Hi, I'm doing 3D electromagnetic simulations with Nelelec and NedelecSZ elements. I would like to collapse some vertices in other to follow the geometry.
The matrix should be singular if you collapse a vertex but according to Luca Heltai: You can get away with it if you add enough constraints to your system so that each collapsed degree of freedom is identical (you can do this by using the ConstraintMatrix class). This should be enough to remove the singularity from the matrix (and it is often used as a trick to deal with singular integrals). https://groups.google.com/forum/#!searchin/dealii/degenerate%7Csort:relevance/dealii/VLXWrUVh_18/ohiblJOlCtUJ I gave it a try with a simple simulation (step-6) with 25 dofs and a rectangular mesh. I used add_line() and add_entry() from AffineConstraints If I collapse the vertex and don't apply the constraint, I still get the right solution and the determinant is non zero. I expected the determinant to be zero for this particular case. The matrix should be singular. I did 3 test which gave the same solution: - Original mesh. determinant(system_matrix) = 6.6e10 - Move vertex and do not apply constraint. determinant(system_matrix) = 6e11 - Move vert and apply constraint. det(system_matrix) = 1.2e12 Below you can find the simulations as you can see I always get the right solution for all the cases. Why the determinant when I collapse the vertex and don't apply the constraint is non-zero? The matrix should be singular. How do I find the dof asociated to a vertex? I just did try and error for this particular test. Can I do the same trick in 3D for the Nedelec and NedelecSZ elements? How do I check the quality of a mesh and that the matrix is not singular? I can't do the determinant for a large matrix. Thanks! Daniel [image: solution_1.png] [image: solution_2.png] -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/e8812f11-3d99-4ab3-847e-4e949262e501%40googlegroups.com.
