[Cactuseinstein] IDAnalyticBH -- making Kerr.c a bit more robust

[Bernard Kelly]

Hi.

This may be something that only affects me, but would it be possible to 
alter the analytic BH data thorns to protect against pathological values 
  on the coordinate origin and axes?

In particular, I have "Kerr.c" in mind. I've been using it with 
"avoid_origin = 'no'", and it doesn't like on-axis points. This could be 
fixed by adding a minimum (small) to a particular variable -- "rho_2" -- 
  which would then propagate through the remaining values. Later 
calculations of analytic derivatives (of the conformal factor) would 
have to be slightly rewritten to avoid pathologies.

To be specific, the few changes below allow me to work on-axis and do 
pointwise convergence tests. Could something like this be implemented in 
CactusEinstein? It should have no adverse effects on existing off-axis 
calculations.

Bernard

******************** suggested code changes in Kerr.c ***************

#define Max(x,y)   (x>y)? x:y // NEW CODE
[...]
CCTK_REAL tmp2; // NEW CODE
[...]
rho_2=xx*xx+yy*yy;
rho_2 = Max(1.e-10,rho_2); // NEW CODE
[...]
if(make_conformal_derivs)
   {
[...]
     tmp2 = zz/rho/R_2; // NEW CODE
     tmp=2/R_2+1/rho_2;
     //  OLD CODE:    d2qdxx=dqdx*(1/xx-xx*tmp);
     d2qdxx=tmp_BEAN * ( 1. - xx * xx * tmp); // NEW
     d2qdxy=-dqdx*yy*tmp;
     //  OLD CODE:    d2qdyy=dqdy*(1/yy-yy*tmp);
     d2qdyy=tmp_BEAN * ( 1. - yy * yy * tmp); // NEW
     d2qdzz=-2*dqdz*zz/R_2;
     //  OLD CODE:    tmp=2/R_2-1/zz/zz;
     //  OLD CODE:    d2qdxz=-zz*dqdx*tmp;
     d2qdxz= (xx/rho/R_2) * (1. - 2.*zz*zz/R_2); // NEW
     //  OLD CODE:    d2qdyz=-zz*dqdy*tmp;
     d2qdyz= (yy/rho/R_2) * (1. - 2.*zz*zz/R_2); // NEW



-- 
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Bernard Kelly * C.G.W.A. * University of Texas at Brownsville

Hedley Lamarr: My mind is a raging torrent, flooded with rivulets of
thought cascading into a waterfall of creative alternatives.
-- Blazing Saddles (1974)
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