Aside from resiliency motivations, the primary driver behind the FANM
method is reduced memory pressure due to the lack of additional storage
beyond that of the linear system in the MCSA method. The nonlinear
benchmark problems we have chosen will let us measure this memory usage
and compare it to conventional Newton-Krylov methods. Furthermore, by
varying the strength of the nonlinearities in those problems (effectively by
increasing the amount of convective transport in the system), the benchmarks
will become more difficult to solve and require even more iterations to
converge. This will give us a means by which to vary the complexity of the
system which we can then compare to memory usage. Additionally, with the
finite element assembly framework we can choose functional discretizations
of varying accuracy, allowing us to vary the degrees of freedom in the system
and therefore also vary the memory required for each problem.