> Is there a way to tell Libmesh that certain variables are neither
> time-evolving or constraints, so that they are not accounted for in the
> factorization?  So I would start with a FEMsystem with all of the tensor
> components, eigenvalues, and eigenvector components in the same system.

Since they are computed as a post-processing step from the tensor components
you definitely do not want them coupled in the linear system, so that calls
for another system.

I have a somewhat similar issue in my compressible NS stuff.  I solve a
large implicit system for (rho, rho*u, rho*v, rho*w, rho*E) -- the so-called
conserved variables.

But other places in the code, and for visualization, I really want access to
(P, u, v, T, M) -- primitive variables + Mach number.  And I don't want them
making my linear system any bigger.

> Would I then just implement the postprocessing functions and use the Gnu
> Scientific Library to compute the eigenvalues/vectors based upon the
> tensor components computed from the current solution.
> 
> Please give me a few pointers...

What I do is add an ExplicitSystem to my EquationSystems.  I then fill it
with these "auxiliary variables."  The benefit of this approach is (i) there
is no matrix allocation for these explicit variables, and (ii) they can be
output to visualization formats in the usual way.

You can either provide your own assemble function for the auxiliary system
which does the processing you want, or do it at the beginning/end of the
assemble of the primary system.

-Ben


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