[Developers] [Patches] Make ADMConstraints GF public

Jonathan Thornburg jthorn at aei.mpg.de
Sun Sep 17 15:34:20 CDT 2006

On Sun, 17 Sep 2006, Erik Schnetter wrote:
| Ok, I see your point.  I hadn't realised we (are so foolish as to)
| compare non-O(1) values with absolute tolerances.  Using relative
| tolerances is *much* preferred...

> Using relative tolerances for constraints does not work.

I agree... but I thought we were discussing quantities with O(1) values
at each grid point.  I very much hope the constraints are a lot smaller
than that...

More generally, clearly values which are significantly larger than O(1)
need to be compared with relative tolerances (except if they have zero
crossings).  For values which are significantly smaller than O(1) but
don't cross through zero, again relative tolerances are good.

The problem case is gridfns which are significantly smaller than O(1),
and/or have zero crossings (eg maybe they oscillate around zero across
the grid).  The constraints are a classic example for this case.
Perhaps the Cactus testsuite checking infrastructure should have some
way to say (in a test.ccl file) that "any value with blah-norm <= this
threshold passes the test"?  (Although that's really more a test on the
norm than on the constraint itself.)

Another idea... we use a relative tolerance, where the scale is set by
a specified norm over the grid.  That is, the test passes if and only if
   gridfn(i,j,k) - reference_gridfn(i,j,k) <= epsilon * norm(reference_gridfn)
This would handle the constraints in a more reasonable way...


-- Jonathan Thornburg <jthorn at aei.mpg.de>      
   Max-Planck-Institut fuer Gravitationsphysik (Albert-Einstein-Institut),
   Golm, Germany, "Old Europe"     http://www.aei.mpg.de/~jthorn/home.html      
   "Washing one's hands of the conflict between the powerful and the
    powerless means to side with the powerful, not to be neutral."
                                      -- quote by Freire / poster by Oxfam

More information about the Developers mailing list