[petsc-users] Problem when solving matrices with identity matrices as diagonal block domains

[Adrián Amor]

Thanks, it's true that with MAT_IGNORE_ZERO_ENTRIES I get the same
performance. I assumed that explicitly calling to KSPSetType(petsc_ksp,
KSPBCGS, petsc_ierr) it wouldn't use the direct solver from PETSC. Thank
you for the detailed response, it was really convenient!

2018-02-01 16:20 GMT+01:00 Smith, Barry F. <bsmith at mcs.anl.gov>:

>
> 1)   By default if you call MatSetValues() with a zero element the sparse
> Mat will store the 0 into the matrix. If you do not call it with zero
> elements then it does not create a zero entry for that location.
>
> 2)   Many of the preconditioners in PETSc are based on "nonzero entries"
> in sparse matrices (here a nonzero entry simply means any location in a
> matrix where a value is stored -- even if the value is zero). In particular
> ILU(0) does a LU on the "nonzero" structure of the matrix
>
> Hence in your case it is doing ILU(0) on a dense matrix since you set all
> the entries in the matrix and thus producing a direct solver.
>
> The lesson is you should only be setting true nonzero values into the
> matrix, not zero entries. There is a MatOption MAT_IGNORE_ZERO_ENTRIES
> which, if you set it, prevents the matrix from creating a location for the
> zero values. If you set this first on the matrix then your two approaches
> will result in the same preconditioner and same iterative convergence.
>
>   Barry
>
> > On Feb 1, 2018, at 2:45 AM, Adrián Amor <aamor at pa.uc3m.es> wrote:
> >
> > Hi,
> >
> > First, I am a novice in the use of PETSC so apologies for having a
> newbie mistake, but maybe you can help me! I am solving a matrix of the
> kind:
> > (Identity                     (50% dense)block
> > (50% dense)block     Identity)
> >
> > I have found a problem in the performance of the solver when I treat the
> diagonal blocks as sparse matrices in FORTRAN. In other words, I use the
> routine:
> > MatCreateSeqAIJ
> > To preallocate the matrix, and then I have tried:
> > 1. To call MatSetValues for all the values of the identity matrices. I
> mean, if the identity matrix has a dimension of 22x22, I call MatSetValues
> 22*22 times.
> > 2. To call MatSetValues only once per row. If the identity matrix has a
> dimension of 22x22, I call MatSetValues only 22 times.
> >
> > With the case 1, the iterative solver (I have tried with the default one
> and KSPBCGS) only takes one iteration to converge and it converges with a
> residual of 1E-14. However, with the case 2, the iterative solver takes,
> say, 9 iterations and converges with a residual of 1E-04. The matrices that
> are loaded into PETSC are exactly the same (I have written them to a file
> from the matrix which is solved, getting it with MatGetValues).
> >
> > What can be happening? I know that the fact that only takes one
> iteration is because the iterative solver is "lucky" and its first guess is
> the right one, but I don't understand the difference in the performance
> since the matrix is the same. I would like to use the case 2 since my
> matrices are quite large and it's much more efficient.
> >
> > Please help me! Thanks!
> >
> > Adrian.
>
>
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