One more question came up when I watched your video "What solver to use".
In there you mentioned that direct solvers in 2d have a complexity of
O(N^2), where N is the number of unknowns.
There is an approximation for N, i.e.
N \approx p^d *|Omega| / h^d.
So from that can one say that solving a linear system with UMFPACK has a
complexity of O(1/h^{4}) for a fixed degree p and d=2?
I ask that because I measured the times for solving two large linear
systems in 2d, one with 1 Million DoFs and the other one with 2 Million
DoFs (reducing h to h/2). The former took 11 seconds, the latter 110
seconds, i.e. they are related by a factor of 10 and not 16.
Backcalculating this, the factor of 10 would follow from a complexity of
O(N^5/3}).
So is this is a plausible rate or is my linear system still not big enough
to see the rate of 16? Is the renumbering scheme, which does UMFPACK
internally, may the source why I see a lower rate?
Best
Simon
Wolfgang Bangerth schrieb am Mittwoch, 2. Juni 2021 um 18:21:56 UTC+2:
> On 6/2/21 10:16 AM, Simon Wiesheier wrote:
> > One more question to the renumbering schemes: I called
> > DoFRenumbering::Cuthill_McKee(dof_handler) before calling the initialize
> > function of the direct solver.
> >
> > So this isn´t really necessary when using UMFPACK because internally a
> > different renumbering scheme is called anyway?
>
> Correct.
> W.
>
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth email: [email protected]
> www: http://www.math.colostate.edu/~bangerth/
>
>
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