We present our solution to project 1 in the course TMA4220 at NTNU Trondheim in autumn semester 2018. The code impelements all required components to solve simple evolutionary and static PDEs in 2D on a triangular mesh. In particular, we implemented a solver for the Helmholtz problem and the homogenous unsteady heat equation. A third solver extends the dynamic solver to cope with the homogenous wave equoation in 2D.

The program is written in Python 3. The installation is shown via pip.

Additional requirements are listed in the setup.py and requirements.txt, namely

• scipy
• matplotlib
• numpy
• tqdm

With pip these packages can be installed by using $ pip install -r requirements.txt. We recommend to create a new virtual environment using venv. Afterwards, install the project using pip: $ pip install -e /path/to/parent/folder/of/setup.py. Now, the main file of the project can be executed by navigating into project_1 and executing $ python main.py.

The program is started by executing the main file located in the root. Without any arguments passed, the software will calculate and plot the solution to the Helmholtz problem.

• -v Visualizes the analytical solution of the Helmholtz problem for debugging the basic functionality of the vis functions.
• -vd Visualizes the analytical solution of the time dependant problem for debugging.
• -m Generates and plots a triangular mesh for debugging.
• -s Solves the Helmholtz problem and plots the solution
• -sd Solves the unsteady heat equation and generates an animation of the solution as well as a picture of the final frame. Video of the solution
• -w Solves the 2D wave equation and generates an animation
• -r Genaterates the required plots for the report, including the error analysis

Several unittests are defined in project_1/tests/test.py. The can be invoked by calling $ python test.py after navigating in the correct folder.