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Paper: inexact GMRES with fast multipole method and low-p relaxation
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Are the errors normalized? #4

Closed labarba closed 9 years ago

labarba commented 9 years ago

The first time we see errors are on the grid-convergence study with the Laplace equation, Figs. 5.2 and 5.3 in the thesis. The vertical axis is labeled "Error" and the caption says "convergence," while the text just mentions that the expected rates of convergence are seen. What was the measure of error? (In total charge or potential, for example? This is not mentioned.) Is it normalized by something?

With the Stokes flow, we have grid-convergence shown on Fig. 6.3, and again the vertical axis is labeled "Error" but we have no definition of the error measure anywhere. The error in this case is in the total drag force. I'd like confirmation that the error measure here was normalized by the exact value of drag.

Errors are again used in the grid-convergence study with a red blood cell. The quantity used is total drag force, but it's not said whether the error is normalized by the extrapolated "exact" value. (Fig. 7.3 of the thesis.)

labarba commented 9 years ago

Ah-ha. The small plots for the paper version do say "relative error" on the vertical axis. This is a good sign, but still I would like to confirm, since the error measure is not defined anywhere that I can find.

slayton58 commented 9 years ago

I compute the exact and approximate answers for a point in the domain and normalise by the exact error:

e = fabs(approx-exact) / fabs(exact)

labarba commented 9 years ago

pls clarify --- "answers for a point" = the value of phi or dphi/dn on one, randomly selected point anywhere?? (for Laplace equation) (if so, I worry about using just one point; why not the norm of the error at all points combined?)

For Stokes: the quantity of interest is already an integral (the drag). Confirm that you used the extrapolated value (with Richardson extrapolation) for normalizing?

slayton58 commented 9 years ago

The code checks against one point in the domain (this is what Chris was doing at the time, so I did the same)

Norm at all points is expensive for actually iterating on code modifications -- the original code checked against many points, and was reduced down when I was seeing the same behaviour from checking a single point

slayton58 commented 9 years ago

For Laplace both phi and dphi/dn were checked, for Stokes u_x and u_y were checked

For Stokes I used an analytical solution for the exact value

On Jun 2, 2015, at 8:28 AM, Lorena A. Barba notifications@github.com wrote:

pls clarify --- "answers for a point" = the value of phi or dphi/dn on one, randomly selected point anywhere?? (for Laplace equation) (if so, I worry about using just one point; why not the norm of the error at all points combined?)

For Stokes: the quantity of interest is already an integral (the drag). Confirm that you used the extrapolated value (with Richardson extrapolation) for normalizing?

— Reply to this email directly or view it on GitHub https://github.com/barbagroup/inexact-gmres/issues/4#issuecomment-107937602.

labarba commented 9 years ago

There's no analytical solution for the red blood cells. I just wanted confirmation that this was normalized with the extrapolated value.

slayton58 commented 9 years ago

Ok, for the RBC yes, this was normalized with the extrapolated value

On Jun 2, 2015, at 1:03 PM, Lorena A. Barba notifications@github.com wrote:

There's no analytical solution for the red blood cells. I just wanted confirmation that this was normalized with the extrapolated value.

— Reply to this email directly or view it on GitHub https://github.com/barbagroup/inexact-gmres/issues/4#issuecomment-108017184.