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# KSPPIPELCG
Deep pipelined (length l) Conjugate Gradient method. This method has only a single non-blocking global reduction per iteration, compared to 2 blocking reductions for standard `KSPCG`. The reduction is overlapped by the matrix-vector product and preconditioner application of the next l iterations. The pipeline length l is a parameter of the method. [](sec_pipelineksp) 
## Options Database Keys

- ***-ksp_pipelcg_pipel -*** pipelined length
- ***-ksp_pipelcg_lmin -*** approximation to the smallest eigenvalue of the preconditioned operator (default: 0.0)
- ***-ksp_pipelcg_lmax -*** approximation to the largest eigenvalue of the preconditioned operator (default: 0.0)
- ***-ksp_pipelcg_monitor -*** output where/why the method restarts when a sqrt breakdown occurs





## Notes
MPI configuration may be necessary for reductions to make asynchronous progress, which is important for
performance of pipelined methods. See [](doc_faq_pipelined)


## Contributed by
Siegfried Cools, University of Antwerp, Dept. Mathematics and Computer Science,
funded by Flemish Research Foundation (FWO) grant number 12H4617N.


## Example usage
```none
    KSP tutorials ex2, no preconditioner, pipel = 2, lmin = 0.0, lmax = 8.0 :
        $mpiexec -n 14 ./ex2 -m 1000 -n 1000 -ksp_type pipelcg -pc_type none -ksp_norm_type natural
           -ksp_rtol 1e-10 -ksp_max_it 1000 -ksp_pipelcg_pipel 2 -ksp_pipelcg_lmin 0.0 -ksp_pipelcg_lmax 8.0 -log_view
    SNES tutorials ex48, bjacobi preconditioner, pipel = 3, lmin = 0.0, lmax = 2.0, show restart information :
        $mpiexec -n 14 ./ex48 -M 150 -P 100 -ksp_type pipelcg -pc_type bjacobi -ksp_rtol 1e-10 -ksp_pipelcg_pipel 3
           -ksp_pipelcg_lmin 0.0 -ksp_pipelcg_lmax 2.0 -ksp_pipelcg_monitor -log_view
```



## References

- **** -*** J. Cornelis, S. Cools and W. Vanroose,
"The Communication-Hiding Conjugate Gradient Method with Deep Pipelines"
Submitted to SIAM Journal on Scientific Computing (SISC), 2018.
- **** -*** S. Cools, J. Cornelis and W. Vanroose,
"Numerically Stable Recurrence Relations for the Communication Hiding Pipelined Conjugate Gradient Method"
Submitted to IEEE Transactions on Parallel and Distributed Systems, 2019.



## See Also
 [](ch_ksp), [](sec_pipelineksp), [](doc_faq_pipelined), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSPCG`, `KSPPIPECG`, `KSPPIPECGRR`, `KSPPGMRES`,
`KSPPIPEBCGS`, `KSPSetPCSide()`, `KSPGROPPCG`

## Level
advanced

## Location
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ksp/ksp/impls/cg/pipelcg/pipelcg.c.html#KSPPIPELCG">src/ksp/ksp/impls/cg/pipelcg/pipelcg.c</A>


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


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