Faces

The computational domain is assumed to be in the shape of a $n$-dimensional `rectangle', which has $2n$ $n-1$ dimensional faces. (Usually $n$ is three.) Each of these $2n$ faces is assigned a specific bit in a word, so that arbitrary subsets can be compactly expressed as a bitwise-or of these individual bits. Macros defining this mapping of subsets to bits will be provided. For the moment there is only CCTK_ALL_FACES, which corresponds to the set of all faces of the domain. If you need face specific calls immediately, please use the old interface for now.

The mapping of bits to faces will likely be the same as that used for the (optional) BOUNDARY_WIDTH array. Precisely, the rule is as follows. For a $d$ dimensional grid variable, label the elements or bits by integers $i$ from $0$ to $2d-1$. Element or bit $i$ gets mapped to face $(-)^{i+1}e_{\lfloor i\rfloor}$, where ${}_{\lfloor \rfloor}$ designates the `floor' function (greatest integer less than its argument), and $e_j$ represents the `$j$-direction' on the grid.