Edges generation

Algorithm generates edges of a conforming 2D/3D triangulation.

Description

Given a conforming triangulation as as matrix of vertices numbers corresponding to each triangular element , the algorithm generates and numbers edges of triangulation, so that edges shared by two elements are counted only once. It also generates list of edges belonging to each triangle a list of elements sharing the same edge.

Knowledge of edges is useful e.g. for the implementation of adaptive mesh refinements and edge-based finite elements such as Raviart-Thomas, Crouzeix-Raviart or Nedelec elements.

To test the functionality of the algorithm, run "test.m".

Performance of my notebook:
2D triangulation: 524288 elements, 263169 nodes --> 787456 edges numbered. Time= 1.23 seconds.
3D triangulation: 196608 elements, 35937 nodes --> 238688 edges numbered. Time= 1.12 seconds.

Acknowledgements

This file inspired Double Porosity Model.

• Required Products: MATLAB Compiler
• MATLAB release: MATLAB 7.5 (R2007b)

[Immanuel Anjam]

Works nicely and very fast for 3D also. The updated code is even more short and elegant than before. Nice.

[Jan Valdman]

I am still working on extension to 3D, I already know one way, how to do it. Hope to provide the code soon.

[Immanuel Anjam]

 

[Immanuel Anjam]

Greetings from Finland!

Thanks for sharing this code. I have been using it alongside a 2D Nedelec-FEM implementation.

This kind of code could be useful in 3D also. It seems that mesh generators always provide elements in terms of nodes, but for edge-based finite elements it is necessary to have the information in terms of edges.