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Re: [Getfem-users] Fokker-Plank equation

From: Magnus Paulsson
Subject: Re: [Getfem-users] Fokker-Plank equation
Date: Fri, 20 May 2011 18:22:00 +0200

Thank you for a nice welcoming message to the email list!
(and sorry for the slow reply, meetings ...)

> Posted by Roman Putanowicz on May 20, 2011 - 03:04:
>> 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?

See last question (not very conclusive) ...

>> 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).

In the specific problem I'm looking at I have a regular mesh with 2 
independent cylinder coordinates (2 x 2D), i.e., r_1,2 and fi_1,2. Now I 
could simply transform the PDE to cylindrical coordinates and use a finite 
difference method. However, for this problem and learning for the future I'd 
prefer to just keep Cartesian coordinates -> curved boundaries. I'll be fine 
with Mesh.add_point().   

> "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.

1: Python lowers the time investment hugely (as does matlab). I'm not that 
scared of the time investment. 
2: I'm curious about the FEM. Since I come from a quantum chemistry background 
I see the similarities, i.e., using a basis and projecting the 
solution to the space spanned by the basis. I think this is the way to go 
and I have the experience with bases formed by radial functions*spherical 
harmonics. The FEM community has a lot of code and experience with localized 
basis sets. This I think will be worthwhile to learn.

>> 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.

A hint on how it would be entered in the C++ interface? I can then dig into 
the documentation.

Thanks again and have a nice weekend. - Magnus 

Magnus Paulsson
Assistant Professor
School of Computer Science, Physics and Mathematics 
Linnaeus University
Phone: +46-480-446308
Mobile: +46-70-6942987 

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