These are the MATLAB files accompanying the paper
Stefan Guettel and John W. Pearson,
A spectral-in-time Newton--Krylov method for nonlinear PDE-constrained optimization,
IMA Journal of Numerical Analysis, 42(2):1478-1499, 2022.
https://doi.org/10.1093/imanum/drab011
There are five driver files that generate all the figures and tables in that paper:
- example_Schloegl_FD_eig.m - Figure 3.1
- example_Schloegl_spectral_beta.m - Figure 3.2 and Table 3.1
- example_Schloegl_FD_n.m - Figure 3.3 and Table 3.2
- example_Schloegl_FD_32_err.m - Figure 3.4
- example_Reactdiff_FD_n.m - Figure 3.5 and Table 3.3
The produced tables will not contain any timings as, to obtain some
statistical reliability, these are produced from ten consecutive runs,
which makes the code run rather slow. If you want to produce timings on
your computer, change the runs variable at the beginning of the scripts
from 0 to 10. This then corresponds exactly to the setting used to
produce the timings in the paper. The timings in the paper were obtained
in MATLAB 2019A on a Windows 10 laptop with 8 GB RAM and an Intel(R)
Core(TM) i7-8650U CPU running at 2 GHz and will vary on different architectures.
The solver code requires Chebfun in the MATLAB path. When first running any of the example files, the code will try to download and install Chebfun automatically. If this fails for some reason, please download Chebfun v4.2.2889 from https://www.chebfun.org/download/chebfun_v4.2.2889.zip and add the folder 'chebfun' in this directory with the other files. This particular Chebfun version was also used in our codes for a previous paper on linear optimal control problems available at http://guettel.com/dccontrol. We use the same for reproducibility and to facilitate comparisons between both solvers.