[petsc-users] Hypre and IC preconditioning

[Hong Zhang]

Umut:
We have incomplete cholesky preconditioner (icc) in petsc, but do not
have support for drop tolerance.

Hyper and superlu support ILUT, which is an unsymmetric preconditioner,
thus cannot be used for cg.

Several years ago, I tried to write ilut for petsc, but did not see
any convincing
benefit  of dropping small matrix entries compared with ilu.
The development was then abandoned.

Note, ilut requires almost full matrix numerical factorization for
dropping entries; the only trade-off is controlled memory for matrix factors.
For numerical stability, row/col pivot is needed in general.
There is no math theory that supports dropping small entries would
still maintain
good approximation of full matrix factorizations.
I would suggest using icc instead.

Hong

> Dear all,
>
> I would like to test some ideas of mine over the CG method with incomplete
> cholesky preconditioner with a drop tolerance.
> I checked the Hypre manual for the preconditioner generation, however there
> is not a direct IC preconditioner but and ILUT which results in an
> unsymmetric preconditioner, is it wise to use this as a preconditioner for
> CG in PETSc?
>
> Best regards,
> Umut