AGMRES

AcronymDefinition
AGMRESAugmented Generalized Minimum Residual
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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.
It increases faster for GMRES than for AGMRES. We note here again that deflation is needed to reach a good accuracy for large values of D.
Nevertheless, AGMRES is still faster than GMRES if we consider the parallel efficiency.
It includes the time to compute the orthonormal basis (with Arnoldi GMRES or QR factorization for AGMRES) and the time to update the eigenvectors U for AGMRES(m, r).
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.