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# PCTFS
A parallel direct solver intended for problems with very few unknowns (like the coarse grid in multigrid). Performs a Cholesky or LU factorization of a matrix defined by its local matrix vector product. 


## Notes
Only implemented for the `MATMPIAIJ` matrices

Only works on a solver object that lives on all of `PETSC_COMM_WORLD`!

Only works for real numbers (is not built if `PetscScalar` is complex)

Implemented by  Henry M. Tufo III and Paul Fischer originally for Nek5000 and called XXT or XYT


## See Also
 `PCCreate()`, `PCSetType()`, `PCType`, `PC`

## Level
beginner

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

## Implementations

<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ksp/pc/impls/tfs/comm.c.html#PCTFS_giop">PCTFS_giop in src/ksp/pc/impls/tfs/comm.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ksp/pc/impls/tfs/comm.c.html#PCTFS_grop">PCTFS_grop in src/ksp/pc/impls/tfs/comm.c</A><BR>


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


[Index of all PC routines](index.md)  
[Table of Contents for all manual pages](/manualpages/index.md)  
[Index of all manual pages](/manualpages/singleindex.md)