> That only seems so. You interpolate in one direction and use the results
> in the next step. In the end every point except the gridpoints at the
> faces depend on all 64 points. Also, the result does not depend on the
> order you apply the interpolations in.

That's reassuring that the order doesn't make a difference.  It seems like
it should give results that make some sense, but it's not immediately
intuitive that the order makes no difference.  It can't be perfectly
isotropic with the modified monotonic cubic interpolation though.

> It is only 64 multiplications and some additions, straight from the
> linear algebra section of any library.

Well, it comes out to a whole lot more than that once you do it the
roundabout way.  This is the slowest part of the simulation, so I was
wondering if there were better techniques.  Reading over the description
again, it seems pretty clear this is what they intended.

Thanks for your help although it looks like I'll still use the same
technique.  I tried simplifying it a little by cutting out twenty-four of
the points and turning it into a sort of 3-D '+'.  That allows for combined
linear and cubic interpolation.  Combined with fourth-order R-K integration
on a ~50x50x50 grid, that makes for roughly 2,500,000 cubic interpolations
per timestep (since the faces and center must be integrated along the
velocity, then the quantities have to be determined after the integration).
 I also might pad the array with either zeros or df/dn=0 for boundary
conditions to prevent having to check whether it is outside the domain or
not for each interpolation.  Pardon my confusion and thanks again for your
help.

 - Ricky

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