[petsc-users] DMPlex with spring elements

Miguel Angel Salazar de Troya salazardetroya at gmail.com
Thu Sep 25 12:57:53 CDT 2014 

Why not? Wouldn't we have a row of zeros except for the diagonal term? The
column that corresponds to that degree of from doesn't have to be zero,
right?

Thanks
Miguel
On Sep 25, 2014 12:38 PM, "Abhyankar, Shrirang G." <abhyshr at mcs.anl.gov>
wrote:

>
>
>   From: Miguel Angel Salazar de Troya <salazardetroya at gmail.com>
> Date: Thu, 25 Sep 2014 11:43:13 -0500
> To: Shri <abhyshr at mcs.anl.gov>
> Cc: <petsc-users at mcs.anl.gov>
> Subject: Re: [petsc-users] DMPlex with spring elements
>
>  I see, and I guess I would have to assign a value of one to the diagonal
> entry of that degree of freedom in the Jacobian right?
>
>  Yes.
>
> Wouldn't this break the symmetry of the Jacobian (in case it were
> symmetric)?
>
>  No.
>
>  Shri
>
> Thanks
> Miguel
> On Sep 25, 2014 11:32 AM, "Abhyankar, Shrirang G." <abhyshr at mcs.anl.gov>
> wrote:
>
>>  The solver does not know anything about the boundary conditions. You
>> would have to specify it to the solver by describing the appropriate
>> equations. For e.g. in the power grid example, there is a part in the
>> residual evaluation
>>
>>   if (bus->ide == REF_BUS || bus->ide == ISOLATED_BUS) {
>>        farr[offset] = 0.0;
>>        farr[offset+1] = 0.0;
>>      break;
>>  }
>>
>>  This sets the residual at the nodes marked with REF_BUS or ISOLATED_BUS
>> to 0.0. You can do something similar.
>>
>>  Shri
>>
>>
>>
>>   From: Miguel Angel Salazar de Troya <salazardetroya at gmail.com>
>> Date: Thu, 25 Sep 2014 10:52:16 -0500
>> To: Shri <abhyshr at mcs.anl.gov>
>> Cc: "petsc-users at mcs.anl.gov" <petsc-users at mcs.anl.gov>
>> Subject: Re: [petsc-users] DMPlex with spring elements
>>
>>  Thanks. Once I have marked the nodes that are fixed nodes using the
>> component data structure, how can I process it later? I mean, at what point
>> does the solver know that those degrees of freedom are actually fixed and
>> how I can tell it that they are fixed?
>>
>>  Miguel
>>
>> On Thu, Sep 25, 2014 at 10:27 AM, Abhyankar, Shrirang G. <
>> abhyshr at mcs.anl.gov> wrote:
>>
>>>
>>>
>>> >Thanks. I think the term "Component" was confusing me, I thought it was
>>> >related to the components of a field. I think this would be useful to me
>>> >if I wanted to assign coordinates to the vertices, wouldn't it?
>>>
>>> Yes. You can put whatever data you want in the component data structure.
>>>
>>> >
>>> >Also, I was wondering how to set up dirichlet boundary conditions,
>>> >basically fixing certain nodes position.
>>> >
>>>
>>> >
>>> >
>>> You can add a component at each node with a field marking whether the
>>> node
>>> is a boundary node.
>>>
>>> >Could I do it as the function SetInitialValues does it in the pflow
>>> >example?
>>> >
>>>
>>> No. You need to put in the component data structure before calling
>>> DMNetworkAddComponent()
>>>
>>>
>>> >These values are used to eliminate the zeroth-order energy modes of the
>>> >stiffness matrix?
>>> >
>>>
>>>
>>> >
>>> >Last question, in my case I have two degrees of freedom per node, when I
>>> >grab the offset with DMNetworkVariableOffset, that's for the first
>>> degree
>>> >of freedom in that node and the second degree of freedom would just be
>>> >offset+1?
>>> >
>>>
>>> Yes.
>>>
>>> Shri
>>>
>>> >
>>> >Miguel
>>> >
>>> >
>>> >On Wed, Sep 24, 2014 at 9:52 PM, Abhyankar, Shrirang G.
>>> ><abhyshr at mcs.anl.gov> wrote:
>>> >
>>> >If you have equations only at the nodes, with a part of it contributed
>>> by
>>> >the edges (springs),  then you can use DMNetwork. If you are planning to
>>> >have equations for the beads in the future, or other higher layers, then
>>> >DMPlex has better functionality
>>> > to manage that.
>>> >
>>> >Shri
>>> >
>>> >
>>> >From: Miguel Angel Salazar de Troya <salazardetroya at gmail.com>
>>> >Date: Wed, 24 Sep 2014 17:38:11 -0500
>>> >To: Shri <abhyshr at mcs.anl.gov>
>>> >Cc: "petsc-users at mcs.anl.gov" <petsc-users at mcs.anl.gov>
>>> >Subject: Re: [petsc-users] DMPlex with spring elements
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >Thanks for your response. I'm attaching a pdf with a description of the
>>> >model. The description of the PetscSection is necessary for the
>>> >DMNetwork? It looks like DMNetwork does not use a PetscSection.
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >Miguel
>>> >
>>> >
>>> >On Wed, Sep 24, 2014 at 1:43 PM, Abhyankar, Shrirang G.
>>> ><abhyshr at mcs.anl.gov> wrote:
>>> >
>>> >
>>> >>Thanks for your response. My discretization is based on spring
>>> elements.
>>> >>For the linear one dimensional case in which each spring has a
>>> >>coefficient k, their jacobian would be this two by two matrix.
>>> >>[  k    -k ]
>>> >>[ -k     k ]
>>> >>
>>> >>and the internal force
>>> >>
>>> >>[ k ( Ui - Uj) ]
>>> >>[ k ( Uj - Ui) ]
>>> >>
>>> >>where Ui and Uj are the node displacements (just one displacement per
>>> >>node because it's one dimensional)
>>> >>
>>> >>For the two dimensional case, assuming small deformations, we have a
>>> >>four-by-four matrix. Each node has two degrees of freedom. We obtain it
>>> >>by performing the outer product of the vector (t , -t) where "t" is the
>>> >>vector that connects both nodes in a spring. This is for the case of
>>> >>small deformations. I would need to assemble each spring contribution
>>> to
>>> >>the jacobian and the residual like they were finite elements. The
>>> springs
>>> >>share nodes, that's how they are connected. This example is just the
>>> >>linear case, I will have to implement a nonlinear case in a similar
>>> >>fashion.
>>> >>
>>> >>Seeing the DMNetwork example, I think it's what I need, although I
>>> don't
>>> >>know much of power electric grids and it's hard for me to understand
>>> >>what's going on. Do you have a good reference to be able to follow the
>>> >>code?
>>> >
>>> >>
>>> >Please see the attached document which has more description of DMNetwork
>>> >and the equations for the power grid example. I don't have anything that
>>> >describes how the power grid example is implemented.
>>> >
>>> >>For example, why are they adding components to the edges?
>>> >>
>>> >>475:     DMNetworkAddComponent
>>> >><
>>> http://www.mcs.anl.gov/petsc/petsc-as/petsc-current/docs/manualpages/DM/
>>> >>D
>>>
>>> >>MNetworkAddComponent.html#DMNetworkAddComponent>(networkdm,i,componentkey
>>> >>[
>>> >>0],&pfdata.branch[i-eStart]);Miguel
>>> >
>>> >Each edge or node can have several components (limited to 10) attached
>>> to
>>> >it. The term components, taken from the circuit terminology, refers to
>>> the
>>> >elements of a network. For example, a component could be a resistor,
>>> >inductor, spring, or even edge/vertex weights (for graph problems). For
>>> >code implementation, component is a data structure that holds the data
>>> >needed for the residual, Jacobian, or any other function evaluation. In
>>> >the case of power grid, there are 4 components: branches or transmission
>>> >lines connecting nodes, buses or nodes, generators that are incident at
>>> a
>>> >subset of the nodes, and loads that are also incident at a subset of the
>>> >nodes. Each of the these components are defined by their data structures
>>> >given in pf.h.
>>> >
>>> >DMNetwork is a wrapper class of DMPlex specifically for network
>>> >applications that can be solely described using nodes, edges, and their
>>> >associated components. If you have a PDE, or need FEM, or need other
>>> >advanced features then DMPlex would be suitable. Please send us a
>>> write-up
>>> >of your equations so that we can assist you better.
>>> >
>>> >Shri
>>> >
>>> >
>>> >>
>>> >>
>>> >>On Tue, Sep 23, 2014 at 11:13 PM, Abhyankar, Shrirang G.
>>> >><abhyshr at mcs.anl.gov> wrote:
>>> >>
>>> >>You may also want to take a look at the DMNetwork framework that can be
>>> >>used for general unstructured networks that don't use PDEs. Its
>>> >>description is given in the manual and an example is in
>>> >>src/snes/examples/tutorials/network/pflow.
>>> >>
>>> >>Shri
>>> >>
>>> >>From:  Matthew Knepley <knepley at gmail.com>
>>> >>Date:  Tue, 23 Sep 2014 22:40:52 -0400
>>> >>To:  Miguel Angel Salazar de Troya <salazardetroya at gmail.com>
>>> >>Cc:  "petsc-users at mcs.anl.gov" <petsc-users at mcs.anl.gov>
>>> >>Subject:  Re: [petsc-users] DMPlex with spring elements
>>> >>
>>> >>
>>> >>>On Tue, Sep 23, 2014 at 4:01 PM, Miguel Angel Salazar de Troya
>>> >>><salazardetroya at gmail.com> wrote:
>>> >>>
>>> >>>Hi all
>>> >>>I was wondering if it could be possible to build a model similar to
>>> the
>>> >>>example snes/ex12.c, but with spring elements (for elasticity) instead
>>> >>>of
>>> >>>simplicial elements. Spring elements in a grid, therefore each element
>>> >>>would have two nodes and each node two components. There would be more
>>> >>>differences, because instead of calling the functions f0,f1,g0,g1,g2
>>> and
>>> >>>g3 to build the residual and the jacobian, I would call a routine that
>>> >>>would build the residual vector and the jacobian matrix directly. I
>>> >>>would
>>> >>>not have shape functions whatsoever. My problem is discrete, I don't
>>> >>>have
>>> >>>a PDE and my equations are algebraic. What is the best way in petsc to
>>> >>>solve this problem? Is there any example that I can follow? Thanks in
>>> >>>advance
>>> >>>
>>> >>>
>>> >>>
>>> >>>
>>> >>>Yes, ex12 is fairly specific to FEM. However, I think the right tools
>>> >>>for
>>> >>>what you want are
>>> >>>DMPlex and PetscSection. Here is how I would proceed:
>>> >>>
>>> >>>  1) Make a DMPlex that encodes a simple network that you wish to
>>> >>>simulate
>>> >>>
>>> >>>  2) Make a PetscSection that gets the data layout right. Its hard
>>> from
>>> >>>the above
>>> >>>      for me to understand where you degrees of freedom actually are.
>>> >>>This is usually
>>> >>>      the hard part.
>>> >>>
>>> >>>  3) Calculate the residual, so you can check an exact solution. Here
>>> >>>you
>>> >>>use the
>>> >>>      PetscSectionGetDof/Offset() for each mesh piece that you are
>>> >>>interested in. Again,
>>> >>>      its hard to be more specific when I do not understand your
>>> >>>discretization.
>>> >>>
>>> >>>  Thanks,
>>> >>>
>>> >>>    Matt
>>> >>>
>>> >>>
>>> >>>Miguel
>>> >>>
>>> >>>
>>> >>>
>>> >>>--
>>> >>>Miguel Angel Salazar de Troya
>>> >>>Graduate Research Assistant
>>> >>>Department of Mechanical Science and Engineering
>>> >>>University of Illinois at Urbana-Champaign
>>> >>
>>> >>
>>> >>>(217) 550-2360 <tel:%28217%29%20550-2360>
>>> >>>salaza11 at illinois.edu
>>> >>>
>>> >>>
>>> >>>
>>> >>>
>>> >>>
>>> >>>
>>> >>>
>>> >>>
>>> >>>
>>> >>>--
>>> >>>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
>>> >>
>>> >>
>>> >>
>>> >>
>>> >>
>>> >>
>>> >>
>>> >>
>>> >>
>>> >>--
>>> >>Miguel Angel Salazar de Troya
>>> >>Graduate Research Assistant
>>> >>Department of Mechanical Science and Engineering
>>> >>University of Illinois at Urbana-Champaign
>>> >>(217) 550-2360
>>> >>salaza11 at illinois.edu
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >--
>>> >Miguel Angel Salazar de Troya
>>> >Graduate Research Assistant
>>> >Department of Mechanical Science and Engineering
>>> >University of Illinois at Urbana-Champaign
>>> >(217) 550-2360
>>> >salaza11 at illinois.edu
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >--
>>> >Miguel Angel Salazar de Troya
>>> >Graduate Research Assistant
>>> >Department of Mechanical Science and Engineering
>>> >University of Illinois at Urbana-Champaign
>>> >(217) 550-2360
>>> >salaza11 at illinois.edu
>>>
>>>
>>
>>
>>  --
>> *Miguel Angel Salazar de Troya*
>> Graduate Research Assistant
>> Department of Mechanical Science and Engineering
>> University of Illinois at Urbana-Champaign
>> (217) 550-2360
>> salaza11 at illinois.edu
>>
>>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20140925/b1bfa8a7/attachment-0001.html>

More information about the petsc-users mailing list