A pipelined conjugate gradient method developed by Bill Gropp. Pipelined Krylov Methods
This method has two reductions, one of which is overlapped with the matrix-vector product and one of which is overlapped with the preconditioner.
KSPPIPECG, which has only a single reduction that overlaps both the matrix-vector product and the preconditioner.
MPI configuration may be necessary for reductions to make asynchronous progress, which is important for performance of pipelined methods. See What steps are necessary to make the pipelined solvers execute efficiently?
Pieter Ghysels, Universiteit Antwerpen, Intel Exascience lab Flanders
KSP: Linear System Solvers, Pipelined Krylov Methods, What steps are necessary to make the pipelined solvers execute efficiently?,