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

[Markus Lohmayer]

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:
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