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Paper: inexact GMRES with fast multipole method and low-p relaxation
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All tests were done with preconditioned GMRES? #13

Closed labarba closed 8 years ago

labarba commented 9 years ago

§5.3, page 54 of the thesis (bottom) says:

"All tests were performed using a canonical right-preconditioned GMRES (algorithm 1) …"

I repeated this in the paper with a similar statement in section 3.1 "We solved [the BEM problem…] using a standard right-preconditioned GMRES…"

But I don't think this is right.

Preconditioning is not mentioned again in chapter 5 (tests with Laplace equation). I don't see it mentioned either in chapter 6 (tests with Stokes equation). But chapter 7 has a short section (7.2.3) reporting results "on multiple ethrocytes, using the block-diagonal and local preconditioners described in §3.3." So it looks like this is the only section that uses preconditioning, and the previous statement ("all tests…") is misleading. Right?

labarba commented 8 years ago

Tests in previous set of results were done with "identity preconditioner" ... i.e., no preconditioning. No explanation was given. But Tingyu made new tests in which he finds that the preconditioned cases take longer runtime, because the first iteration has a higher residual and the relaxed p is not as low.

In sum, we do not use preconditioning in this study, because it hinders relaxation. A question remains whether one could argue that the speed up should be with respect to the preconditioned unrelaxed case.