[petsc-dev] Problem with assembly of Jacobian in ex12 & ex77

[Matthew Knepley]

On Tue, Jun 28, 2016 at 6:47 PM, Sander Arens <Sander.Arens at ugent.be> wrote:

> Please reply to all, so that other people can also read this discussion on
> the mailing list.
>
> I do currently have problems understanding the inner workings of PetscFE.
>> For example how the element matrix is assembled. As far as I could deduce
>> from your example, g3_uu_3d is the fourth-order elasticity tensor which
>> means that we should form the double-dot product of it with the strain for
>> it to be the integrand of the gradient of the basis functions ( int_omega
>> [g3:epsilon]•grad(v) d omega). So for a linear elastic problem, according
>> to my understanding, g3 *should* be the elasticity tensor and g0,g1,g2 =
>> NULL if there is no volumetric force. And the residual should be f0 = 0 ;
>> f1= the cauchy stress tensor.
>>
>> Yes, that seems correct.
>

> I also have troubles understanding how to apply boundary conditions. There
>> seems to be the concept of DMAddBoundary() and the PetscDSSetBdJacobian()
>> and PetscDSSetBdResidual(). I struggle to understand what sets them apart
>> from each other. My impression is that DMAddBoundary() is for Dirichlet and
>> Neumann conditions and that PetscDSSetBdJacobian() and
>> PetscDSSetBdResidual() are for BC types that do not fall in those
>> categories?
>
> Note that you can also use PetscDSAddBoundary now (if you use the master
> branch). DMAddBoundary is basically used to tell which boundary region to
> apply which bc. If it's a Dirichlet bc you have to provide a function to
> prescribe the values on the boundary, if it's a Neumann bc you just give it
> NULL. PetscDSSetBdJacobian() and PetscDSSetBdResidual() are for Neumann
> bcs.
> The reason why there's this difference for Dirichlet and Neumann bcs is
> because for finite elements you need to assemble stuff for non-zero Neumann
> bcs while for Dirichlet you set some dofs to some prescribed value.
>
> ex77 works with the options you provided me with. However the solver does
>> not seem to converge.
>>
> What do you mean that it works but it doesn't converge? Did you use all
> the options I provided you? In case not, you should send the output of
> -snes_view.
>

The output of -ksp_view -ksp_monitor_true_residual -ksp_converged_reason


> The problem I have with the documentation online so far is that I fail to
>> fully understand how to apply petscFE. I did for example not know that you
>> had to set the order of the finite element space and I have the feeling
>> that there is much more I am missing.
>>
>
> I don't really understand what you mean with "applying PetscFE".
> I think the simplest way to learn how to use it is to start from one of
> the examples and if you don't understand what a function does you look it
> up in the documentation. If you want to see what kind of options there are
> for some object, for example petscspace, you add "-help|grep petscspace" to
> the command line.
>

PetscFE is a Ciarlet triple (P, P', K) meaning a PetscSpace for the primal
space P, PetscDualSpace for the dual space P', and reference
cell K which is a DM. The main function of PetscFE is to tabulate the basis
at quadrature points, and to act with dual space basis vectors
on functions.

  Thanks,

    Matt


> Thanks,
> Sander
>
> On 28 June 2016 at 17:47, <rickcha at googlemail.com> wrote:
>
>> Yes, that was vague, I should have formulated that better.
>> What I’m trying to accomplish is writing a FEM code to calculate
>> deformation and stress of structure. As a first step analysing a linear
>> elastic and static problem in 2D, which I plan to extend to a
>> elastic-plastic transient analysis for a 3D case.
>>
>> I do currently have problems understanding the inner workings of PetscFE.
>> For example how the element matrix is assembled. As far as I could deduce
>> from your example, g3_uu_3d is the fourth-order elasticity tensor which
>> means that we should form the double-dot product of it with the strain for
>> it to be the integrand of the gradient of the basis functions ( int_omega
>> [g3:epsilon]•grad(v) d omega). So for a linear elastic problem, according
>> to my understanding, g3 *should* be the elasticity tensor and g0,g1,g2 =
>> NULL if there is no volumetric force. And the residual should be f0 = 0 ;
>> f1= the cauchy stress tensor.
>>
>> I also have troubles understanding how to apply boundary conditions.
>> There seems to be the concept of DMAddBoundary() and the
>> PetscDSSetBdJacobian() and PetscDSSetBdResidual(). I struggle to understand
>> what sets them apart from each other. My impression is that DMAddBoundary()
>> is for Dirichlet and Neumann conditions and that PetscDSSetBdJacobian() and
>> PetscDSSetBdResidual() are for BC types that do not fall in those
>> categories?
>>
>> ex77 works with the options you provided me with. However the solver does
>> not seem to converge.
>>
>> The problem I have with the documentation online so far is that I fail to
>> fully understand how to apply petscFE. I did for example not know that you
>> had to set the order of the finite element space and I have the feeling
>> that there is much more I am missing.
>>
>> Thank you for your precious time,
>>
>> M. Hartig
>>
>>
>> On 28 Jun 2016, at 14:30, Sander Arens <Sander.Arens at ugent.be> wrote:
>>
>> What are you trying to do with it? I don't think there's more
>> documentation on how to use PetscFE than what's already in the online
>> documentation and in the examples.
>> What do you mean with "grasp the concept"?
>>
>> Thanks,
>> Sander
>>
>> On 27 June 2016 at 17:41, <rickcha at googlemail.com> wrote:
>>
>>> That did do the trick with the examples, thank you. I am still
>>> struggling with my own simple example however. Is there any documentation
>>> available on how to use petscFE? I could not find anything besides the
>>> three examples. And I yet have to grasp the concept.
>>>
>>>
>>> Thanks in advance,
>>> M. Hartig
>>>
>>> On 27 Jun 2016, at 15:49, Sander Arens <Sander.Arens at ugent.be> wrote:
>>>
>>> I think you forgot to set the order of the finite element spaces, which
>>> default to 0. Does it work if you try for example ex77 with the following
>>> options found here?
>>> <https://bitbucket.org/petsc/petsc/src/8bc5349a152c81f25b59a9592e1e5936c01866af/config/builder.py?at=master&fileviewer=file-view-default#builder.py-562>
>>>
>>> Thanks,
>>> Sander
>>>
>>> On 27 June 2016 at 15:28, <rickcha at googlemail.com> wrote:
>>>
>>>> Dear Petsc developer team,
>>>>
>>>> while learning the ways of the petscFE I came across a curiosity I’d
>>>> like to point out to you. The Jacobians that are created from the petscFE
>>>> object seem to have only 0-entries (apart from the obviously empty regions)
>>>> in examples 12 and 77. That might be due to a limited understanding from my
>>>> side on how exactly petscFE and the mentioned examples work, but it struck
>>>> me as unusual.
>>>>
>>>> Thanks in advance,
>>>>
>>>> M. Hartig
>>>
>>>
>>>
>>>
>>
>>
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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