## Setup

This tutorial solves a simple mass-spring oscillator with two masses and three springs. The system is cut at the middle spring and solved in a partitioned fashion:

Note that this case applies a Schwarz-type coupling method and not (like most other tutorials in this repository) a Dirichlet-Neumann coupling. This results in a symmetric setup of the solvers. We will refer to the solver computing the trajectory of $m_1$ as `Mass-Left`

and to the solver computing the trajectory of $m_2$ as `Mass-Right`

. For more information, please refer to [1].

## Available solvers

This tutorial is only available in Python. You need to have preCICE and the Python bindings installed on your system.

*Python*: An example solver using the preCICE Python bindings. This solver also depends on the Python libraries`numpy`

, which you can get from your system package manager or with`pip3 install --user <package>`

.

## Running the Simulation

### Python

Open two separate terminals and start both participants by calling:

```
cd python
./run.sh -l
```

and

```
cd python
./run.sh -r
```

## Post-processing

Each simulation run creates two files containing position and velocity of the two masses over time. These files are called `trajectory-Mass-Left.csv`

and `trajectory-Mass-Right.csv`

. You can use the script `plot-trajectory.py`

for post-processing. Type `python3 plot-trajectory --help`

to see available options. You can, for example plot the trajectory by running

```
python3 plot-trajectory.py python/output/trajectory-Mass-Left.csv TRAJECTORY
```

This allows you to study the effect of different time stepping schemes on energy conservation. Newmark beta conserves energy:

Generalized alpha does not conserve energy:

For details, refer to [1].

## References

[1] V. SchÃ¼ller, B. Rodenberg, B. Uekermann and H. Bungartz, A Simple Test Case for Convergence Order in Time and Energy Conservation of Black-Box Coupling Schemes, in: WCCM-APCOM2022. URL