# PCKSP#

Defines a preconditioner as any `KSP`

solver. This allows, for example, embedding a Krylov method inside a preconditioner.

## Options Database Key#

use the matrix that defines the linear system, Amat as the matrix for the inner solver, otherwise by default it uses the matrix used to construct the preconditioner, Pmat (see**-pc_use_amat -**`PCSetOperators()`

)

## Note#

The application of an inexact Krylov solve is a nonlinear operation. Thus, performing a solve with `KSP`

is,
in general, a nonlinear operation, so `PCKSP`

is in general a nonlinear preconditioner.
Thus, one can see divergence or an incorrect answer unless using a flexible Krylov method (e.g. `KSPFGMRES`

, `KSPGCR`

, or `KSPFCG`

) for the outer Krylov solve.

## Developer Note#

If the outer Krylov method has a nonzero initial guess it will compute a new residual based on that initial guess
and pass that as the right-hand side into this `KSP`

(and hence this `KSP`

will always have a zero initial guess). For all outer Krylov methods
except Richardson this is necessary since Krylov methods, even the flexible ones, need to “see” the result of the action of the preconditioner on the
input (current residual) vector, the action of the preconditioner cannot depend also on some other vector (the “initial guess”). For
`KSPRICHARDSON`

it is possible to provide a `PCApplyRichardson_PCKSP()`

that short circuits returning to the `KSP`

object at each iteration to compute the
residual, see for example `PCApplyRichardson_SOR()`

. We do not implement a `PCApplyRichardson_PCKSP()`

because (1) using a `KSP`

directly inside a Richardson
is not an efficient algorithm anyways and (2) implementing it for its > 1 would essentially require that we implement Richardson (reimplementing the
Richardson code) inside the `PCApplyRichardson_PCKSP()`

leading to duplicate code.

## See Also#

KSP: Linear System Solvers, `PCCreate()`

, `PCSetType()`

, `PCType`

, `PC`

,
`PCSHELL`

, `PCCOMPOSITE`

, `PCSetUseAmat()`

, `PCKSPGetKSP()`

, `KSPFGMRES`

, `KSPGCR`

, `KSPFCG`

## Level#

intermediate

## Location#

## Examples#

src/ksp/ksp/tutorials/ex71.c

src/ksp/ksp/tutorials/ex60.c

src/ksp/ksp/tutorials/ex87.c

Index of all PC routines

Table of Contents for all manual pages

Index of all manual pages