collier_continuity

This is a discussion of the paper, The Cost of Continuity: Performance of Iterative Solvers on Isogeometric Finite Elements, which has been submitted for publication. The preprint is available from arxiv at the link above.

The three preconditioners employed in the paper are:

Diagonal Jacobi
Successive Overrelaxation
Incomplete LU

The domains are combined via an additive Schwarz preconditioner, either over decomposed over the basis or the elements. The authors make a claim that multigrid methods could be employed as more advanced preconditioners, but are unable to back this up with strong computational results.

The most interesting result out of the paper is the robustness and capability of the ILU preconditioner over the more traditional (and theoretically well-understood techniques). This suggests at least two possible veins of investigation:

Does the performance of the ILU preconditioner extend beyond the application explored in the paper?
Can more advanced preconditioners be employed in this situation that outperform ILU?