1. Triangulations

3. If two triangles have some intersection, it is either on common vertex or a common full edge. In particular, two different triangles do not overlap. Situations not admitted in triangulations.

4. Triangulations This mesh is stored in 3 matrices 1)Matrix P which store the coordinates of the nodes 2)Matrix e which store the boundary nodes 3)Matrix t which stores local labeling.vs. global labeling

5. 1 2 3 4 5 6 7 8 9 10 11 12 13 Element Labeling 14 15 16 16 triangles 16 elements

6. Node Labeling (global labeling) 12 34 5 6 7 8 9 1011 1213 121110987654321 0.750.25 0.7510.50 1001x 0.25 0.75 0.50 1 0011y X-coordinate and y-coordinate Matrix p(2,#nodes) 13 nodes

7. Boundary node vector e(#boundary node) e8e7e6e5e4e3e2e1 98764321start 14329876end 12 34 5 6 7 8 9 1011 1213

8. Node Label (local labeling) 12 3 Each triangle has 3 nodes. Label them locally inside the triangle

9. Local label.vs. global label Matrix t(3,#elements) 16151413121110987654321 131211105555432132141 1211101312111013 12111087692 8769131211108769121110133 12 34 5 6 7 8 9 1011 1213 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

10. Export 3 matrices

11. delaunay >> x=[0 1 0 1 0.5] >> y=[0 0 1 1 0.5] >> TRI = delaunay(x,y); >> triplot(TRI,x,y)

12. Exercise1 Triangulations The adjacent Figure shows a small triangulation of an L-shape domain. The mesh has eight nodes and six triangles. Find the matrices p, e, t

13. Exercise2 Triangulations The adjacent Figure shows a set of point in the domain (0,3)X(0,3). Use delaunay Matlab command to generate a triangulation with these points as a nodes. Then find the matrix p and t. What are the nodes of the triangle 11 12 4 3 5 78 6 910 12 11