On Fri, 6 Feb 1998, Edwin E Evans Jr. wrote:

>  Wai Mo suggested that you have already done some preliminary work in adding  
>  functionality for solving the momentum constraints in BAM.  If you don't  
>  mind I would like to see what you have done.  I wouldn't hurry though  
>  since I haven't even had time to take a proper look at thorn_BAM yet. 
>  					Ed Evans 
>   


Hi Ed!

BAM is prepared for systems of coupled equations. Examples are
- the three momentum constraints, or all four constraints together 
- minimal distortion shift, potentially coupled with a lapse condition

"All" that is needed is some code that computes the elliptic operator
L(u) that has to vanish, L(u) = 0.

Relaxation methods as those employed in BAM need L(u) in form of a
simple function call: for example for the Poisson equation on a grid,
L(u) = Laplace(u) - rho, so the function call returns 

(u(i-1) - 2 u(i) + u(i+1))/h^2 + ... - rho(i) 

with h the grid spacing. Really simple even if u is a vector. The point
is that all the vector loops are already in BAM, but untested. Perhaps
more importantly, BAM uses a method that is more or less known to work
well for the constraints and minimal distortion. 


So, you write this function L(u), I plug it in, and off we go!

The place to start is that you should have a look at York's paper of 1979
on the 3+1 decomposition, look up the formula for the "vector laplacian",
and code this up. I have a Mathematica script that could be of some help.
You first should have a look at the problem yourself.

Don't hesitate to ask questions.
Keep me posted, or better even, post to the project page,
Bernd

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