[Carpet] Proper nesting

[Ian Hinder]

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

> Actually, I couldn't follow the calculation in your
> email.  The calculation in your figure is correct.  Note that Carpet add

Yes, the one in the email was difficult to describe (and possibly
misleading), which is why I added the figure.

> Your figure assumes that the outermost active fine grid point coincides
> with a coarse grid point.  This is not required, and if not, you may
> need one more active point on the next coarser grid.

Yes - I deliberately made this assumption to simplify the discussion.

Thanks for all the information - I will have a look at the documentation
you pointed to as well.

-- 
Ian Hinder
hinder at gravity.psu.edu
http://www.gravity.psu.edu/~hinder