[petsc-users] ILU performance for 1d 2d and 3d

[Hong Zhang]

Gong Ding :

> Hi all,
> In my piratical, I found that ILU preconditioner has different performance
> (acceleration of GMRES/BCGS) for physical problems (i.e. poisson's
> equation) with different dimensions. Of course, ILU is exact for 1D
> problem. And for 2D, ILU usually works very well. However, ILU is less
> efficient for 3D problems.
>
> I guess this can be explained by matrix bandwidth and fill-in, however, is
> there any theoretical paper on this topic?
> And what about the optimized k of ILU(k) preconditioner for 3D problem?
>
There is no theory about ILU, purely empirical.
Increase level k would reduce number of total iterations at cost of
execution time, not a good choice
in general. For  poisson's equation, you may try multigrid preconditoner.

Hong

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