libmesh-users

[Libmesh-users] Get XYZ location of global DOFs

[David X. <dx...@my...>]

Hi All,

After I used 3rd order hermite shape function, I realized the resulting
dimension of the assembled system matrices is not equal to the number of
mesh nodes as in the case of using 2nd order Lagrange. The dimension equals
the number of DOFs. I was wondering how to get xyz physical location of each
of the global DOF points. Is there an iterator available like the one for
mesh nodes?

Thanks,

David

Re: [Libmesh-users] Get XYZ location of global DOFs

[David X. <dx...@my...>]

Roy,

Thanks. The reason why I need xyz of the DOFs is that my system matrices are
solved by an eigenvalue solver outside libmesh and the size of the
eigenvector solution produced by the solver equals to the dimension of the
system matrices (or DOFs). I'd like to plot the eigenvector solutions, thus
I need to the correspondent xyz coordinates of each of the eigenvector value
for visualization purpose.

It was easy to do for the 2nd order Lagrange because the size of the
eigenvector = n_nodes, now I'm stuck at plotting the results from 3rd order
hermite, which have much better accuracy.

David

On 7/26/06, Roy Stogner <roy...@ic...> wrote:
>
> On Wed, 26 Jul 2006, David Xu wrote:
>
> > After I used 3rd order hermite shape function, I realized the resulting
> > dimension of the assembled system matrices is not equal to the number of
> > mesh nodes as in the case of using 2nd order Lagrange. The dimension
> equals
> > the number of DOFs. I was wondering how to get xyz physical location of
> each
> > of the global DOF points. Is there an iterator available like the one
> for
> > mesh nodes?
>
> No, there isn't.  If you want to be dangerous, you can use the
> DOFObject interface of a node in the mesh of an initialized
> EquationSystems to view every global degree of freedom index on that
> node.  Keep in mind that for many elements (including the HERMITE
> elements for p=4 and above, I think) there are also degrees of freedom
> associated with the Elem itself.
>
> Why do you need the physical location of non-Lagrange degrees of
> freedom?  That's kind of unusual.
> ---
> Roy Stogner
>

Re: [Libmesh-users] Get XYZ location of global DOFs

[Roy S. <roy...@ic...>]

On Wed, 26 Jul 2006, David Xu wrote:

> Thanks. The reason why I need xyz of the DOFs is that my system matrices are
> solved by an eigenvalue solver outside libmesh and the size of the
> eigenvector solution produced by the solver equals to the dimension of the
> system matrices (or DOFs). I'd like to plot the eigenvector solutions, thus
> I need to the correspondent xyz coordinates of each of the eigenvector value
> for visualization purpose.

No, you don't.  Those XYZ coordinates *overlap* - each Hermite point
will have 2 degrees of freedom in 1D, 4 in 2D, and 8 in 3D.  You can
throw away all but the first degree of freedom on each node and plot
each piecewise cubic element as a piecewise linear, but if you want an
accurate representation of your results you'll either need plotting
software that can handle higher polynomials or you'll need to
subdivide your mesh elements.

The most general way you can do things is to load your eigenvector
solutions back into libMesh (preferably into the same running process
that gave you the original matrix, so there's no question of node
renumbering).  Then you can use the libMesh plotting functions
(assuming you're happy with the limitations of those output formats)
or use the libMesh FE objects to get an arbitrarily dense cloud of
points for your own plotting software.
---
Roy Stogner

Re: [Libmesh-users] Get XYZ location of global DOFs

[Roy S. <roy...@ic...>]

On Wed, 26 Jul 2006, David Xu wrote:

> After I used 3rd order hermite shape function, I realized the resulting
> dimension of the assembled system matrices is not equal to the number of
> mesh nodes as in the case of using 2nd order Lagrange. The dimension equals
> the number of DOFs. I was wondering how to get xyz physical location of each
> of the global DOF points. Is there an iterator available like the one for
> mesh nodes?

No, there isn't.  If you want to be dangerous, you can use the
DOFObject interface of a node in the mesh of an initialized
EquationSystems to view every global degree of freedom index on that
node.  Keep in mind that for many elements (including the HERMITE
elements for p=4 and above, I think) there are also degrees of freedom
associated with the Elem itself.

Why do you need the physical location of non-Lagrange degrees of
freedom?  That's kind of unusual.
---
Roy Stogner

Re: [Libmesh-users] Get XYZ location of global DOFs

[Roy S. <roy...@ic...>]

On Wed, 26 Jul 2006, David Xu wrote:

> On 7/26/06, Roy Stogner <roy...@ic...> wrote:
> 
> I see. Do you any of the plotting software that can handle higher
> polynomials?

No.  If I knew of any I'd be using it myself.  ;-)  As it is I usually
get good enough plots from the bisected piecewise linear plots that
libMesh's output functions produce by default.

> I remember you mentioned lagrange only support up to 2nd order. If that's
> correct,

That's correct.

> I may also want to try higher order hierarchic (up to p=5?).

The polynomial degrees supported by each finite element class depend
on the geometric element.  Check out the definition of
FEInterface::max_order() if you want to see what each supports.

On HEX27 elements, the hierarchics support "unlimited" polynomial
degree - but ill conditioning and floating point error will probably
screw up your solution around p=11.

> Will hierarchic (p>2) have the same node re-numbering problem for
> getting xyz?

Wait wait wait - you're talking about two problems here.  When I
mentioned node renumbering before, I was talking about the difficulty
of loading old solutions into new meshes.  The problem in plotting
solutions on non-lagrange elements is different, and yes, the
hierarchics will be equally tricky.

>> The most general way you can do things is to load your eigenvector
>> solutions back into libMesh (preferably into the same running process
>> that gave you the original matrix, so there's no question of node
>> renumbering).  Then you can use the libMesh plotting functions
>> (assuming you're happy with the limitations of those output formats)
>> or use the libMesh FE objects to get an arbitrarily dense cloud of
>> points for your own plotting software.
>
> That sounds like a project to me.  Would you please point me to the possible
> classes/functions I need to load the eigenvector solutions back into libMesh

Yes:  NumericVector<>::set()  We don't have any "load numeric vector
from file" function, but it shouldn't be too hard to read in a file
and set the coefficients yourself.

> and to plot them? Currently, for the 2nd order lagrange, I just concatenate
> the node xyz locations with the the eigenvector solutions, and then plot
> them in Matlab.

Okay.  If Matlab doesn't have any particular requirements for the
ordering of the points you plot, then it's easy:

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.

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.
---
Roy

Re: [Libmesh-users] Get XYZ location of global DOFs

[David X. <dx...@my...>]

On 7/26/06, Roy Stogner <roy...@ic...> wrote:
>
> On Wed, 26 Jul 2006, David Xu wrote:
>
> > On 7/26/06, Roy Stogner <roy...@ic...> wrote:
> >
> > I see. Do you any of the plotting software that can handle higher
> > polynomials?
>
> No.  If I knew of any I'd be using it myself.  ;-)  As it is I usually
> get good enough plots from the bisected piecewise linear plots that
> libMesh's output functions produce by default.
>
> > I remember you mentioned lagrange only support up to 2nd order. If
> that's
> > correct,
>
> That's correct.
>
> > I may also want to try higher order hierarchic (up to p=5?).
>
> The polynomial degrees supported by each finite element class depend
> on the geometric element.  Check out the definition of
> FEInterface::max_order() if you want to see what each supports.
>
> On HEX27 elements, the hierarchics support "unlimited" polynomial
> degree - but ill conditioning and floating point error will probably
> screw up your solution around p=11.
>
> > Will hierarchic (p>2) have the same node re-numbering problem for
> > getting xyz?
>
> Wait wait wait - you're talking about two problems here.  When I
> mentioned node renumbering before, I was talking about the difficulty
> of loading old solutions into new meshes.  The problem in plotting
> solutions on non-lagrange elements is different, and yes, the
> hierarchics will be equally tricky.
>
> >> The most general way you can do things is to load your eigenvector
> >> solutions back into libMesh (preferably into the same running process
> >> that gave you the original matrix, so there's no question of node
> >> renumbering).  Then you can use the libMesh plotting functions
> >> (assuming you're happy with the limitations of those output formats)
> >> or use the libMesh FE objects to get an arbitrarily dense cloud of
> >> points for your own plotting software.
> >
> > That sounds like a project to me.  Would you please point me to the
> possible
> > classes/functions I need to load the eigenvector solutions back into
> libMesh
>
> Yes:  NumericVector<>::set()  We don't have any "load numeric vector
> from file" function, but it shouldn't be too hard to read in a file
> and set the coefficients yourself.
>
> > and to plot them? Currently, for the 2nd order lagrange, I just
> concatenate
> > the node xyz locations with the the eigenvector solutions, and then plot
>
> > them in Matlab.
>
> Okay.  If Matlab doesn't have any particular requirements for the
> ordering of the points you plot, then it's easy:


No, the ordering of the points is not important in matlab plotting, I think.
Basically I loaded a matrix that contains x, y, z, eigenvectors as inividual
columns and used surface/mesh/line plot. The only requirement is the each
xyz physical location is correspondent to the eigenvector solution.

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

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?


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?

Thanks,

David

Re: [Libmesh-users] Get XYZ location of global DOFs

[Roy S. <roy...@ic...>]

On Wed, 26 Jul 2006, David Xu wrote:

> On 7/26/06, Roy Stogner <roy...@ic...> 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 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
> loaded eigenvectors?

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

Re: [Libmesh-users] Get XYZ location of global DOFs

[David X. <dx...@my...>]

On 7/26/06, Roy Stogner <roy...@ic...> wrote:
>
> On Wed, 26 Jul 2006, David Xu wrote:
>
> > On 7/26/06, Roy Stogner <roy...@ic...> 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
> > loaded eigenvectors?
>
> 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
>

Re: [Libmesh-users] Get XYZ location of global DOFs

[Roy S. <roy...@ic...>]

On Wed, 26 Jul 2006, David Xu wrote:

> 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.

See example 13 for how to get solution values at quadrature points.
You just sum the basis function falues weighted by the local
coefficients from the solution.
---
Roy