A custom integrator is required to handle the theta^n term in the lane emden equation, that is written as NonlinearPowerIntegrator which is a mfem::NonlinearFormIntegrator and defines methods to assemble its element vector (function value) and element gradient matrix (jacobian). This is then, along with built in mfem vectors for M Q and D, incorporated into the PolytropeOperator which defines methods for Mult (calculate the residuals of the variational form) and GetGradient (find the jacobian of the system)
Instead of treating the polytrope as a free boundary problem I have defined an interpolating polynominal, accurate to within 0.01 percent over n=[0,5) which is used to set the size of the domain for a given n
the polytrope module will be used as an initial guess to the solver. A skeleton of this has been imported from https://github.com/tboudreaux/FEMPolytrope
This module will need major updates still to handle 3D, proper boundary conditions, and to incorporate it with the rest of our meshing scheme
