dolfin team mailing list archive

[cosby@xxxxxxxxx]

> On Fri, Feb 15, 2008 at 02:46:25PM +0100, cosby@xxxxxxxxx wrote:
>> > On Thu, Feb 14, 2008 at 05:15:46PM +0100, cosby@xxxxxxxxx wrote:
>> >> > On Thu, Feb 14, 2008 at 10:06:43AM +0100, Kristen Kaasbjerg wrote:
>> >> >> Anders Logg wrote:
>> >> >> > On Wed, Feb 13, 2008 at 10:50:23PM +0100, cosby@xxxxxxxxx wrote:
>> >> >> >
>> >> >> >>>> On Wed, Feb 13, 2008 at 08:49:09PM +0100, Shilpa Khatri
>> wrote:
>> >> >> >>>>
>> >> >> >>>>> We (Dag and I) are doing this because we would like to have
>> >> Dolfin
>> >> >> >>>>> solve
>> >> >> >>>>> the
>> >> >> >>>>> Stokes/Navier-Stokes equations as one part of a timestep in
>> our
>> >> >> code
>> >> >> >>>>> where we
>> >> >> >>>>> are moving interfaces that are defined as a random set of
>> >> points
>> >> >> in the
>> >> >> >>>>> domain.
>> >> >> >>>>>
>> >> >> >>>>> Thanks,
>> >> >> >>>>> Shilpa
>> >> >> >>>>>
>> >> >> >>>> Then I suggest first finding out which cells those points lie
>> >> in,
>> >> >> then
>> >> >> >>>> then for each cell with a point get the expansion
>> coefficients
>> >> >> within
>> >> >> >>>> that cell, then multiply those coefficients with the values
>> of
>> >> the
>> >> >> >>>> basis functions at the points.
>> >> >> >>>>
>> >> >> >>>> The basis functions are available from the
>> ufc::finite_element.
>> >> >> >>>>
>> >> >> >>>> We can implement a suitable interface for this at some point
>> but
>> >> >> >>>> until then, you can do it manually.
>> >> >> >>>>
>> >> >> >>> Sounds good. Is the GTS_Interface still in place for
>> searching?
>> >> >> >>>
>> >> >> >>> /Dag
>> >> >> >>>
>> >> >> >> I'm a little lost here. How is the ufc module used to get hold
>> >> >> >> of the basis functions ?
>> >> >> >>
>> >> >> >> Kristen
>> >> >> >>
>> >> >> >
>> >> >> > You need to get hold of a ufc::finite_element and then call
>> >> >> > evaluate_basis_function (see UFC manual). If you have a
>> ufc::form,
>> >> >> > then you can create a ufc::finite_element by calling
>> >> >> > create_finite_element. If you have a dolfin::Form, then first
>> get
>> >> the
>> >> >> > ufc::form by calling form().
>> >> >> >
>> >> >> >
>> >> >> Ok, so this is doable via the python interface ?
>> >> >> In case yes, where is the dolfin::Form then hidden ?
>> >> >>
>> >> >> Kristen
>> >> >
>> >> > Yes, you can use it from the Python interface by calling the JIT
>> >> > compiler:
>> >> >
>> >> >   (compiled_form, compiled_module, form_data) = jit(a)
>> >> >
>> >> > You can then call compiled_form.create_finite_element(i) etc
>> >> > since this will be a Python wrapper for a ufc::form.
>> >> >
>> >> > BUT: If you are using the Python interface, then everything is
>> already
>> >> > available through the Python interface, so if you have a
>> >> > FiniteElement, you can tabulate it's values at any point by calling
>> >> > element.tabulate(). Note that this gives you values on the
>> reference
>> >> > element so you need to map the values to the physical element.
>> >> >
>> >> > Another comment is that things like this are better (more
>> efficiently)
>> >> > implemented as C++ components in DOLFIN and then wrapped back to
>> >> > Python for general use.
>> >>
>> >> Yes, I know. I only have to evaluate the potential at very few points
>> >> (< 100) though, so this wont be too expensive.
>> >> What about the expansion coefficients - there must be a set for each
>> >> cell ?
>> >
>> > You mean getting hold of the expansion coefficients so you can
>> > multiply them with the basis functions? These are in the Vector of
>> > degrees of freedom that each Function has:
>> >
>> >   x = u.vector()
>> >
>> > Then you need to get hold of the local-to-global mapping (which values
>> > in this vector that are the coefficients on any given element).
>> >
>> > The easiest way to do this is to let DOLFIN handle it by calling
>> > u.interpolate() to get the coefficients on a given cell.
>> >
>>
>> well, it seems to be an awful lot easier than I expected.
>> It is hard to penetrate these things when an proper overview
>> of the whole program structure is absent.
>
> Yes, the manual is in a sorry state.
>
>> If I understand you correctly then u.interpolate() returns the
>> coefficients of the basis on a given cell, correct?
>
> Yes.
>
>> These then
>> have to be multiplied by expansion coefficient from u.vector()
>> which again have to multiplied by the returned array from
>> element.tabulate(0,([x,y])).
>
> No, it's enough to multiply what you get from u.interpolate() with the
> values of the basis functions. (What the interpolation does is just to
> pick the correct values from the vector.)
>
>> One more thing. How are the coefficient extracted from the vector
>> from u.vector()
>
> It is done by tabulating the local-to-global mapping (dofmap) on a
> cell and then picking the values from the locations in the vector
> given by the local-to-global mapping.
>
>> and what is the difference between ufc::cell and
>> dolfin::Cell (arguments for the interpolate attribute of Function)?
>
> ufc::cell is a simple class that is used to pass data through the
> UFC-interface (which is not DOLFIN-specific and can be used by other
> libraries).
>
> dolfin::Cell is the DOLFIN implementation of a cell in a mesh. What we
> do is that we take the dolfin::Cell and then extract the values we
> need and put into the ufc::cell. There is a simple class UFCCell (yes,
> a third cell class) which helps you do this.

OK, so I now have the outputs from u.interpolate and element.tabulate.
Then I need the wrapping from the reference element to the physical
element. Any easy ways to do this from Python ?

Kristen


>
> --
> Anders
>
>
>
>> Kristen
>>
>>
>> >
>>
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