[petsc-users] DMPlex with spring elements

[Abhyankar, Shrirang G.]

>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.
>
>
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>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
>>
>>
>>
>>
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>>
>>
>>--
>>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
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>-- 
>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
>
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>-- 
>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