They only deal with the 2D case, but I can point you to the work of some of my colleagues on https://doi.org/10.1137/17M1157155 . Using the off-diagonal low-rank structure in a recursive fashion, they can reach quasi-linear cost for the 2D case.
Abdullah, thank you for the plug for our materials. We have repackaged these as a Massive Open Online Course (MOOC) on edX titled "LAFF-On Programming for High Performance". It is free for auditors. For info, see http://ulaff.net.
The premier open source implementation of the BLAS is the BLAS-like Library Instantiation Software (BLIS). There is ...
This landmark paper by George proves that a nested dissection ordering of a regular,
four-node element, finite element mesh produces minimum fill-in.
Although it is straightforward to produce such an ordering by inspection,
the graph algorithms that attempt to do this for a general sparse
structure only approximate this ordering.
Assuming you are obtaining ...