petsc-3.14.6 2021-03-30

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 CG. 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.

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
	see KSPSolve() for additional options

Notes

MPI configuration may be necessary for reductions to make asynchronous progress, which is important for performance of pipelined methods. See the FAQ on the PETSc website for details.

Contributed by

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

Example usage

[*] KSP 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 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.

Level

advanced

Location

src/ksp/ksp/impls/cg/pipelcg/pipelcg.c
Index of all KSP routines
Table of Contents for all manual pages
Index of all manual pages