[Carpet] Proper nesting

[Erik Schnetter]

On Apr 3, 2008, at 12:35:33, Ian Hinder wrote:
> Erik Schnetter wrote:
>
>> much larger than expected.  Therefore Carpet does not enforce proper
>> nesting in the loose sense above.
>
> OK - so that is why it allows the 14 cell example, even though it is
> improperly nested.
>
> Now, it looks like CarpetRegrid2 (which I am not using) claims to
> "enforce" proper nesting.  To do this, it seems to work from the  
> coarse
> grids to the fine ones, and for each grid, it works out whether the
> current grid would need to be enlarged to contain the next finest one.
> It then enlarges it if necessary, and then goes to the next finest and
> repeats.  Is this roughly right?

This is right, except that it works from finest to coarsest grid.   
There are no quotes around "enforce", since it actually does enforce  
proper nesting by enlarging grids if necessary.  Only if the second- 
coarsest grid is too large, there is an error, since otherwise the  
basegrid would need to be enlarged, which would be confusing.

>  Is this procedure supposed to ensure
> proper nesting, in the sense that no points are used for prolongation
> that are themselves prolongated?

Yes.  In addition, it also requires a certain distance between the  
boundaries of fine and coarse grids, i.e., a certain number of grid  
points which are neither interpolated from the next coarser nor serve  
to interpolate to the next finer grid.

> How can it do this if it doesn't know
> about the number of buffer zones, which are only added later in the  
> routine?

?

It should know about the buffer zones.  Maybe there is an error...

> It also seems like the algorithm computes the size of the fine grid,  
> but
> does not take into account the fact that the fine grid might
> subsequently be enlarged.

There are several consistency conditions.  Proper nesting is one,  
having (if desired) a rotating-180 symmetry is another.  Plus there  
are conditions on inter-grid spacings, distances from outer boundaries  
etc.  These are currently enforced in a "random" order.  What really  
should happens is that these are all enforces simultaneously, or in a  
loop until nothing changes any more.  Note that errors in these  
consistency conditions are still caught by Carpet later on, so that  
error detection here is somewhat optional.

-erik

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

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