I talked with Shoaib about some changes I could make to the FEA model to improve convergence and reduce memory usage. Summary:

• use a hex mesh rather than tetrahedral
• Use more structured meshes. In particular, I can make an angled swept the mesh in the tapered portions rather than using a free mesh in these regions, defining the mesh only on one boundary
• Use a nonconformal mesh, so adjacent domains do not need to have matching meshes. This could allow transitions to coarser meshes as the fiber becomes thicker or contacts the horn
• try using curved elements so the curvature isn't just approximated by the number of regular mesh elements
• Might try scaling the model uniformly by some factor (100, 1000), which could avoid machine precision issues

I'll get these implemented this week and see if the computation goes through.