[petsc-users] A question regarding a potential use case for DMNetwork

[Matthew Knepley]

On Wed, Nov 28, 2018 at 3:51 PM Markus Lohmayer via petsc-users <
petsc-users at mcs.anl.gov> wrote:

> Dear PETSc users and developers,
>
> in particular those experienced with the relatively new DMNetwork object,
> I would like to get some advice on wether it makes sense for my
> application to be built using this PETSc feature
> or if I am equally well served if I use plain Vec and Mat objects.
>
> In the latter case, you might nevertheless have some good advice for a
> novice PETSc user
> or you might know about something that helps me to come up with a well
> architected solution.
>
> So the application context is closely linked to LTI state-space models
> (and in particular two-port / n-port network models and their
> interconnections):
> x,t = A x + B u
> y   = C x + D u
>
> More specifically, input ‘u' and output ‘y' are vectors (of same length
> for all components).
> Different components will have different dimension of state ‘x' (and hence
> also ‘A', ‘B', ‘C').
>
> These component models then have to be interconnected according to a given
> topology:
>

If the interconnection topology is 1D, then yes DMNetwork is designed to do
this. At the simplest level, you
could just use a 1D DMPlex, which is inside DMNetwork, and hand code the
Section (data layout) and residual/Jacobian
assembly. DMNetwork is a higher level around this that lets you put
"components" down on vertices and edges
that translate to data layout and residual evaluation. I confess to not
understanding the residual part all the way.
If you start trying to modify an example, we can help you I think.

  Thanks,

     Matt


> Some pair of outputs of model 1  feeds into  the corresponding pair of
> inputs of model 2  (and also the other way round by symmetry), etc.
>
> After most (or even all) of the original inputs 'u_i' / outputs 'y_i' have
> been eliminated (based on the given interconnection structure amongst
> components),
> it will be necessary to use an iterative eigenvalue solver to obtain
> eigenvectors for some interesting part of the spectrum.
>
> The models will probably not be "very large" in the foreseeable future but
> this still doesn’t make e.g. MATLAB’s control toolbox an option.
>
> I have seen the presentation by Hong Zhang (1) at this year’s user meeting
> and I have looked at the paper “Scalable Multiphysics Network Simulation
> Using PETSc DMNetwork”.
> The use cases and concept of network presented therein were slightly
> different from this one of interconnected multi-ports in state-space
> formulation.
>
> Thanks you very much for your advice and reading this post.
>
> Best,
> Markus



-- 
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

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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