Chevron and Hydrodynamics Kernels and Operator Centerings

[Jeffrey Oldham]

Attached is a new document explaining the similarities between the
hydrodynamics kernel and the Chevron kernel.  Both algorithms compute
cells' faces' normals and then corner fluxes.  This presents
interesting challenges since face-centered and cell-centered
operations (operators) occur.  Fields with different granularities are
also used, but the previous proposal for interpolation and restriction
operators suffices.  Pseudocode for computing the corner fluxes is
presented.  Also, my attempt to explain to myself all possible
centerings for a d-D polytope is appended.

The second document, the proposal to add interpolation and restriction
operators to Pooma, has been revised to better address operators with
input fields having different centerings than the resulting output
fields.  When the input and output fields have different centerings,
the centerings must be explicitly specified.  Semantics for a few such
operators are provided.

To compute with fields with different centerings, Scott Haney proposed
conversion operators to convert from one centering to another.  I do
not know what the semantics of such a statement means.  For example,
the number of values in a face-centered field is signiicantly
different than in a cell-centered field.  Thus, a one-to-one matching
is not possible.  Instead, I propose extending interpolation and
restriction operators to accommodate different centerings.  For
example, one operator adds all face-centered values incident on a
cell to form a cell-centered value.

Unresolved is a consistent notation for referring to incident
geometric objects, e.g., given a face, refer to incident vertices.

Thanks,
Jeffrey D. Oldham
oldham at codesourcery.com
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