$ Is there a similar method for 3D hexahedrons? $\endgroup$ Dec 31, 2011 at 22:18
  • 2
    $\begingroup$ Hex meshes are usually done by sweeping quad meshes and then smoothing (robust, but have to decompose domains). You can also create hex meshes by recombination using H-Morph (Owen and Saigal, 2000; osti.gov/energycitations/servlets/purl/756062-uQ2PGj/…), a method similar to Q-Morph referenced above, but it is difficult to maintain quality. $\endgroup$
    – Jed Brown
    Jan 2, 2012 at 0:00
  • 1
    $\begingroup$ Yes, gmsh has supported quads for a while now. $\endgroup$ Jan 4, 2012 at 4:02
  • $\begingroup$ This answer is about two years old now and I believe this is still a very pertinent question. Has there been significant evolution on unstructured quad and especially hex meshing? I was wondering if there were any new software (commercial or open source) which allow for 3D unstructured hex meshing. I know gmsh can do 3D hex by extruding 2D quads, but i'm looking for something more appropriate for complex geometries. $\endgroup$
    – BlaB
    Nov 8, 2018 at 16:55
  1. It would be great if gmsh would further include mesquite as 3rd party.
  2. I am from the engineering field, where structured grid is possible and strongly advised.
  3. CUBIT seems to be the mesquite's professional version, or commercial version.
  4. mesquite project ended a few year ago, though some other guys seems to continue keep it going. (meshkit?)
  5. I have a very very good GUI experience with gmsh, it's easy going, light weighted, etc.!

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