[Carpet] Proper nesting

[Ian Hinder]

Hi,

I now have a question about proper nesting.  My current understanding is
that in order to be "properly nested", prolongation into the buffer
zones of a fine grid should not use any points from the coarse grid
which are themselves filled via prolongation.  Is this correct?

For a system with 12 buffer points, and equal numbers of points on each
refinement level, I think this means that using grids of 16 cells (17
points) (in radius) would be properly nested, but 14 cells (15 points)
would not be.  For simplicity, I am only considering the positive half
of the grid; imagine a symmetry on the other side, and also that there
are an even number of cells on each level, meaning that the last point
owned by the fine grid is also present on the coarse grid.

See the attached diagram for my reasoning.  It goes something like this:

* We want to determine the minimum number of grid cells we can have in
the coarse region.

* This region contains the fine buffer points, plus two extra coarse
points needed to interpolate into the fine grid.

* This comes to 12/2 + 2 coarse grid cells. Any points to the right of
these are not used in prolongation, and can themselves be buffer points,
so in the minimum setup, they will be.

* The total number of cells on a level is twice the number in the coarse
region, which would be 12 + 2*2 = 16.

However, when I construct a grid of 14 cells, Carpet does not complain.
 Using 12 gives the error

WARNING[L1,P0] (CarpetLib): [ml=0 rl=1 c=0] The following grid structure
consistency check failed:
   The communicated region must be contained in the active part of the
domain
   comm <= domain_active

which I assume has replaced the "Not properly nested" warning from
Carpet 3.  I have verified, in the case of 14 cells, that the points I
expect appear in the 1D ASCII output, and I am using CarpetRegrid to
construct the grid.  So my question is: why is Carpet not complaining
when I use only 14 cells?  Is my argument above incorrect?

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