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General / Special quadrature rules in FFC

 

Some recent discussions and problems that have cropped up have led me to
need/want to add some specialized quadrature rules to FFC.  These include
"optimal" combinatorially-derived rules for given order polynomials for the
n-simplex, as well as rules that can be explicitly guaranteed to have
certain properties (positivity, all-internal-nodes, etc)

Does anyone else need anything like this?  I already have implementations of
a few nice rules for higher-dimensional applications, but have started to
adapt them for this purpose.  Ideally we would be able to specify a rule in
the ffc command.  I'm looking at where to put this.

There are other potential benefits to this move.  If we were to switch to
rules we have definite information about, we could use, say, group symmetry
properties, combined with symmetry properties of the unknowns, for further
optimization of the form compilation by quadrature.  We would already win,
especially in 3D, by getting away from the squashed rules and towards rules
that are more optimal.

- Peter

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