🚀 go-pugleaf

In article <1992Dec16.095858.5370@dutrun2.tudelft.nl>, rcpshdb@dutrun2.tudelft.nl (Han de Bruijn) writes:
|> In article <1992Dec15.092610@roper.mc.ti.com> W. Donald Rolph:
|> > You are indeed confused.
|> 
|> I am never confused about these things.
|> 
|> >  Any approximation procedure must have trial functions.
|> 
|> No, no.
|> 
|> > In traditional FEA they are called shape functions, choose the name you like
|> > but all FEA procedures must have some approximating function over the domain
|> > space.
|> 
|> *All* procedures?
|> 
|> Gee, how then could I calculate the temperature distribution in a sodium pump
|> by an direct FE method, WITHOUT ever needing such "approximating functions"?
|> (An accompanying article is called "Multimode Heat Transfer in Sodium Pumps".
|> It is found in the Proceedings of the 0Xth Conference on Numerical Methods
|> in Thermal, or whatever, Problems, Swansea U.K., 197X. Look it up ;-)
|> 
|> I also did some work on pure advection without shape functions. But who am I?
|> There exists CFD code named "FLOTRAN", which has a "streamline upwind" scheme
|> in it, derived directly without shape functions. It's all in my SUNA articles.
|> 
|> And almost any Finite Element book starts with the assembly of resistor-like
|> elements, without approximations. The element-matrix of an electrical resistor
|> is derived directly by applying the laws of Ohm and Kirchhoff, giving:
|> 
|>          | +1/R  -1/R |
|>          | -1/R  +1/R |
|> 
|> Just define the connectivity (no coordinates) of your resistor-network,
|> two voltages as a boundary condition, and go ...
|> -- 
|> * Han de Bruijn; Applications&Graphics | "A little bit of Physics * No
|> * TUD Computing Centre; P.O. Box 354   | would be NO idleness in  * Oil
|> * 2600 AJ  Delft; The Netherlands.     | Mathematics" (HdB).      * for
|> * E-mail: Han.deBruijn@RC.TUDelft.NL --| Fax: +31 15 78 37 87 ----* Blood

When you defined your resistor network you assumed a trial function which is
linear between the nodes.  You also incidentally also assumed triangular elements
if you applied this over 2D surfaces (I assume tetrahedrals over 3D but I haven't
worked that problem out.).  In short just because you chose lumped elements did
not remove you from choosing a trial function, it just hid the trial function
from your observations!  Good luck I enjoy talking with you!!
-- 

Regards.
 
Don Rolph  a722756@pan.mc.ti.com WD3 MS10-13 (508)-699-1263