🚀 go-pugleaf

In article <1992Dec16.164320@roper.mc.ti.com> a722756@roper.mc.ti.com (W.  
Donald Rolph) writes:
> 
> In article <1992Dec15.225304.11571@porthos.cc.bellcore.com>,  
bhatia@bigcat.bellcore.com (Raman Bhatia) writes:
> |> In article <1992Dec14.181725@roper.mc.ti.com>, a722756@roper.mc.ti.com (W.  
Donald Rolph) writes:
> |> |> 
> |> |> This is by no means a trivial question.  You must first ask the class  
of FEA to
> |> 
> |> Raman Bhatia (bhatia@bigcat.bellcore.com)
> 
> I have an interesting proof that show that the triangularization schemes all
> violate controllability theory at any given point in the model.  The effect  
is
> that in 3D, with typcial dimensions in orthoganoal directions which have
> significantly different scales (1.4 in thick by 5 inches wide by 20 inches  
long),
> the triangularizations schemes produce highly unsatisfactory meshes for many
> classes of problems, particularly nonlinear problems.  It is interesting to  
note
> the CFd codes are gradually adopting Laplacian mesh generation schemes,  
schemes
> which were popular as early as 1960 for fea.  It should be noted that CFD can  
be
> very suseptible to poor meshes, and perhaps there is a message here!  
> 
> I have simplistic proof which suggests that Laplacian mapping produces the
> "optimal mesh" fgor certain classes of problems, based on the givven mesh  
density
> provided as input.  I also have s ample program which generates hexahedral  
meshes
> off an arbitray boundary rep trimmed nurb solid model, demonstrating that the
> technogy is feasible, and the input is not overly burdensome.
> -- 
> 
> Regards.
>  
> Don Rolph  a722756@pan.mc.ti.com WD3 MS10-13 (508)-699-1263

Yes. That is true. However, it is possible to control the "aspect ratio"
in meshes, be it 2-D or 3-D. I assume that in 2-D it is triangular elements
and in 3-D it is tetrahedral elements. Laplacian mapping is one way to improve
the aspect ratio. There is also a very good paper in mesh smoothing. I shall
mail it or post it if there is any interest. I don't remember it off my head.

-Muthu
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S. N. Muthukrishnan                | muthu@mecad.uta.edu |
Dept.of Mech. Engg., UT, Arlington | muthu@fem.uta.edu   |(NeXT mail)
Arlington, TX  76019               | muthu@newton.uta.edu|
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"Perception is a reality. Reality is myth"
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