[petsc-users] Combining preconditioners

[Barry Smith]

On Jun 27, 2014, at 11:22 PM, Qin Lu <lu_qin_2000 at yahoo.com> wrote:

> Hello,
> 
> I would like to combine two preconditioners in PETSc linear solver. The first preconditioner is user defined, the second one is just PETSc ILU, and the residual is updated after application of each preconditioner (the multiplicative form). There are two questions:
> 
> 1. Shall I use PCShellSetApply to set the user defined preconditioner, and then use PCCompositeAddPC to combine the 2 preconditioners?

   Yes

> 2. The user defined preconditioner only applies to part of the components of the unknowns, in other words, the rank of the first preconditioner matrix is less than the rank of the full matrix. How can I let PETSc know how to update the residual after the application of the first preconditioner? Can I define a routine of residual updating for PETSc?

   At first just use PCCOMPOSITE and let PETSc compute the residual by doing the usual complete matrix-vector product. Usually the cost of the matrix vector product is much less then a preconditioner so it is not worth optimizing.

   If the composed preconditioner works very well and the shell PC affects only a small percentage of the components of the problem then you can switch to PCFIELDSPLIT which does support only updating a portion of the residual.

   Barry

> 
> Many thanks for your help.
> 
> Best Regards,
> Qin