[Trilinos-Users] [EXTERNAL] Behavior of ML preconditioner
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:
> 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
> 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!
> Eric Marttila
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> Trilinos-Users at trilinos.org
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