Practical Applications of Mesh Relaxation
Judy Hill
Geometric Modeling Project
Spring, 1998

Boender (1994) presented the results of mesh relaxation for three real-world FEM meshes. The results of one test is presented.

Figure R1. An FEM mesh (a) before and (b) after relaxation. Boender (1994)

Figure R1 above illustrates the FEM mesh before and after mesh relaxation has been applied. Initially, an L-shaped plate was triangulated by the constrained Delaunay algorithm which resulted in a graded triangulation as shown in Figure R1a. After mesh relaxation, Figure R1b, it is eveident that the distribution of the elements is more even around the singularity at the notch. Furthermore, close examination reveals that the element shape has been improved.

Table R1 below quantitatively illustrates the improvement due to mesh relaxation compared with the initial mesh. Delaunay properties have been preserved by the mesh relaxation. Furthermore, the minimum and maximum angles in the mesh have been improved. Thus, we can conclude that the relaxation has had a significant effect on the element shape and distribution throughout the mesh.