[Trilinos-Users] [EXTERNAL] Behavior of ML preconditioner

Raymond Tuminaro rstumin at sandia.gov
Thu Sep 27 11:22:07 EDT 2018

   I took a look at the matrices. Overall, they seem very different from the type of matrices that ML would do well on. 
In particular, the sparsity pattern is highly non-symmetric. There are some rows where the off-diagonals are much larger 
than the diagonal. However, it does seem that the matrix eigenvalues are primarily real and positive. It is a little 
hard for me to figure things out just staring at matrix entries, but the pattern doesn't look like a standard PDE type 
stencil. Perhaps ... some re-ordering of the equations is possible to make things look more 'standard'. Is this a PDE 

The short summary is that I wouldn't expect ML to do so well on this type of matrix. I'd probably just try an ILU 
preconditioner in Trilinos instead.


On 09/05/18 20:24, Eric Marttila wrote:
> Hello,
> I am seeing some interesting behavior with the ML preconditioner.
> I have two matrices which appear to be nearly identical, but when I create the ML preconditioner with matrix1, I see a 
> warning message from ML:
>           Gen_Prolongator warning : max eigen <= 0.0
> I do not see the warning message when I create the preconditioner with matrix2.
> When I use matrix1 (along with the ML preconditioner generated with matrix1) to perform a linear solve with AztecOO, the 
> solution will converge.
> However, when I use matrix2 (along with the ML preconditioner generated with matrix2) to perform a linear solve with 
> AztecOO, the solution will *not* converge.
> So my questions are:
> 1) Why does ML generate two (apparently) very different preconditioners when the two input matrices appear to be nearly 
> identical?
> 2) In the case with matrix1 (where I get the Gen_Prolongator warning), is ML entering some sort of 'fail-safe' mode in 
> order to generate a usable preconditioner?
> 3) Are there any ML settings that I should use to help ML generate a usable preconditioner for these types of matrices?
> I've attached the two matrices (they are fairly small), as well as some source code I've used to generate the 
> preconditioner. Also attached is the output of running the code with the two different matrices.
> Any thoughts are greatly appreaciated!
> Thanks,
> Eric Marttila
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Ray Tuminaro                  phone: (925) 294-2564
MS 9159                       fax:   (925) 294-2234
Sandia National Laboratories  email: rstumin at sandia.gov
PO Box 969
Livermore, CA 94551

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