I wrote a finite element code in fortran 90.
This code is really fast, except the meshing process.
I used triangle and tetgen for meshing in 2D and 3D, respectively, so this process is fast, of course.
For example, for the unit square [0,1]x[0,1] in 2D I have a file with the coordinates of its nodes (for example, a mesh with 5 nodes):
1 0.0 0.0 # coordinates of node 1
2 1.0 0.0 # coordinates of node 2
3 1.0 1.0 # coordinates of node 3
4 0.0 1.0 # coordinates of node 4
5 0.5 0.5 # coordinates of node 5
called coordinate.dat, which have 4 elements (triangles) with nodes called element.dat
1 1 5 4 # vertices of triangle 1
2 1 2 5 # vertices of triangle 2
3 2 3 5 # vertices of triangle 3
4 5 2 4 # vertices of triangle 4
I also have a file where each row i is the number of its initial an final node, called edge.dat:
1 1 2 # initial and final node of edge 1
2 2 3 # initial and final node of edge 2
3 3 4 # initial and final node of edge 3
4 4 1 # initial and final node of edge 4
5 1 5 # initial and final node of edge 5
6 5 2 # initial and final node of edge 6
7 2 5 # initial and final node of edge 7
8 5 4 # initial and final node of edge 8
With this files, I need to generate the following information:
(1) Given an element (triangle or tetrahedron), I need to know the number of its sides (edges and faces, respectively). For example, I need to generate the following structure or file, called struct1.dat:
1 5 8 4 # triangle 1 has the edges number 5, 8 and 4
2 1 6 5 # triangle 2 has the edges number 1, 6 and 5
3 6 2 7 # triangle 2 has the edges number 6, 2 and 7
4 7 3 8 # triangle 4 has the edges number 7, 3 and 8
(2) Furthermore, given a side (edge or face) I need to know the element numbers of the 2 elements (or only one if the side is on the boundary) shared by that side. For example, I need to generate the following structure (or file) called struct2.dat:
1 2 0 # edge number 1 is only on element 2
2 3 0 # edge number 2 is only on element 3
3 4 0 # edge number 3 is only on element 4
4 1 0 # edge number 4 is only on element 1
5 1 2 # edge number 5 is sharing by elements 1 and 2
6 3 2 # edge number 6 is sharing by elements 3 and 2
7 4 3 # edge number 7 is sharing by elements 4 and 3
8 1 4 # edge number 8 is sharing by elements 1 and 4
For both of these structures, struct1.dat and struct2.dat, my code is very slow because I used a brute force approach with a lot of loops..
I am looking for an algorithm (a paper, or better: a subroutine in fortran available for download) optimized for this? I want to continue using triangle and tetgen, but I am willing to listen to other options.
