I realize this might be a too general question but here goes nothing:
I am trying different re-ordering strategies and checking the fill-in of $A=LU$.
I have 2D ($p=1$, $h=1/40$ on $\Omega = [-1,1]^2$) discretizations of the Helmholtz equation and I was genuinely surprised to see Reverse Cuthill-McKee (RCM) outperform Nested dissection in all cases that I tried out.
Now, I was left in the belief that Nested dissection is state of the art. What am I missing? Does the strength of Nested Dissection lie in the hierarchical elimination using multifrontal methods? Is it 2D vs 3D? Or is RCM actually better?
I am grateful for any tips/pointers/directions and answers :)