[CIG-MC] ConMan issues report

Wolfgang Bangerth bangerth at tamu.edu
Thu Aug 18 10:54:15 PDT 2016

On 08/18/2016 11:46 AM, John Naliboff wrote:
> I’ll see how this compares to the iterative solver for the 2-D tests I’m
> running.

My rule of thumb has always been that direct solvers are really hard to 
beat for everything with less than 100,000 unknowns. That limit may 
actually be 200-300,000 today. That's good enough for most 2d problems.

In 3d, the complexity is different because the size of the front direct 
solvers have to work through is no longer the N^{1/2} from 2d (in 
essence, the number of degrees of freedom that are located on a line 
that sweeps the domain), but N^{2/3} (the number of DoFs that are 
located on a surface that sweeps the domain). This means far more memory 
consumption, and far more computations. So in 3d, direct solvers are 
often not competitive already for much smaller problems.


Wolfgang Bangerth          email:                 bangerth at colostate.edu
                            www: http://www.math.colostate.edu/~bangerth/

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