def test_pefrl(self):
# Given.
integrator = PEFRLIntegrator(fluid=PEFRLStep())
equations = [SHM(dest="fluid", sources=None)]
self._setup_integrator(equations=equations, integrator=integrator)
tf = np.pi
dt = 0.1 * tf
# When
energy = []
def callback(t):
x, u = self.pa.x[0], self.pa.u[0]
energy.append(0.5 * (x * x + u * u))
callback(0.0)
self._integrate(integrator, dt, tf, callback)
# Then
energy = np.asarray(energy)
self.assertAlmostEqual(np.max(np.abs(energy - 0.5)), 0.0, places=4)
def test_pefrl_is_fourth_order(self):
# Given.
integrator = PEFRLIntegrator(fluid=PEFRLStep())
equations = [SHM(dest="fluid", sources=None)]
self._setup_integrator(equations=equations, integrator=integrator)
# Take a dt, find the error, halve dt, and see that error is drops as
# desired.
# When
tf = np.pi
dt = 0.1 * tf
energy = []
def callback(t):
x, u = self.pa.x[0], self.pa.u[0]
energy.append(0.5 * (x * x + u * u))
callback(0.0)
self._integrate(integrator, dt, tf, callback)
energy = np.asarray(energy)
err1 = np.max(np.abs(energy - 0.5))
# When
self.pa.x[0] = 1.0
self.pa.u[0] = 0.0
energy = []
dt *= 0.5
callback(0.0)
self._integrate(integrator, dt, tf, callback)
energy = np.asarray(energy)
err2 = np.max(np.abs(energy - 0.5))
# Then
self.assertTrue(err2 < err1)
self.assertTrue(err1 / err2 > 16.0)