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

Wed Jul 6 08:24:09 CDT 2016

```> On 28 Jun 2016, at 23:45, Matthew Knepley <knepley at gmail.com> wrote:
>
> On Tue, Jun 28, 2016 at 6:47 PM, Sander Arens <Sander.Arens at ugent.be <mailto: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.
Ok, that makes sense. I did not find documentation on PetscDSAddBoundary but I managed to use the old functions to impose the correct BC.
>
> 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
I must have made some changes without noticing when i tried to follow the workings of the ex77 sourcecode, my apologies. I copied the example again and it runs and converges fine now with the options you provided. If I change -dim to 2 however it does not converge and / or produce the correct Jacobian. But as far as I understand, ex77 is not intended to run in 2D.
>
> 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.
>
I have troubles to understand what you mean with “tabulate the basis” and I am not too familiar with the concept of dual spaces. My intention is to use the  PetscFE  infrastructure to construct the global Jacobian to give to the nonlinear solver. As a simple example, I tried using snes for solving a linear elastic problem in 2D and PetscFE to create the Jacobian and to impose the BC.
I do now have a program that runs and gives the correct solution if I use the matrix-free SNES solver. -snes_type test gives a ratio of 0.45 however and I am almost certain that the stiffness tensor I create is correct (I checked the assembly algorithm in numpy and it gives the expected cauchy stress tensor). The only explanation I have left is some misunderstanding on my side about how the double contraction works in Petsc.

Thank you,

M. Hartig
>   Thanks,
>
>     Matt
>
> Thanks,
> Sander
>
> On 28 June 2016 at 17:47,  <rickcha at googlemail.com <mailto: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 <mailto: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 <mailto: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.
>>
>>
>> M. Hartig
>>
>>> On 27 Jun 2016, at 15:49, Sander Arens <Sander.Arens at ugent.be <mailto: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 <mailto: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.
>>>
>>>
>>> M. Hartig
>>>
>>
>>
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> --
> 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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