A few curious lines of code in the stiffness matrix computation

[qiongsiwu]

After calling quadrature_single_point, the code constructs a solver, computes some eigenvalues and eigen vectors, and reassigns H.

What is this code doing? I am not sure where in the notes/lecture this was discussed. Help/pointers are appreciated!

https://github.com/dilevin/CSC2549-a3-finite-elements-3d/blob/98c2e373e8a5c779da31eb7106a2c40530a98fea/src/d2V_linear_tetrahedron_dq2.cpp#L17-L29

[dilevin]

We will talk about this general trick next class but this is ensuring that the hessian for Newton’s method is positive definite. This guarantees that the newton search direction is, locally, a descent direction and helps make the solver more robust.

Thanks for asking this, it’s a great question.

[dilevin]

As an aside, I wanted to provide the code for these little tricks since I figure everyone already has enough to implement in this class :) but I can add a comment to the source code to make it less opaque.