Re: [Getfem-users] Fokker-Plank equation

[Roman Putanowicz]

> Dear GetFEM++ users,
> 
> I would like to play around with transport equations and while writing the 
> questions below I realised that the stiffness matrix will not be 
> symmetrical. So before we start: can GetFEM calculate the non-symmetric 
> stiffness matrix? There is no need to solve the linear system. From the 
> mailing list it seems that the answer is no.

I have done thermo-elastic coupling in GetFEM which gives non-symmetric
tangent matrix and there was no problem with it. Could you pleas indicate
to which posting in the mailing list are you referring?

> NO: can you suggest any other FEM package that can handle 
> these kind of equations in more than 3 dimensions?

> 
> YES: Please read on.
> 
> I would like to play around a little bit with the Fokker-Planck (FP) 
> equation: (a PDE that has many names so you may recognise is as (at 
> least similar to) Klein-Kramers, Liouville, Boltzmann-transport 
> equation etc ...). However, I have limited experience with FEM and 
> thus problems in deciding whether or not FEM is the way to go and to 
> decipher the user manual.

You have indicated that you would like to solve problems in space
with dimension > 3. I might be wrong but besides selecting FEM
solver you may encounter problems  generating n-dimensional discretisation
of the space (triangulation) unless the space is simple hypercube
(though some tools can handle n-dimensional space, if I recall correctly
qhull for instance).

"whether or not FEM is the way to go" is a good question. Personally given
a PDE to solve I would ask myself if I need unstructured meshes for any
reason. If so (for instance to handle complex geometries, to capture 
discontinuities in solution or initial data) then yes, FEM might be a way to go.
Otherwise if I can go with topologically regular meshes and the solution 
is fairly regular I would consider sort of  FDM.

I would look at the above question not purely from the point of view of
numerical methods but considering the issue : what is the advantage of
investing in new software tools, especially if I can solve the problem with
the means I already have. If the drive is scientific curiosity, the yes, I can
go, but otherwise pragmatic approach seems to be most fruitful.

It may sound a bit bitter but biggest deficiency of most of the software
packages is the insufficient support in overcoming steep learning curves.
In most cases this is not the fault of the authors of the tools but a tip
of a more general problem (and a topic for separate long discussion).

> The main question:
> 0: Can the GetFEM++ handle the first order derivatives? Do they not give a 
> non-symmetric stiffness matrix?
As I mentioned I do not see that a lack of symmetry of the tangent matrix
is any problem for GetFEM.
> 1: How do I enter the first order derivative terms, i.e., A.grad(u) terms?
> Where A is a vector or vector field. (Preferentially in the python 
> interface)

This is possible in C++ interface, but unfortunately  I cannot comment 
if also in the Python interface.

Regards,

Roman
-- 
Roman Putanowicz, PhD  < address@hidden  >
Institute for Computational Civil Engng (L-5)
Dept. of Civil Engng, Cracow Univ. of Technology
www.l5.pk.edu.pl, tel. +48 12 628 2569, fax 2034