Add ReferenceCell::volume() and ::barycenter().

[bangerth]

I've needed something like a midpoint quadrature in ASPECT, and that turned out to be surprisingly difficult to generate for general cell shapes. Knowing the volume and barycenter is a good first step.

/rebuild

[bangerth]

So updated.

[kronbichler]

Sorry for nit-picking, but shouldn't this work:

Suggested change

	std::unique_ptr<FiniteElement<dim>> fe;
	if (reference_cell == ReferenceCells::Line)
	fe = std::make_unique<FE_Q<dim>>(1);
	else if (reference_cell == ReferenceCells::Triangle)
	fe = std::make_unique<FE_SimplexP<dim>>(1);
	else if (reference_cell == ReferenceCells::Quadrilateral)
	fe = std::make_unique<FE_Q<dim>>(1);
	else if (reference_cell == ReferenceCells::Tetrahedron)
	fe = std::make_unique<FE_SimplexP<dim>>(1);
	else if (reference_cell == ReferenceCells::Wedge)
	fe = std::make_unique<FE_WedgeP<dim>>(1);
	else if (reference_cell == ReferenceCells::Pyramid)
	fe = std::make_unique<FE_PyramidP<dim>>(1);
	else if (reference_cell == ReferenceCells::Hexahedron)
	fe = std::make_unique<FE_Q<dim>>(1);
	// Set up the objects to compute an integral on the reference cell
	FEValues<dim> fe_values(*fe, *q, update_JxW_values);
	FE_Nothing<dim> fe;
	// Set up the objects to compute an integral on the reference cell
	FEValues<dim> fe_values(fe, *q, update_JxW_values);

Since you never evaluate any of the shape functions?

[peterrum]

I would hope this does not work ;) But there is a FE_Nothing version that takes a reference cell!

[kronbichler]

Same here

Suggested change

	std::unique_ptr<FiniteElement<dim>> fe;
	if (reference_cell == ReferenceCells::Line)
	fe = std::make_unique<FE_Q<dim>>(1);
	else if (reference_cell == ReferenceCells::Triangle)
	fe = std::make_unique<FE_SimplexP<dim>>(1);
	else if (reference_cell == ReferenceCells::Quadrilateral)
	fe = std::make_unique<FE_Q<dim>>(1);
	else if (reference_cell == ReferenceCells::Tetrahedron)
	fe = std::make_unique<FE_SimplexP<dim>>(1);
	else if (reference_cell == ReferenceCells::Wedge)
	fe = std::make_unique<FE_WedgeP<dim>>(1);
	else if (reference_cell == ReferenceCells::Pyramid)
	fe = std::make_unique<FE_PyramidP<dim>>(1);
	else if (reference_cell == ReferenceCells::Hexahedron)
	fe = std::make_unique<FE_Q<dim>>(1);
	FE_Nothing<dim> fe;

[kronbichler]

OK apart from the comments regarding the test.

[bangerth]

I had assumed that FE_Nothing doesn't work for anything other than hypercubes, and didn't know about the added ability of that class. Thanks for teaching me about it :-)

So fixed now!

[drwells]

Also picky, but we could use ReferenceCell::get_gauss_type_quadrature(2)) here for improved genericity.

[bangerth]

Would you allow me to do this as a follow-up for cloned tests? I think there is value in testing the equivalence of the output since what constitutes a "Gauss" formula is not unique for anything other than tensor-product formulas (and the function you propose may or may not return the formulas I use above).

[drwells]

and here