15 February 2011

Unstructured Meshes

Last term for me I was studying meshes and the physics of what goes on when the radiator is on. The most common mesh is structured meshes, like calendars, all squares all evenly distributed. i.e.

This was taken from my iCal on my mac. (note sure who I ask permission to use this image, if you know can you reply in the comments)

Structured meshes are good for rectangle type of shapes but what if they are not rectangle? For this type of problem we can triangles and view this as an unstructured mesh.
An example would be a rectangle split into triangles (because i can claim its my own work and its easy to draw)

This image was made by the software Paintbrush
Now before we get into the how a computer works with unstructured meshes we first need to know each triangles neighbour.
1: has neighbours 2 & 3.
2: has neighbours 1 & 4.
3: has neighbours 1 & 6.
4: has neighbours 2 & 5.
5: has neighbours 4, 6 & 7.
6: has neighbours 3 & 5.
7: has neighbours 5 & 8.
8: has neighbour 7.

Now we create three vectors, one will be the neighbours so something like
The second will be to determine how many where the neighbours finish for that triangle i.e. for triangle 3 it would be 6, the vector will look like:
The last matrix will be the coefficients for those triangles so something like:

Then you can use Successive over relation or Gauss Seidel or even the Jacobi method. Other iterative methods are available.

One last bit of advice do not use my triangle arrangement to solve problems mainly because it is not evenly spread out and so any results you get will be wrong or at least not very accurate.

This should be pre dated to 30th January 2011

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