In this set of tutorials, we will use the Gridap software library developed by @santiagobadia and co-workers. This library provides tools for the numerical approximation of partial differential equations using mesh-based techniques (finite element methods in general). The library is written in Julia, a somehow recent programming language that combines the expressiveness of dynamic languages like Python and the performance of static languages like C++ or FORTRAN.
The tutorials are mainly about understanding the steps in a finite element software (mesh generation, creation of finite element spaces, bilinear forms, linear system, and solver) and justifying the results obtained using what we have learned from their mathematical analysis. The Julia requirements for this unit are quite low and can be understood with the guidance and examples in the tutorials.
For this practical work, you need to install Julia locally on your computer. Installing all the tools that are needed for running these notebooks locally is pretty simple. The first thing that you have to do is to download Julia from here. I would recommend you install the newest stable release. Pick the one for your operating system. If you use Windows and a not-too-old computer, download the 64-bit installer.
If you install Julia on Windows, you can accept the proposed directory for installation (unless you want to change it for some reason), press NEXT, tick (very important) Add Julia Path in the next window, press NEXT. You can tick Run Julia if you like in the last window and FINISH. You will have now the Julia app in Windows, and you can use it to open new Julia windows. I think something very similar will work on Mac.
If you install Julia in Linux, you will need to manually add the folder with the Julia executable to the environment variable PATH in your .bashrc, e.g. (for version 1.6.1):
export PATH=$HOME/Progs/julia-1.6.1/bin
On the other hand, you need a good editor for Julia. I recommend using VSCode. You can install the latest version for your operating system here. Simply click the link for last stable version.
In Windows, run the executable file you have downloaded. Accept the agreement, press NEXT, accept the folder proposed or change it if you want, NEXT, NEXT, then you can tick Create a desktop icon and keep ticked Add to PATH (very important), NEXT, INSTALL. After installation, FINISH. I think something very similar will work on Mac. If you are on Linux, you don't need help :-)
Now, open VSCode (if not already open) and click on Extensions (the icon with four squares on the left side). Now, you can search in Extension for Julia. The first result will be Julia Language Support. We want to install this plug-in. Click on Install on this extension.
If everything worked, now you should be able to open a Julia REPL (a Julia terminal) in VSCode. You can just press CTRL+SHIFT+P (to open a search menu) and type Julia: Start REPL. Click on the first result. If a Julia REPL opens, you got it!
I will create tutorials for this specific unit. Every tutorial is related to one chapter of the lecture note. You will find the tutorials below (during the semester):
- Practical tutorial Chapter 1 or run it with Binder
Besides, if you are interested in more complex problems and more advanced tutorials, you can always check the Gridap tutorials here. I recommend to take a look at the three first tutorials in the list, if interested.
The tutorials are Pluto notebooks (a more advanced version of Jupyter notebooks for Julia). Please, follow the installation instructions here. You can simply download the notebook. Next, run Pluto, which will open a tab in the browser. In the browser, open the notebook file you have downloaded. Voila!
It is better to download the whole project from Github (click the Code icon in the main page. Then, go to File -> Open Folder (or just click on the Explorer icon on the left) and open MTH3340. Next, open a Julia REPL (as explained above). You have in the bottom of your VSCode windows
julia>
This is the standard mode of the Julia REPL, in which you can run commands. However, in order to run the tutorials, we need to activate and instantiate the MTH3340 project:
# Type ] to enter in pkg mode
(MTH3340) pkg> activate .
(MTH3340) pkg> instantiate
This will automatically download all required packages.
Note that ] will change the prompt to package mode ((Tutorials) pkg>). To go to normal mode again you just press backspace key. It is good to know that you can have the REPL in these two modes. The standard mode julia> is the one that you will use all the time to run commands. The package mode is only used for packages related things (e.g., activate or instantiate a project or install new packages). Activate will pick the environment (the MTH3340 project in our case). Instantiate will install the Julia packages that are required to run the tutorials (Gridap and its dependencies). It will take some time. If there are no errors, you can start running the tutorials.
You can now run the tutorials using Pluto:
julia> using Pluto
julia> Pluto.run()It will open a new tab in your browser (hopefully). Then, you can just open the one you want in notebooks/.
We can also run files apart from notebooks without Pluto. First, open the file (e.g., open src/SampleFile.jl). You can just go to the Explore icon on the top-left and click on the file you want to run.
First, check that you are in standard mode julia>, if you are in package mode (MTH3340) pkg> type backspace. You can run a Julia file in many different ways. I would probably start running the whole file to check that everything is OK. As usual, open the VSCode search using CTRL+SHIFT+P and search for Julia execute file in REPL and choose this option.
For reading the comments (in which I explain what we are doing in the code), I recommend using "soft wrapping of lines". Just press ALT+Z or go to View > Toggle Word Wrap.
In order to go through code files, I strongly recommend executing line by line from the very beginning. You can do that with CTRL+ENTER on a line. Then, you can see the result in the REPL, and try to understand the numbers you are getting. If you click on the Julia link on the left (the three circles) you will be able to see the Workspace (as in Matlab) with all the variables and their values.
Now, you can run the whole code and understand what we are doing at every stage. Try to check how the code relates to the lecture notes, and check that we are implementing exactly matches what we explain there.
Let me know if there is any technical problem or doubts in the tutorial. Have fun!
I have not created specific tutorials for basic Julia. The reason is that there are already excellent tutorials out there. You can take a look at the tutorials here. I recommend to read this here. It provides the basics of what we will need during this unit (and more). But you can certainly explore other tutorials in the list above. And please ask me if you have questions!