[Users] Improve finite differencing in Exact

[Erik Schnetter]

The enclosed patch improves the finite differencing that is used in  
Exact to calculate the extrinsic curvature.  These finite differences  
are independent of the Cactus grid spacing.  This is prompted by a  
remark by Peter Diener that the current finite differencing accuracy  
for the extrinsic curvature from thorn Exact is only about nine digits.

It introduces new parameters "exact_order" and "exact_eps" that choose  
the order (2nd or 4th) and stencil size (default 1e-6).  It also  
introduces new functions Exact__metric_deriv and Exact__metric_deriv2  
that evaluate these finite differences.

Some finite differencing terms for the spatial derivative of the shift  
have to be rewritten, which may lead to differences on the order of  
the finite differencing accuracy.

The code could be rewritten to evaluate each stencil point only once  
in all calls to the new finite differencing operators.  This would  
reduce the number of evaluations.  Since thorn Exact is often very  
fast, this does not seem necessary at this point.

Unfortunately, this patch causes five of the AHFinderDirect test cases  
to fail.

-erik

-- 
Erik Schnetter <schnetter at cct.lsu.edu>   http://www.cct.lsu.edu/~eschnett/


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