DG parallelization

[lihanyu97]

This is work in progress to parallelize DG scheme relying MFEM's parallel communication infrastructure (ExchangeFaceNbrData). The first phase of this work to configure residual computation in parallel is complete. The main effort is to properly prepare input data that includes ghost dofs for Functional and record the correct index in element restriction to ensure the evaluation and AD at each quadrature point accesses the right ghost dof value. The comment associated with each major implementation is included.

Please point out anything that is obviously wrong or clumsy, and I will avoid them in the next phase.

[tupek2]

So, maybe I'm going dense... but where is the test that you get the same field solution on both sides of the dg interface for pre-specified linear/quadratic fields?

Looks like amazing progress. Are you intending to push this in incrementally, or wait until the jacobian is done?

[lihanyu97]

So, maybe I'm going dense... but where is the test that you get the same field solution on both sides of the dg interface for pre-specified linear/quadratic fields?

Looks like amazing progress. Are you intending to push this in incrementally, or wait until the jacobian is done?

The new test is here: https://github.com/LLNL/serac/blob/42804174f653ba821530ff9d09210a401aa283e6/src/serac/numerics/functional/tests/dg_ghost_face_index.cpp

I would say let's push everything in after jacobian is fixed bacause this PR is making some fundamental changes on the typedef.
mfem::Mesh --> mfem::ParMesh
mfem::FiniteElementSpace --> mfem::ParFiniteElementSpace

[lihanyu97]

@tupek2 @btalamini This DG PR is ready for review. All debug footprints (std::out / mpi::out) are removed.