Adaptive refinement of quadrilateral meshes.

Quadrilateral mesh generator with refinement capabilities, available in complete source code form !

What is QUAD-REF ?

The principal advantage of quadrilateral finite elements over triangles is superior accuracy of numerical results obtained upon completion of the FEA stage. Our set of world-class 100% quadrilateral mesh generators consists of several programs capable to produce high quality meshes on geometries of arbitrary complexity. Such specific features as internal boundaries and entities, stress concentrators, etc. are often encountered in real-life models and can be automatically processed by our mesh generation software.

However, despite the fact that quadrilaterals are very successful in obtaining good numerical solutions, some physical problems can only be solved with necessary precision if the solution is performed as an iterative process with elements' sizes decreasing from one iteration to another. The problem becomes even more complex if mesh refinement on the entire domain leads to elements so small that time expenses of the FEA stage itself become excessive. In such cases, it is desirable that the mesh generator performs only partial refinement, ie. elements' sizes are reduced only in a small area within the domain, where high gradients of the physical fields are to be expected.

One example of such problem is crack propagation. Around the crack tip, stresses can change very significantly between neighbouring points in a vicinity of the crack, whereas in the remaining part of the domain stress gradients can remain low. In that case, the solution process is built in an iterative manner: at the first step, the solution is obtained on a rather coarse mesh, and then is made more accurate on meshes refined around the crack tip.

Our product QUAD-REF is developed to solve problems as described above. It is a powerful, general-purpose mesh generator, based on our core product QUAD-GEN. Possessing all capabilities of QUAD-GEN, it can also generate sequences of meshes in which, around a user-defined point and within a distance named "radius of influence", the average elements' size will decrease from one iteration to another. Most importantly, all meshes are backwards compatible: all nodes generated at a particular iteration will retain their coordinates on subsequent iterations. This allows using numerical results obtained at a particular iteration as initial values for the next one, which is important for the iterative process' stability and efficiency. On images below, the second mesh is obtained from the first one by the QUAD-REF mesh refinement algorithm.

Delivery, licensing and support.

QUAD-REF was completely developed by our company and contains no third party code. We provide full, one-off commercial licence, and free support for 12 months. If you purchase QUAD-REF, you will be provided with:

- complete, fully commented source code in C;

- a User Manual, containing detailed description of input and output data structures and an example driver program;

- and graphical visualisation program QUAD-PRO (for Windows platforms only). QUAD-PRO allows displaying initial regions that are to be meshed, as well as generated quadrilateral meshes.

Please contact us on the address below (or, preferably, by e-mail) . We can also help with other mesh generation and finite element analysis needs.

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