Supplemented computer code

Introduction

This is the supplemental computer code for the book "Electromagnetics with finite elements: static problems", ISBN 978-9090380933. The code contains numerical experiments that illustrate application of the finite element method to problems in electro- and magnetostatics. A number of boundary value problems formulated in terms of electric scalar potential, total magnetic scalar potential, reduced magnetic scalar potential, magnetic vector potential, and current vector potential are solved numerically on two- and three-dimensional problem domains.

The documentation of the computer code and the numerical experiments exists in a form of online Logbook. The Logbook can be found at https://cembooks.nl.

Installation

To run the code do the following.

1. Get deal.II version 9.7.0 or newer and install it. The best is to build the latest version of deal.II from the source by following the installation instructions available at www.dealii.org. No optional interfaces to other software packages are needed. The default configuration will do.

   Set an environment variable by adding the following line to /etc/profile:

   export DEAL_II_DIR=/path/to/dealii

   where /path/to/dealii is the directory in which the deal.II is installed. Reboot. Check if the variable exists by typing the following into CLI:

   printenv | grep DEAL

   Check if the version of deal.II in the CMakeLists.txt files is correct. To do so, change into static/ directory and type the following:

   find . -name "CMakeLists.txt" -exec grep "find_package(deal.II" {} +

   If the version is not correct, change it. For example, to change the version from 9.3.2 to 9.7.0 type the following into CLI:

   find . -name "CMakeLists.txt" -exec sed -i 's/deal.II 9.3.2/deal.II 9.7.0/g' {} +

2. Install gmsh, gnuplot, texlive, and GNU parallel. This can be done as the following:

   sudo apt-get install gmsh gnuplot texlive parallel

3. Install a program for viewing vtk files. VisIt software package of the Lawrence Livermore National Laboratory is a good option. However, VisIt cannot open files that contain the higher-order cells. Many numerical experiments use the second-order mapping. To be able to view the vtu files Paraview version 5.5.0 or higher is needed. Paraview can open vtk files as well. So, strictly speaking Paraview is enough. I recommend to install both, Paraview and VisIt.

4. Extract the archive of the supplemental computer to static/ directory.

5. Change into the static/ directory and run

   ./clean
   ./setup
   ./build
   ./run-all

   This will build and execute all numerical experiments. The last two steps will take some time... Alternatively, you can build and run only the experiments you are interested in. To do so, change into static/ and run

   ./clean
   ./setup

   Then change into the directory of the experiment you are interested in, say mms/. In this directory change into build/Release/ and run

   ./clean
   ./build

   After that change into mms/bin/Release/ and run

   ./run-all

   This will execute the mms experiment. The results of the simulations are in mms/bin/Release/Data/ directory.

   Note that running the ./clean script is a must. You need to run it even if you operate on a clean copy of the code. The git removes empty directories. But the empty directories are needed for running the code. The ./clean script restores all missing (empty) directories.