Playground for semi-explicit DAE DiscontinuousTestDAE using the new semi-implicit SDC-DAE sweeper (#420)

* Added DAE playground

* Added numpy array's

Author: lisawim

pySDC/playgrounds/DAE/DiscontinuousTestDAE.py

@@ -0,0 +1,104 @@
+import numpy as np
+from pathlib import Path
+import matplotlib.pyplot as plt
+
+from pySDC.helpers.stats_helper import get_sorted
+from pySDC.projects.DAE.sweepers.SemiImplicitDAE import SemiImplicitDAE
+from pySDC.projects.DAE.problems.DiscontinuousTestDAE import DiscontinuousTestDAE
+from pySDC.implementations.controller_classes.controller_nonMPI import controller_nonMPI
+
+from pySDC.implementations.hooks.log_solution import LogSolution
+
+
+def simulateDAE():
+    r"""
+    Main function where things will be done. Here, the problem class ``DiscontinuousTestDAE`` is simulated using
+    the ``SemiImplicitDAE`` sweeper, where only the differential variable is integrated using spectral quadrature.
+    The problem usually contains a discrete event, but the simulation interval is chosen so that the state function
+    does not have a sign change yet (the discrete event does not yet occur). Thus, the solution is smooth.
+    """
+    # initialize level parameters
+    level_params = {
+        'restol': 1e-12,
+        'dt': 0.1,
+    }
+
+    # initialize problem parameters
+    problem_params = {
+        'newton_tol': 1e-6,
+    }
+
+    # initialize sweeper parameters
+    sweeper_params = {
+        'quad_type': 'RADAU-RIGHT',
+        'num_nodes': 3,
+        'QI': 'IE',
+        'initial_guess': 'spread',
+    }
+
+    # initialize step parameters
+    step_params = {
+        'maxiter': 60,
+    }
+
+    # initialize controller parameters
+    controller_params = {
+        'logger_level': 30,
+        'hook_class': [LogSolution],
+    }
+
+    # fill description dictionary for easy step instantiation
+    description = {
+        'problem_class': DiscontinuousTestDAE,
+        'problem_params': problem_params,
+        'sweeper_class': SemiImplicitDAE,
+        'sweeper_params': sweeper_params,
+        'level_params': level_params,
+        'step_params': step_params,
+    }
+
+    # instantiate controller
+    controller = controller_nonMPI(num_procs=1, controller_params=controller_params, description=description)
+
+    t0 = 1.0
+    Tend = 3.0
+
+    P = controller.MS[0].levels[0].prob
+    uinit = P.u_exact(t0)
+
+    Path("data").mkdir(parents=True, exist_ok=True)
+
+    # call main function to get things done...
+    uend, stats = controller.run(u0=uinit, t0=t0, Tend=Tend)
+
+    plotSolution(stats)
+
+
+def plotSolution(stats):
+    r"""
+    Here, the solution of the DAE is plotted.
+
+    Parameters
+    ----------
+    stats : dict
+        Contains all the statistics of the simulation.
+    """
+
+    u_val = get_sorted(stats, type='u', sortby='time')
+    t = np.array([me[0] for me in u_val])
+    y = np.array([me[1].diff[0] for me in u_val])
+    z = np.array([me[1].alg[0] for me in u_val])
+
+    plt.figure(figsize=(8.5, 8.5))
+    plt.plot(t, y, label='Differential variable y')
+    plt.plot(t, z, label='Algebraic variable z')
+    plt.legend(frameon=False, fontsize=12, loc='upper left')
+    plt.xlabel(r"Time $t$")
+    plt.ylabel(r"Solution $y(t)$, $z(t)$")
+
+    plt.savefig('data/solution.png', dpi=300, bbox_inches='tight')
+    plt.close()
+
+
+if __name__ == "__main__":
+    simulateDAE()