[Carpet] CarpetReduce

[Erik Schnetter]

On Apr 27, 2006, at 04:59:26, Ian Hawke wrote:

> On Thu, 2006-04-27 at 10:44 +0200, Christian David Ott wrote:
>
>> Do people think that the grid _outer_ boundary zones should
>> be included in reduction operations like the "sum" reduction?
>
> I think it should be optional. It depends whether you see the  
> points as
> being inside your physical domain, and the boundary condition  
> implying a
> genuine physical update for them, or outside your physical domain, and
> the boundary condition just providing data such that the interior is
> "correct". In a way what you "believe" is encoded in the CoordBase
> parameters about how the boundary points are defined and shifted.
>
> However, this gets complex when using many different thorns with
> different possible boundary conditions. I would say that for safety  
> they
> should be _not_ included by default.

CoordBase lets you specify the boundaries in two steps.  First you  
specify the location of the physical boundary.  This is independent  
of the discretisation.  Then you specify the location of the grid  
points with respect to this boundary.  This also lets you label a  
certain number of grid points as "boundary points".  A drawback of  
this scheme may be that it applies to all grid functions, whereas you  
may want to treat different grid functions differently.

One of the concepts behind the current workings of CarpetReduce is  
the following.  If you integrate the function f(x)=1 over a domain D,  
then the result is the volume V of the domain.  I wanted to have the  
same property for any resolution h.  This makes it e.g. easy to check  
global mass conservation, since the total mass as reported by  
CarpetReduce has then no discretisation error.  However, this is not  
necessary -- one could have reduction operations that differ from  
their continuum counterpart by terms that converge to zero with h.

If you want to have outer boundary points ignored by CarpetReduce,  
then you have to tell CoordBase to place these points outside of the  
domain.  You already do this for symmetry points.  This may or may  
not be what you want.

If you do not refine near the outer boundary, then you also have the  
option to stagger the outer boundary between grid points.  Points  
exactly on the boundary (unstaggered points) are counted one half  
towards the sum reduction; staggered points have weights of either  
one or zero.

-erik

-- 
Erik Schnetter <schnetter at cct.lsu.edu>

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