Creating Volume Mesh

The surface meshes that we end up with from the CAD designs or medical scans are often of too high density and we certainly don't need that many elements to work with. Especially, when we need to create a volume mesh for finite element calculations, we do not want these to take too long. Even though, one does need to make sure that the density is not too low and it provides results comparable with the a mesh of higher density.

In Cleaning/Repairing Surface Mesh we've learned how to reach a mesh of healthy parameters, such as the aspect ratio of the longest edge of an element to its shortest edge. At the end of that blog entry we ended up with mesh of smaller number of triangles already.
We reduced it from 16784 to 13176 triangles, which is 22% reduction and already could be low enough to go ahead and create the volume mesh.

In Gmsh, go to File > Merge and look for your repaired STL files to load.
Then, click on Geometry > Elementary entities > Add > Volume and follow the instructions on the screen. Next, click on Mesh > 3D and if your STL file was "healthy" enough to begin with then Gmsh was able to create the 3D mesh. Also, use the available optimization methods. Click on Mesh > Save, you'll have to then convert the resulting msh file to whatever type your processor requires to run. I have written a small Matlab script for that. The resulting volume mesh has 20440 tetrahedral elements.

In this example, it looks like there might be insufficient number of 3D elements across the wall of the aortic root as for the classical finite element methods at least 3 layers are usually required. I, however, use special finite element method that takes care of this issue and will show it in later blog entries. Therefore, for me, this number of elements is sufficient. In fact, I could go even lower and simplify the surface mesh even more before creating the volume mesh.



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