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Basic numerical methods for time-domain waves

2. Basic numerical methods for time-domain waves#

In this section we work our way through the steps leading to a first finite element method for the wave-type equations from Section 1 using the high-order finite element library Netgen/NGSolve.

Note that this is not the time and place to present a full-sized introduction the the finite element method in all its glory. What follows is a shortened and adapted version of the first chapters of Joachim Schöberl’s iFEM introduction, which is also a highly recommended read for the interested student.

2.1. Running NGSolve#

By now there exist various ways to run NGSolve

Local installation#

Install a recent Python. Then it should be easy to install NGSolve using

pip install jupyter numpy scipy matplotlib
pip install --pre ngsolve
pip install webgui_jupyter_widgets

To check the installation of NGSolve run in a terminal:

python3 -c "import ngsolve; print(ngsolve.__version__)"

Then, open jupyter-notebook (or jupyter-lab or VS Code), create a new notebook, create and execute a cell with

from ngsolve import *
from ngsolve.webgui import Draw
Draw (unit_cube.shape);

Known issues are

  • Use pip3 instead of pip if there is no pip

  • If you get an error like externally-managed-environment, then either use virtual environments, or add the flag --break-system-packages to the pip command, see explanation

  • If you have conflicts with other packages, you may install NGSolve in a virtual environment. For example

    python3 -m venv /Users/XXXXX/numpde
source /Users/XXXXX/numpde/bin/activate

  • If NGSolve compuatations are working, but you don’t get the rendering: For jupyter notebook version < 7.0.0 you have to run additionally

    jupyter nbextension install --user --py webgui_jupyter_widgets
jupyter nbextension enable --user --py webgui_jupyter_widgets

Run NGSolve remote or via jupyter-lite#

If local installation does not work, there are alternatives:

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