Defines a preconditioner that can consist of 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 PCSetOperators())
Using a Krylov method inside another Krylov method can be dangerous (you get divergence or
the incorrect answer) unless you use KSPFGMRES as the other Krylov method
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 neccessary 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.