Ciro Santilli @cirosantilli 35

Firstly, in 2012, while he was at École Polytechnique, Ciro Santilli was introduced to LaTeX (thank God for French mathematical obsession), and his mind was blown:he though. Why isn't everyone doing that!

One particular event stood out: Ciro made a small change to his teacher's course material, who blessed be him (dude's a legend, Ciro just noticed he has some Chinese publications with another French dude, e.g. www.amazon.co.uk/高效算法-应试与提高必修128例-克里斯托弗-Christoph-Durr/dp/B078SJQPVK "High-efficiency algorithm competitions 128 examples", did he write it the Chinese himself?? Must be of course to complement the notoriously low French professor salaries), made it available, and then Ciro gave him back the .tex file. Ciro was just a bit worried about how the teacher would be able to tell what he had changed in the file to validate the change. The teacher just said of course, "no problem, I'll just use diff". Ciro had never heard of diff. Let alone Git of course, though yes, this was a bit early in Git's history version control systems had been around since forever of course. This was 2011 or 2012, about 4 or 5 years into a superior education curricula with various courses involving computers, some requiring quite a lot of "fill these empty functions" style programming. Education is a joke. Anyways, this was a prelude to exactly what Ciro wanted to do in OurBigBook.com. This might have been the one actually: webia.lip6.fr/~durrc/Iut/Notes580.pdf

Not long afterwards, Ciro started playing with Linux. Until then, Ciro had had some contacts with the mysterious operating system at university, and was a bit puzzled what the point of it was! He clearly remembers:University should be forced to use only open source software and hardware in undergrad teaching courses by law BTW.

Then came an Ubuntu live disk on his own machine, and finally a measly 40GB dual book partition in a Microsoft Windows machine on a laptop. At first, it took a lot of time to learn all the crazy new terminal stuff! Yes, at this point, Ubuntu was already usable enough without the terminal, an accomplishment actually. But as a programmer, Ciro felt obliged to learn. Many hours were spent reading man pages at the library. But it all just felt so right, and sometimes powerful... true wizardry.

And ten years later, Ciro was seriously considering buying a computer without Windows pre-installed. He had not used Windows a single tie on a personal machine even once in those ten years!

Finally, to finish things off Ciro found two websites that changed his life forever, and made be believe that there was an alternative: Stack Overflow and GitHub.

The brutal openness of it all. The raw high quality content. Ugliness and uselessness too no doubt. But definitely spark in a sea of darkness.

Specifies fixed values.

Can be used for elliptic partial differential equations and parabolic partial differential equations.

Numerical examples:

One big advantage over FreeFem is that it uses plain old Python to describe the problems instead of a domain-specific language. Matplotlib is used for plotting by default, so we get full Python power out of the box!

Also uses variational formulation of a partial differential equation like FreeFem which is a pain.

One downside is that its documentation is a Springer published PDF link.springer.com/content/pdf/10.1007%2F978-3-319-52462-7.pdf which is several years out-of-date (tested with FEnics 2016.2. Newbs. This causes problems e.g.: stackoverflow.com/questions/53730427/fenics-did-not-show-figure-nameerror-name-interactive-is-not-defined/57390687#57390687

system of partial differential equations are mentioned at: link.springer.com/content/pdf/10.1007%2F978-3-319-52462-7.pdf 3.5 "A system of advection–diffusion–reaction equations". You don't need to manually iterate between the equations.

On Ubuntu 20.04 as per fenicsproject.org/download/Before 2020-06, it was failing with:but they seem to have created the Ubuntu 20.04 package as of 2020-06, so it now worked! askubuntu.com/questions/866901/what-can-i-do-if-a-repository-ppa-does-not-have-a-release-file

TODO heat equation hello world.

Besides being useful in engineering, it was very important historically from a "development of mathematics point of view", e.g. it was the initial motivation for the Fourier series.

Some interesting properties:

Sample numerical solutions:

Linear combination of a Dirichlet boundary condition and Neumann boundary condition at each point of the boundary.

Examples:

Used for example in FreeFem and FEniCS Project as the input description of the PDEs, TODO why.