Hi all,

Today's Bernd's update of his CACTUS thorn_BAM_Elliptic
enables to treat Robin boundary condition  u=1+c/r in solving elliptic
equations. I tried this with solving Poisson equation for LaneEmden
stars, and find this option works almost properly. I only checked at 33*3
at Indy. The solution seems to be similar with exact solution, but
not fit as well as the fixing boudary with u=1+c/r. This might be
from the resolution, but overshooting even at single star case, and
more overshoot for binary. 

By the way,
in the recent review by Oohara-Nakamura-Shibata [1], they describe
how to fix boundaries to solve elliptic equations in their simulation
in detail (appendix B and C in [1]).  They fix outer boundary for 
Poisson equations not at the order (1/r) but at (1/r^2) in order to 
solve the equation for time-derivative of potential in the same way
with original Poisson. They say such a technique is crucial for 
solving conformal factor in evolution. 
They also solve momentum constraint at the order (1/r^3) in order 
to treat the interface of the solver same way regardress of the 
existence of the linear momentum.   

I am not sure this is essential, but for our future, 
I request the followings:

  Robin BC.. not only for 1+c/r, but also c0+c1/r, if possible. 

  Robin BC.. not only for c0+c1/r, but also c0+c2/r**2 and 
             c0+c3/r**3, if possible.

  bug? .... BAM_Elliptic with 
            bound="flat bamrobin" 
            grid ="BAM full" 
            runs at 33^3 but complains and stops at 65^3 at Origin2000.  


[1] K. Oohara, T. Nakamura and M. Shibata 
"A way to 3D Numerical Relativity", in 
Progress of theoretical physics Supplement 128 (1997 Dec, p183),
"Perturbative and Numerical approaches to Gravitational Waves"
ed. by T. Nakamura. 



Hisaaki SHINKAI                               
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