ffc team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Wed, Aug 13, 2008 at 04:36:48PM -0400, Shawn Walker wrote:
> ok, but I have a couple other questions/comments?
>
> 1. Has there been a decision on what kinds of curved meshes will be  
> allowed?  And what would the mesh format be?  This seems to be the first  
> decision.  It would seem natural to only allow polynomial based maps  
> (for now), i.e. a quadratic triangle would require a 2nd order polynomial 
> mapping (instead of a 1st order map).  You could also have higher degrees 
> if you wanted.  I think the 'curved' mesh feature could be implemented  
> first.  And the assembly could just IGNORE the extra curvy info for each  
> triangle (for now).
>
> 2. For the assembly, I think it is still possible to compute the matrices 
> exactly in SOME cases.  For example, a mass matrix could be computed  
> exactly, as well as \int_{\Omega} q div(u), because the det(J) would  
> cancel the 1/det(J) part of the inverse of the gradient map.  Of course,  
> the stiffness matrix cannot be computed exactly.  For this, I think  
> quadrature is the only way.  Or one could maybe take advantage of doing 
> an
> asymptotic expansion (taylor series) of the algebraic expression and  
> compute that using enough terms based on the desired number of digits of  
> accuracy.  I don't know.

I think it's be possible to do it "exactly" since FFC precomputes
integrals on the reference cell (when using its so-called tensor
representation of the form).

> 3. One could add another boolean property to each triangle called:
>
> Is_Straight
>
> This could give a switch between computing exactly, and using quadrature. 
> Most meshes will have straight interior elements; you don't really need  
> them inside so much.  only the triangles with a face on the boundary  
> would be curved.  So this would help prevent possible performance hit of  
> doing high order quadrature.

Sounds good.

> 4. How hard would it be to understand UFC~FFC for someone who knows just 
> a little Python and a decent amount of C++?

Not that hard. Start by looking at the UFC manual. It's the only one
of our manuals that is in good shape. Then look at the generated code,
then at the form compiler.

> If there is anything written up on how FENICS wants to do this (i.e.  
> desired mesh format, etc...) please tell me.

No, nothing. But maybe it is better to go for isogeometric rather than
isoparametric as Matt suggests?

-- 
Anders


> - Shawn
>
> On Wed, 13 Aug 2008, Anders Logg wrote:
>
>> On Wed, Aug 13, 2008 at 11:56:11AM -0400, Shawn Walker wrote:
>>> Hello.  I know this isn't very critical on the list of things to do, but
>>> is there any document somewhere saying how they propose to implement
>>> curved meshes with the UFC/FFC code?
>>>
>>> - Shawn
>>
>> No, I guess they have no idea how to do this. ;-)
>>
>> It would require an extension of UFC and it would require someone
>> willing to spend the time on making it work. It's not on the top of my
>> TODO list, but anyone wishing to investigate is welcome.
>>
>>

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