# PCFieldSplitSetSchurFactType
sets which blocks of the approximate block factorization to retain in the preconditioner 
## Synopsis
```
#include "petscpc.h" 
PetscErrorCode PCFieldSplitSetSchurFactType(PC pc, PCFieldSplitSchurFactType ftype)
```
Collective on pc


## Input Parameters

- ***pc  -*** the preconditioner context
- ***ftype -*** which blocks of factorization to retain, `PC_FIELDSPLIT_SCHUR_FACT_FULL` is default



## Options Database Key

- ***-pc_fieldsplit_schur_fact_type <diag,lower,upper,full> -*** default is full





## Notes
The FULL factorization is

```none
   (A   B)  = (1       0) (A   0) (1  Ainv*B)  = L D U
   (C   E)    (C*Ainv  1) (0   S) (0     1)
.vb
    where S = E - C*Ainv*B. In practice, the full factorization is applied via block triangular solves with the grouping L*(D*U). UPPER uses D*U, LOWER uses L*D,
    and DIAG is the diagonal part with the sign of S flipped (because this makes the preconditioner positive definite for many formulations, thus allowing the use of KSPMINRES). Sign flipping of S can be turned off with PCFieldSplitSetSchurScale().

    If A and S are solved exactly
.vb
      *) FULL factorization is a direct solver.
      *) The preconditioned operator with LOWER or UPPER has all eigenvalues equal to 1 and minimal polynomial of degree 2, so `KSPGMRES` converges in 2 iterations.
      *) With DIAG, the preconditioned operator has three distinct nonzero eigenvalues and minimal polynomial of degree at most 4, so `KSPGMRES` converges in at most 4 iterations.
```


If the iteration count is very low, consider using `KSPFGMRES` or `KSPGCR` which can use one less preconditioner
application in this case. Note that the preconditioned operator may be highly non-normal, so such fast convergence may not be observed in practice.

For symmetric problems in which A is positive definite and S is negative definite, DIAG can be used with `KSPMINRES`.

A flexible method like `KSPFGMRES` or `KSPGCR` must be used if the fieldsplit preconditioner is nonlinear (e.g. a few iterations of a Krylov method is used to solve with A or S).


## References

- **** -*** Murphy, Golub, and Wathen, A note on preconditioning indefinite linear systems, SIAM J. Sci. Comput., 21 (2000).
- **** -*** Ipsen, A note on preconditioning nonsymmetric matrices, SIAM J. Sci. Comput., 23 (2001).



## See Also
 `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurScale()`

## Level
intermediate

## Location
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ksp/pc/impls/fieldsplit/fieldsplit.c.html#PCFieldSplitSetSchurFactType">src/ksp/pc/impls/fieldsplit/fieldsplit.c</A>

## Examples
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/dm/impls/stag/tutorials/ex4.c.html">src/dm/impls/stag/tutorials/ex4.c.html</A><BR>

## Implementations

<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ksp/pc/impls/fieldsplit/fieldsplit.c.html#PCFieldSplitSetSchurFactType_FieldSplit">PCFieldSplitSetSchurFactType_FieldSplit in src/ksp/pc/impls/fieldsplit/fieldsplit.c</A><BR>


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[Edit on GitLab](https://gitlab.com/petsc/petsc/-/edit/release/src/ksp/pc/impls/fieldsplit/fieldsplit.c)


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