Motivation

With the introduction of MFEM's Sesquilinear forms into MOOSE, we can now solve complex-value problems. However, so far these are limited to square operators (where the test and trial spaces are the same). In order to allow us to access a larger gamut of weak forms, it is necessary to introduce Mixed Sesquilinear Forms.

Design

The ParMixedSesquilinearForm class will follow a very similar structure to that of mfem::ParSesquilinearForm, but with the relevant adjustments given we are dealing with rectangular operators. Changes have to be made to the way essential degrees of freedom are eliminated, both on the mass matrix and on the RHS of the equation.

Impact

This enhancement will add a new class to MOOSE, thus allowing us to implement mixed problems in frequency space. It will not change any existing APIs.