No subject

interpolation uses the points i-2, i-1, i, i+1, i+2, i+3.  In other
words, when interpolating to any given point, there is a preferred
direction.  Shouldn't this mean that the interpolation is no longer
invariant when (for example) a reflection symmetry thorn is used?  A
polynomial interpolation which uses 6 points has a fitting polynomial of
degree 5 (this gives the order in the parameter), and an interpolation
error of order 6.  Is this correct so far?

Now, if I want to perform an interpolation, I assume that the nearest
grid point to the coordinate that I want to interpolate to will be
labeled i, and I will need at least three points in a neighbourhood of i
to be available to perform the interpolation.  In CarpetLib/src/dh.cc,
we have

prolongation_stencil_size () = ... prolongation_order_space / 2

which I understand will give 2, as C rounds integer arithmetic down.  I
would have expected to have 3, as the required number of points.  Is
this not the intent of this parameter?

Finally, since the number of ghost zones required is 3, we could
implement 6th order prolongation (with a 7th order error) for a small
computational cost, without requiring any more ghost zones, and without
introducing a preferred direction.

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