Computation time scaling for dimensions other than two?
Hello Kwant Community, In the 2014 kwant paper New J. Phys. 16 063065, Fig. 6 gives the conductance computation time scaling for 2D systems of side length L: O(L^2) for construction, O(L^3) for solving with the MUMPS-based solver, and O(L^4) for solving with RGF. I was wondering what the general scaling is for other dimensions. I presume it is known to experts and might be helpful to many users. Thank you.
Hi Xiaoxiao,
MUMPS uses nested dissection, which has an asymptotic scaling of
L^(3d-3) for d>1, however the prefactor matters a lot and the
asymptotic scaling might not be reached until relatively large system
sizes. Also keep in mind that this is nominal performance: pivoting
may create additional slowdown in poorly conditioned problems.
Best,
Anton
On Thu, 2 Sept 2021 at 09:51,
Hello Kwant Community, In the 2014 kwant paper New J. Phys. 16 063065, Fig. 6 gives the conductance computation time scaling for 2D systems of side length L: O(L^2) for construction, O(L^3) for solving with the MUMPS-based solver, and O(L^4) for solving with RGF. I was wondering what the general scaling is for other dimensions. I presume it is known to experts and might be helpful to many users. Thank you.
Hello Anton, Thank you for your helpful reply. What is the case for d=1 and do you happen to know the scaling of RGF?
participants (2)
-
Anton Akhmerov -
xiaoxiao.zhang＠riken.jp