Allow passing a maximum degree quadrature to a measure

[JHopeCollins]

If you have a complicated or non-polynomial expression in a form then UFL may (rightly or wrongly) estimate a very high quadrature degree, then TSFC spits out the dreaded message:

tsfc: WARNING Estimated quadrature degree more than tenfold greater than any argument/coefficient

You can avoid this by telling TSFC exactly what quadrature degree to use with:
inner(expr, v)*dx(degree=fixed_degree).

However, this hardcodes the degree and if you change something in expr it will still use fixed_degree even if now UFL may estimate something lower.

This PR allows passing a maximum quadrature degree that will only be used if UFL estimates a higher degree. If UFL estimates a lower degree then that will be used. This max degree is passed via the measure metadata:

inner(expr, v)*dx(metadata={'max_quadrature_degree': max_degree})

By default nothing will be printed to screen if the maximum degree is chosen, but if you change the logging level to INFO then you can see when it happens.

[pbrubeck]

We should also explain this in the manual

[JHopeCollins]

Just to make sure I don't mislead anyone:

If you passed form_compiler_parameters={"max_quadrature_degree": degree} to a solver, would it appear in the parameters here? Would it get overridden if you had passed a different one to the measure of a particular term?

[connorjward]

Just to make sure I don't mislead anyone:

If you passed form_compiler_parameters={"max_quadrature_degree": degree} to a solver, would it appear in the parameters here? Would it get overridden if you had passed a different one to the measure of a particular term?

I don't know. The easiest thing to do is try and see what happens.

[pbrubeck]

If you passed form_compiler_parameters={"max_quadrature_degree": degree} to a solver, would it appear in the parameters here? Would it get overridden if you had passed a different one to the measure of a particular term?

Are you asking about the design we want? Basically we want the analogues to dx(degree=q) and form_compiler_parameters["quadrature_degree"] . The metadata in the Measure should override anything passed on in form_compiler_parameters.

[JHopeCollins]

Are you asking about the design we want?

No, I was checking what will actually happen so I make sure I don't write the wrong thing in the manual!

The metadata in the Measure should override anything passed on in form_compiler_parameters.

Ok great, this is the main thing I wanted to check (and actually use myself).

[JHopeCollins]

We should also explain this in the manual

@pbrubeck I've added a paragraph to the manual page on quadrature rules.

[pbrubeck]

We need a test, it could be something like

mesh = UnitIntervalMesh(1)
x, = SpatialCoordinate(mesh)
form = (x**4)*dx
assert np.isclose(assemble(form, fcp={"max_quadrature_degree": 2}), assemble(form, fcp={"quadrature_degree": 2}))
assert np.isclose(assemble(form, fcp={"max_quadrature_degree": 5}), assemble(form))

and similar tests for dx(metadata={"max_quadraute_degree": q})

[pbrubeck]

This looks great, thanks. It makes much more sense to emphasize max_quadrature_degree as early as possible in the manual.