On 7/26/06, Roy Stogner <roystgnr@ices.utexas.edu> wrote:
On Wed, 26 Jul 2006, David Xu wrote:

> On 7/26/06, Roy Stogner <roystgnr@ices.utexas.edu> wrote:
>
>> Loop over all the elements.  On each geometric element, reinit your FE
>> object with a grid quadrature rule whose order at least equals your
>> polynomial degree.  Get the XYZ coordinates and the solution value at
>> each quadrature point, and output them.

I kinda get it, but still vague about how to implement it. Once I load the eigenfunction value points from file to libMesh using NumericVector<>::set(), how does libMesh provide me with the eigenfunction point at requested quadrature point? I think I'm missing something here. I know how to get xyz at requested quadrature point from the examples.

>
> I do this after I load the eigenvector solutions back to libMesh, correct?

Yes.

> If I reinit FE object with a grid quadrature rule, how can Imake sure the
> XYZ coordinates at each quadrature point are the ones correspondent to the

You don't.  You're not plotting eigenvector coefficients, you're
plotting eigenfunction points.  Depending on the finite element space
you use, your coefficients may correspond to function points, but they
may also correspond to mixed second derivatives, projection
magnitudes onto orthogonal function spaces, or the phase of the moon!
So forget about trying to plot the coefficients themselves, and just
worry about how to plot the function they represent.

> Can I just ouput the xyz at each quadrature point at the element matrices
> (Ke, Me) assembly step? Output them to a file and concatenate with the
> eigenvector solutions? Will that work?

No.

>> That will output vertex and edge points multiple times, but the plot
>> should look the same.  If your elements are so large that the plot
>> still looks faceted, use a quadrature rule with more points.
>
> Same question here, if  I use a quadrature rule different from the one used
> to assemble Ke, Me, will the xyz coordinates at the each quadrature point be
> correctlycorrespondent to the eigenvector solutions with the size of global
> DOFs?

No, they won't.  That's why you don't just get the xyz coordinates at
each quadrature point, you get the solution value at each quadrature
point too.
---
Roy