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

[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?  

Gong Ding