This little project is finished. I posted the preprint to arxiv.org/abs/2101.05408. I do not plan to pursue publication.
The program fas1.py in directory py/ demonstrates by example how the full approximation storage (FAS) multigrid scheme works. It solves an easy nonlinear ODE BVP using piecewise-linear finite elements and a nonlinear Gauss-Seidel smoother.
Read fas.pdf in doc/ after generating it:
$ cd doc/
$ make
Clean up the LaTeX clutter in doc/ with
$ make clean
To get started do
$ cd py/
$ ./fas1.py -h
Do the following simple run using FAS V-cycles on a mesh of 2^6=64 subintervals:
$ ./fas1.py -K 6 -monitor -show
The following solves to discretization error on fine meshes in a single F-cycle using 9 WU:
$ for KK in 2 4 6 8 10 12 14 16; do ./fas1.py -mms -fcycle -K $KK -cyclemax 1; done
See also the convergence study, using a version of the problem with a known exact solution (method of manufactured solutions), in py/study/converge.sh. Solver complexity (optimality), namely runtime and work units, is studied in in py/study/optimal.sh and py/study/slow.sh. These are described in section 6 of doc/fas.pdf.
Run software tests:
$ make test