I will look through this in detail as soon as I can. We are in the middle
of a simulated mission right now, so I can't even breathe until Friday.
Sorry, but I'm sure we can straighten this out in relatively short order.
Ben
Original Message
From: Michael Povolotskyi [mailto:povolotskyi@...]
Sent: Wednesday, February 16, 2005 11:18 AM
To: KIRK, BENJAMIN (JSCEG) (NASA)
Cc: 'Roy Stogner'; libmeshusers@...
Subject: Re: [Libmeshusers] hanging nodes and triangular elements
Today we performed a set of tests in order to understand where the problem
is (if any). We are solving the equation
\nabla^2 u = exp((x^2 + y^2))
on a square 1.0<= x <= 1.0, 1.0<= y <= 1.0
The boundary conditions are as follows:
u = 1.0 if 1.0<=x<=0.8, y = 1.0
u = 1.0 if 0.8<=x<=1.0, y = 1.0
u = 0.0 if 0.4<=x<=0.4, y = 1.0
For the rest of the boundary we assume natural boundary conditions (von
Neumann).
In order to implement the Dirichlet boundary conditions we DON'T use the
penalty function method
shown in the examples.
Instead we assign boundary values to the nodes that lie on the boundary.
We found that the code produces a reasonable solution if:
a) there is no mesh refinement;
b) if there is uniform mesh refinement;
We have tested both triangular and rectangular finite elements, both first
and second approximation
order.
The "problems" start to appear when we use the adaptive mesh refinement.
Detailed study shows that
the same problems occur BOTH with triangular and rectangular elements (in
contrast to what I
informed yesterday).
We send a solution visualised by GMV program in files example_fullview.pdf
and
example_magnified.pdf. One can see in Fig. example_magnified.pdf that the
solution at some points
(indicated by red circles) is not continuous.
We tried different solvers. The solution changes very slightly, but the
problem persists.
In order to be more specific we attach our code (Poisson.C) and the input
file Poisson.in that the
program reads.
We don't understand if we are using libmesh in a wrong way or if there is a
problem in libmesh itself.
Thank you for your time,
Michael.
KIRK, BENJAMIN (JSCEG) (NASA) wrote:
> Are you using CG as the iterative solver? I just realized that the
> constraints are inserted into the system matrix in such a way that the
> solution vector automatically satisfies the constraints, but this is
> not symmetric.
>
> Try running your problem when CG and then with GMRES or BiCG. If the
> latter two work then the aforementioned problem is probably the source
> of your difficulty. Let me know & I'll get a patch together.
>
> Ben
>
>
>
> Original Message
> From: libmeshusersadmin@...
> [mailto:libmeshusersadmin@...] On Behalf Of Roy
> Stogner
> Sent: Tuesday, February 15, 2005 12:18 PM
> To: Michael Povolotskyi
> Cc: libmeshusers@...
> Subject: Re: [Libmeshusers] hanging nodes and triangular elements
>
>
> On Tue, 15 Feb 2005, Michael Povolotskyi wrote:
>
>
>>Yes, the code works correctly with uniformly refined triangular
>>elements.
>>
>>Could you, please, tell how can I check if the nodes are in a correct
>>order?
>
>
> If you're getting good results with uniform refinement, there's likely
> nothing wrong with your coarse mesh  the distorted triangle problem
> was just the only thing I'd ever seen that would give you problems
> with a triangular mesh but not a quadrilateral mesh.
>
> Could you specify exactly what problems you're getting with adaptive
> triangles that you aren't seeing with uniform triangles or adaptive
> quads? Is it a bad convergence rate, a crash, or something else?
> 
> Roy Stogner
>
>
> 
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> _______________________________________________
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>


Michael Povolotskyi, Ph.D.
University of Rome "Tor Vergata"
Department of Electronic Engineering
Viale Politecnico, 1  00133 Rome  Italy
Phone + 39 06 72597367
Fax + 39 06 2020519
http://www.optolab.uniroma2.it/pages/moshe/moshe.html

