Trixi.jl: Adaptive high-order numerical simulations of hyperbolic PDEs in Julia

This is the companion repository for the tutorial on the Julia programming language and Trixi.jl, given at the University of Kassel on May 24, 2023.

In case of questions before the beginning of the tutorial, please get in touch with Hendrik or create an issue. For Trixi.jl-specific questions, you can also create an issue in the Trixi.jl GitHub repository or join the Trixi.jl Slack workspace.

Tutorial files

Item	nbviewer	mybinder
`introduction_to_julia.ipynb`
`introduction_to_trixi.ipynb`

Note: The Jupyter notebook files will be provided at the latest on the day of the tutorial. You can, however, already follow the instructions below to set up a local Julia/Jupyter installation, including installing Julia/IJulia and the required Julia packages.

Additional tutorials are available in the documentation of Trixi.jl.

Abstract

Trixi.jl is a numerical simulation framework for adaptive, high-order discretizations of conservation laws. It has a modular architecture that allows users to easily extend its functionality and was designed to be useful to experienced researchers and new users alike. In this two-part tutorial, we will first give a brief introduction to the Julia programming language. In the second part, we will demonstrate what you can do with Trixi.jl and how you can use it (and extend it) for your own research. You can follow the tutorials interactively using reproducible Jupyter notebooks provided in a companion repository. In addition, we will end with a hands-on session where you can try out Julia and Trixi.jl for yourself using these notebooks.

Note: The tutorial is intended for researchers who are already familiar with at least one other high-level language scientific programming language such as Python, C, C++, or Fortran.

Getting started

You can view a static version of the Jupyter notebooks *.ipynb

directly on GitHub (select the notebook; this may fail sometimes)
or on nbviewer.jupyter.org (select the "render" badges in the table of contents above)

These static versions do not contain output of the code cells.

Below you will find information on how to use the notebooks either via mybinder.org or by setting up a local installation. As an alternative to using Jupyter, you may also just copy the code from the notebooks into the Julia REPL and execute it there.

General note: Make sure that you execute the examples (either in the notebook or in the REPL) in order, at least for the first time. Both the notebook and the Julia REPL maintain an internal state and and some snippets depend on earlier statements having been executed.

Using mybinder.org

The easiest way to get started is to click on the Launch Binder badges in the table of contents above. This launches the notebook for interactive use in your browser without the need to download or install anything locally.

In this case, you can skip the rest of this Getting started section. A Jupyter instance will be started automagically in the cloud via mybinder.org, and the notebook will loaded directly from this repository.

Note: Depending on current usage and available resources, it typically takes a few minutes to launch a notebook with mybinder.org (sometimes a little longer), so try to remain patient. Similarly, the first two cells of the notebook take much longer to execute than usual (around 1.5 minutes for the first Trixi.jl simulation and about 1 minute for the first plot), since Julia compiles all methods "just-ahead-of-time" at first use. Subsequent runs will be much faster.

Setting up a local Julia/Jupyter installation

Alternatively, you can also clone this repository and open the notebook on your local machine. This is recommended if you already have a Julia + Jupyter setup or if you plan to try out Julia anyways.

Installing Julia and IJulia

To obtain Julia, go to https://julialang.org/downloads/ and download the latest stable release (v1.9.0 as of 2023-05-10; neither use the LTS release v1.6 nor Julia Pro!). Then, follow the platform-specific instructions to install Julia on your machine. Note that there is no need to compile anything if you are using Linux, MacOS, or Windows.

After the installation, open a terminal and start the Julia REPL (i.e., the interactive prompt) with

julia

To use the notebook, you also need to get the IJulia package, which provides a Julia backend for Jupyter. In the REPL, execute

using Pkg
Pkg.add("IJulia")

to install IJulia. For more details, especially on how to use an existing Jupyter installation, please refer to the IJulia documentation. From here on, we assume that you have a working installation of Julia, Jupyter, and the Julia kernel for Jupyter.

Installing the required Julia packages

To make the notebook fully reproducible, we have used Julia's package manager to pin all packages to a fixed release. This ensures that you always have a Julia environment in which all examples in this notebook work. Later you can always install the latest versions of Trixi.jl and its dependencies by following the instructions in the Trixi.jl documentation.

If you have not done it yet, clone the repository where this notebook is stored:

git clone https://github.com/trixi-framework/tutorial-2023-kassel.git

Then, navigate to your repository folder and install the required packages:

cd tutorial-2023-kassel
julia --project=. -e 'using Pkg; Pkg.instantiate()'

This will download and build all required packages, including the ODE package OrdinaryDiffEq.jl, the visualization package Plots.jl, and of course Trixi.jl. The --project=. argument tells Julia's package manager Pkg.jl to use the Project.toml and Manifest.toml files from this repository to figure out which packages to install.

Starting JupyterHub from Julia

You can finally start JupyterHub from Julia using the following command inside the repository folder:

julia -e 'using IJulia; jupyterlab(dir=".")'

Using the Julia REPL

If you want, you can also directly execute the notebook contents in the Julia REPL. In this case, please also follow the instructions on installing the required Julia packages above. Then, start the REPL inside the repository folder with

julia --project=.

Authors

This repository was created by Hendrik Ranocha. It is based on a tutorial previously given at ICOSAHOM 2021, which was initiated jointly by Hendrik Ranocha, Michael Schlottke-Lakemper, and Andrew R. Winters and the 2023 tutorial of Michael Schlottke-Lakemper given in the context of the DFG research unit SNuBIC.

License

The contents of this repository are licensed under the MIT license (see LICENSE.md).