[petsc-users] DMPlex with spring elements

Thu Sep 25 13:49:42 CDT 2014

On Thu, Sep 25, 2014 at 1:46 PM, Abhyankar, Shrirang G. <abhyshr at mcs.anl.gov
> wrote:

> You are right. The Jacobian for the power grid application is indeed
> non-symmetric. Is that a problem for your application?
>

If you need a symmetric Jacobian, you can use the BC facility in
PetscSection, which eliminates the
variables completely. This is how the FEM examples, like ex12, work.

  Matt

> Shri
>
> From:  Miguel Angel Salazar de Troya <salazardetroya at gmail.com>
> Date:  Thu, 25 Sep 2014 12:57:53 -0500
> To:  Shri <abhyshr at mcs.anl.gov>
> Cc:  <petsc-users at mcs.anl.gov>
> Subject:  Re: [petsc-users] DMPlex with spring elements
>
>
> >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,componentke
> >>>y
> >>>[
> >>>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
>
>

-- 
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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