AGMRES

AcronymDefinition
AGMRESAugmented Generalized Minimum Residual
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2 that in such a case, it is still beneficial to have an augmented basis in AGMRES.
With 8 subdomains, GMRES needs fewer iterations than AGMRES for all values of the restart length.
For the same reasons, AGMRES needs more iterations than GMRES for 16 subdomains and a large value of m.
For 32 subdomains, AGMRES needs fewer iterations than GMRES for all restart lengths.
Nevertheless, AGMRES is still faster than GMRES if we consider the parallel efficiency.
In order to compare the methods with similar memory requirements, we choose m = 24 for AGMRES and m = 48 for GMRES, since AGMRES needs to store the two systems Ws and Vs.
Another advantage of AGMRES over GMRES is the communication volume.
The numerical results on the VARGAS supercomputer (IBM Power 6 processors) confirm that AGMRES communicates less than GMRES and produces a faster solution of large linear systems.