\section{Conclusions and Implications}
\label{sec:conclusion}

  In \citetitle{qe2paper}, \citeauthor{qe2paper} conclude that the proposed
  implementation of solving the \gls{nem} equations with the \gls{jfnk} method
  after performing local elimination and using the physics-based preconditioner
  provides improved convergence rate and reduced computation time compared to
  their implementation of the \gls{pi} method. It is difficult to argue with
  these results as presented. However, \sref{sec:critique} has shown that it is
  the data omitted from the results that merits consideration. Without
  additional data, it is difficult to extend the results of
  \citeauthor{qe2paper} to broader applications of the \gls{jfnk} method for
  solving the \gls{nem} equations.

  A first step for better interpreting the results presented is to compare the
  \gls{jfnk} method to a \gls{pi} method using the \gls{ws} as in the work by
  \citeauthor{jfnk_wielandt}. It would also be useful to investigate
  preconditioning with a few \glspl{pi} as this has been demonstrated to be the
  preferable preconditioning by others \cite{gill_azmy,jfnk_wielandt}.
  Additionally, the \gls{nem} should be implemented in the \gls{cmfd}
  formulation to investigate improved computational efficiency and allow for
  compatibility with existing production-quality computer programs 
  \cite{palmtagThesis,smith_nonlinear}.

  In their concluding remarks, \citeauthor{qe2paper} claim that their method
  will be extended to ``improve the computational efficiency for large-scale
  complicated multiphysics coupled problems in nuclear reactor analysis''
  \cite{qe2paper}. This may seem like a straightforward extension, but a new
  residual function and Jacobian approximation will likely be required.

  The authors' claim of incorporating multiphysics effects is extremely bold
  given both the omission of important results and other publications in the
  field. Specifically, \citeauthor{caslJFNK} investigated this exact application
  of \gls{jfnk} to large-scale multiphysics simulations. Such an application
  required significant work in the formation of the Jacobian including
  constructing approximations of temperature derivatives of cross sections.
  These cross section derivatives were specific to a particular type of reactor
  (\glspl{pwr}) but \citeauthor{qe2paper} attempt to simulate both \glspl{pwr}
  and pebble bed reactor designs. Succinctly, in reactor multiphysics
  simulations, it was determined that without the calculation of cross section
  derivatives, the \gls{jfnk} method was unacceptable as it required a
  burdensome amount of cross section processing time during the simulation
  \cite{caslJFNK}.

  The results of \citeauthor{caslJFNK} are not the end of the narrative. 
  Applying the \gls{jfnk} method to the \gls{nem} equations may be useful for
  certain nuclear reactor multiphysics simulations. However, insufficient data 
  is provided by \citeauthor{qe2paper} to make such a conclusion. Additional
  attention must be paid in the application of the \gls{jfnk} method to the
  \gls{nem} equations to determine if such an implementation would provide
  a benefit compared to existing methods. When drawing conclusions about
  improvements in computational efficiency due to a new method, it is crucial to 
  compare optimized codes to determine if any improvement is true, or merely due
  to a suboptimal implementation.
