[petsc-users] DMPlex with spring elements

Thu Sep 25 10:52:16 CDT 2014

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/20140925/49e7e314/attachment-0001.html>