ffc team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Thu, Jul 08, 2010 at 08:03:35PM +0100, Garth N. Wells wrote:
>
>
> On 08/07/10 19:42, Anders Logg wrote:
> >On Thu, Jul 08, 2010 at 02:36:09PM +0100, Garth N. Wells wrote:
> >>
> >>
> >>On 08/07/10 13:13, Anders Logg wrote:
> >>>On Thu, Jul 08, 2010 at 01:02:43PM +0100, Garth N. Wells wrote:
> >>>>
> >>>>
> >>>>On 08/07/10 12:59, Anders Logg wrote:
> >>>>>On Thu, Jul 08, 2010 at 12:00:38PM +0100, Garth N. Wells wrote:
> >>>>>>
> >>>>>>
> >>>>>>On 08/07/10 11:49, Kristian Oelgaard wrote:
> >>>>>>>On 8 July 2010 08:22, Garth N. Wells<gnw20@xxxxxxxxx>     wrote:
> >>>>>>>>On Jul 8 2010, Anders Logg wrote:
> >>>>>>>>
> >>>>>>>>>On Wed, Jul 07, 2010 at 10:34:39PM +0100, Kristian Oelgaard wrote:
> >>>>>>>>>>
> >>>>>>>>>>On 7 July 2010 20:22, Garth N. Wells<gnw20@xxxxxxxxx>     wrote:
> >>>>>>>>>>>
> >>>>>>>>>>>
> >>>>>>>>>>>On 07/07/10 20:14, Anders Logg wrote:
> >>>>>>>>>>>>
> >>>>>>>>>>>>On Wed, Jul 07, 2010 at 06:26:20PM +0100, Kristian Oelgaard wrote:
> >>>>>>>>>>>>>
> >>>>>>>>>>>>>Supporting CellVolume makes it possible to do:
> >>>>>>>>>>>>>
> >>>>>>>>>>>>>CG = FiniteElement("Lagrange", triangle, 2)
> >>>>>>>>>>>>>DG = FiniteElement("DG", triangle, 0)
> >>>>>>>>>>>>>v = TestFunction(DG)
> >>>>>>>>>>>>>f = Coefficient(CG)
> >>>>>>>>>>>>>vol = triangle.v
> >>>>>>>>>>>>
> >>>>>>>>>>>>Would it be better to call it vol or volume instead of v? Or does it
> >>>>>>>>>>>>have to be a one-letter word?
> >>>>>>>>>>>>
> >>>>>>>>>>>
> >>>>>>>>>>>. . . or call it 'volume'.
> >>>>>>>>>>
> >>>>>>>>>>It can be whatever we want, I just followed what was already there.
> >>>>>>>>>>Should we then rename 'd', 'n' and 'x' to 'geometric_dimension',
> >>>>>>>>>>'facet_normal', and 'spatial_coordinate' while we're at it?
> >>>>>>>>>
> >>>>>>>>>I think d, n, x are fine, but v does not necessarily look like a
> >>>>>>>>>volume to me (it looks like a test function).
> >>>>>>>>>
> >>>>>>>>
> >>>>>>>>I agree - d, n and x are all commonly used, but v for volume isn't.
> >>>>>>>
> >>>>>>>I changed 'v' to 'volume' and fixed a few bugs along the way.
> >>>>>>>
> >>>>>>>On a related note, should we implement CellDiagonal too?
> >>>>>>>We use cell.diagonal() for MeshSize in SpecialFunctions.h of DOLFIN
> >>>>>>>and since we often use MeshSize for the 'h' coefficient in DG forms
> >>>>>>>e.g., PoissonDG we could remove the need for this function evaluation.
> >>>>>>>The code to compute the CellDiagonal could just be copied from
> >>>>>>>IntervalCell, TriangleCell and TetrahedronCell of DOLFIN and dumped in
> >>>>>>>codesnippets.py.
> >>>>>>>
> >>>>>>
> >>>>>>What if we call it 'Circumradius'?
> >>>>>>
> >>>>>>I recall that the agreed not have have CellSize because of the
> >>>>>>ambiguity in its definition, but circumradius is unambiguous, so I
> >>>>>>vote to add it.
> >>>>>
> >>>>>Isn't 'diameter' better? It is shorter and well-defined
> >>>>>(2*circumradius).
> >>>>>
> >>>>
> >>>>'diameter' isn't well defined. We can use it, but we would need to
> >>>>define it as being 2*circumradius.
> >>>>
> >>>>Garth
> >>>
> >>>Why isn't it well-defined? The diameter of a set T is
> >>>
> >>>   d = sup_{x,y \in T} ||x - y||
> >>>
> >>>and that should be the same as 2*circumradius unless I'm mistaken.
> >>>
> >>
> >>What's the set T? At a glance, the above is true if T is not the
> >>polygon, but the set of all points inside the circle inside which
> >>the polygonal can be inscribed.
> >
> >Yes, don't know what I was thinking. Let's try again... For a
> >polygon, the diameter should be the same as the longest edge which
> >should be very easy to compute so why not use that?
> >
>
> Longest edge and circumradius (which is also called the radius of a
> polygon, just to make things confusing) are not the same.

I see that but I was suggesting having 'diameter' in addition to
'circumradius' since 'diameter' is shorter and simpler and easier to
compute. It also seems to me like the difference between the two is
small, in particular for thin triangles where the two should be the
same (diameter = 2*circumradius).

--
Anders

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