Re: [Getfem-users] Assembly of 1D Poiseuille term

[Yves Renard]

Dear Domenico,

In the two assembly languages, the gradient has indeed the dimension of the 
mesh, i.e. a 3D one in this case. It is along the tangent direction of the line 
in this case.
One way to obtain the tangent vector is to use "element_K" from the high-level 
generic assembly (gradient of the geometric transformation).
The assembly string
" -p*Grad_u.element_K "
should work. May be "element_K" have to be transposed.

Additionally, if you need to interpolate some field from the 3D mesh to the 1D 
mesh and perform some matrix assembly, the use of the high-level generic 
assembly is far more simple (see 
http://download.gna.org/getfem/html/homepage/userdoc/gasm_high.html#interpolate-transformations).


Yves.


----- Original Message -----
From: "Domenico Notaro" <address@hidden>
To: "getfem-users" <address@hidden>
Sent: Sunday, July 26, 2015 7:30:42 PM
Subject: [Getfem-users] Assembly of 1D Poiseuille term

Dear Users, 




I am studying a coupled 3D-1D problem, for the sake of simplicity let's imagine 
a straight line immersed in a box. 


I am wondering how to assemble the matrix corresponding to the weak formulation 
of the Poiseuille term in the 1D problem, -(p, du/ds), being p the pressure of 
the fluid inside the segment, u the velocity and s the arc length along the 
segment. I have to idea how to write the derivative inside the generic_assembly 
since the only way I know to compute derivate is "Gradient(#..)" that is a 
vector. 

Do I need to project the gradient along the direction of the segment? If this 
is the case, I don't know how to compute the tangent versor. Thank you in 
advance. 






Regards, 

domenico_notaro 

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