PCKSP#

Defines a preconditioner as any KSP solver. This allows, for example, embedding a Krylov method inside a preconditioner.

Options Database Key#

-pc_use_amat - 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())

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.