[Users] Failing AHFinderDirect test cases.

[Peter Diener]

Hi,

I have been looking at why some of AHFinderDirect test cases fail.

First I checked the tests running on 1 processor and found that the cause 
of the failing test cases was a bug fix made in 2005 where the tests had
not been updated afterwards. For those tests I regenerated the output.

One additional test failed by not producing output because it didn't 
converge to the specified tolerance. I wasn't able to find a version of 
the code (after the date that the test case had been created) that I was 
able to compile and that passed the test. For that reason (after 
discussing with Erik) I disabled that test by renaming the parameter file 
to someting not ending in .par.

After that I realized that a lot of the tests failed when running on 2 
procs. After some investigating, I realized that the cause was to be find 
in Exact. When going from 1 to 2 procs, the coordinates setup by CoordBase 
and CartGrid3d can differ at the roundoff level. In the particular case I 
was looking at in one case the y-coordinate was

-3.3999999999999999

while in the other it was:

-3.4000000000000004

so a difference only in the last digit.

This introduced a difference of the computed 4-metric in the 2 last 
digits. Now Exact uses 2nd order finite differencing with an epsilon of 
1.e-6 to calculate time derivatives of the 3-metric and and the spatial 
derivatives of the shift that is needed to calculate the extrinsic 
curvature. In this process there is a significant cancelletion of digits 
leading to a loss of 6-7 digits so the extrinsic curvature only agreed
to 9-10 digits. In other grid points the coordinates were identical and
so was the extrinsic curvature. So essentially the process of constructing 
the extrinsic curvature iteself lead to some arbitrary noise at the 9-10 
digit level. When this was fed into AHFinderDirect the differences were
amplified even more leading to differences in the mass at the 6th digit
level.

Currently Erik is working on improving this (by using higher order finite 
differencing with a larger epsilon), but the main conclusion is that we 
have to be very careful when making tests based on initial data from the 
current version of Exact and may have to reduce the accuracy criteria for 
pass/fail significantly.

Cheers,

   Peter