A scalable GMRES (Generalized Minimal RESidual) solver developed at the Intel lab Flanders has been implemented in the well-known and widely-used PETSc library (see here for the actual implementation). PETSc is a suite of data structures and routines for the scalable (parallel) solution of scientific applications modeled by partial differential equations.

The algorithm, called pipelined GMRES, is described in detail in our report (ExaScience report number 04.2012.1 available from our publications page). The method achieves good scalability by removing the expensive global synchronization points from standard GMRES. Impressive speedups have been observed for strong scaling experiments.

Thanks to Jed Brown for the actual PETSc implementation.