Suggestion for future capability

[Alan Bromborsky]

My suggestion is to implement what I call a pde to finite element
translator. One would input a system of pde's and parameterized
approximating functions (such as certain classes of polynomials or
cardinal spline functions) and get the equivalent finite element
equations for the designated approximating functions. One thing this
would require is the ability to evaluate symbolic integrals of the
approximating functions overlap integrals over tetrahedral volumes and
surfaces.

[someone]

Hi,

I think this should continue the work in [1]
and then finally integrate with fenics[2].

[1] https://code.google.com/p/symfe/
[2] http://fenicsproject.org/applications/

[Tim Lahey]

SymFE doesn't appear to exist anymore as the Hg repository is gone.
There is SfePy which is still ongoing, though. That said, I'm not sure
how much it relates to SymFE. It does do 2D and 3D systems.

I implemented a Raleigh-Ritz approach for deriving FE element mass and
stiffness matrices in Maple (but only for beams). It's not as general as
a Galerkin approach, but was suitable for the systems I was solving.
I've been meaning to port it (as well as the solver code) to
SymPy/NumPy, but other things have been getting in the way.

One of the problems with trying to implement a system where you just
input a system of PDEs and parameterizing functions is that you can run
into problems for certain kinds of functions. I know of a thesis where
L-Splines were used, but they found problems at the boundaries of the
elements and found locking.

Cheers,

Tim.

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[Ondřej Čertík]

There is also this, as part of [2]:

https://launchpad.net/fenics-syfi

Ondrej