def main():
# Create Dahlquist's test problem using implicit mid-point rule time integration
dahlquist_lvl0 = Dahlquist(t_start=0, t_stop=5, nt=101, method='MR')
# Create Dahlquist's test problem using backward Euler time integration
dahlquist_lvl1 = Dahlquist(t_start=0, t_stop=5, nt=51, method='BE')
# Setup an MGRIT solver and solve the problem
mgrit = Mgrit(problem=[dahlquist_lvl0, dahlquist_lvl1])
info = mgrit.solve()
def test_dahlquist_step_fe():
"""
Test step()
"""
dahlquist = Dahlquist(method='FE', t_start=0, t_stop=1, nt=11)
dahlquist_res = dahlquist.step(u_start=VectorDahlquist(1),
t_start=0,
t_stop=0.1)
np.testing.assert_almost_equal(dahlquist_res.get_values(), 0.9)
def main():
t_interval = np.linspace(0, 5, 17)
dahlquist_0 = Dahlquist(t_start=0, t_stop=5, nt=65)
dahlquist_1 = Dahlquist(t_interval=dahlquist_0.t[[0,3,10,12,14,17,23,27,33,34,55,57,59,61,63,64]])
dahlquist_2 = Dahlquist(t_interval=dahlquist_1.t[::2])
dahlquist_3 = Dahlquist(t_interval=dahlquist_2.t[::2])
dahlquist_4 = Dahlquist(t_interval=dahlquist_3.t[::2])
mgrit = Mgrit(problem=[dahlquist_0, dahlquist_1, dahlquist_2, dahlquist_3,dahlquist_4], tol=1e-10, nested_iteration=False)
#mgrit.plot_parallel_distribution(time_procs=6, save_name='test.png')
info = mgrit.solve()
def test_dahlquist_constructor():
"""
Test constructor
"""
dahlquist = Dahlquist(t_start=0, t_stop=1, nt=11)
np.testing.assert_equal(
True, isinstance(dahlquist.vector_template, VectorDahlquist))
np.testing.assert_equal(
True, isinstance(dahlquist.vector_t_start, VectorDahlquist))
np.testing.assert_equal(dahlquist.vector_t_start.get_values(), 1)
np.testing.assert_equal('BE', dahlquist.method)
def main():
# Create Dahlquist's test problem with 101 time steps in the interval [0, 5]
dahlquist = Dahlquist(t_start=0, t_stop=5, nt=101)
# Construct a two-level multigrid hierarchy for the test problem using a coarsening factor of 2
dahlquist_multilevel_structure = simple_setup_problem(problem=dahlquist, level=2, coarsening=2)
# Set up the MGRIT solver for the test problem and set the solver tolerance to 1e-10
mgrit = Mgrit(problem=dahlquist_multilevel_structure, tol=1e-10)
# Solve the test problem
info = mgrit.solve()
def main():
# Option 1: Use PyMGRIT's core function simple_setup_problem()
dahlquist_multilevel_structure_1 = simple_setup_problem(problem=Dahlquist(
t_start=0, t_stop=5, nt=101),
level=3,
coarsening=2)
Mgrit(problem=dahlquist_multilevel_structure_1, tol=1e-10).solve()
# Option 2: Build each level using t_start, t_end, and nt
dahlquist_lvl_0 = Dahlquist(t_start=0, t_stop=5, nt=101)
dahlquist_lvl_1 = Dahlquist(t_start=0, t_stop=5, nt=51)
dahlquist_lvl_2 = Dahlquist(t_start=0, t_stop=5, nt=26)
dahlquist_multilevel_structure_2 = [
dahlquist_lvl_0, dahlquist_lvl_1, dahlquist_lvl_2
]
Mgrit(problem=dahlquist_multilevel_structure_2, tol=1e-10).solve()
# Option 3: Specify time intervals for each grid level
t_interval = np.linspace(0, 5, 101)
dahlquist_lvl_0 = Dahlquist(t_interval=t_interval)
dahlquist_lvl_1 = Dahlquist(
t_interval=t_interval[::2]) # Takes every second point from t_interval
dahlquist_lvl_2 = Dahlquist(
t_interval=t_interval[::4]) # Takes every fourth point from t_interval
dahlquist_multilevel_structure_3 = [
dahlquist_lvl_0, dahlquist_lvl_1, dahlquist_lvl_2
]
Mgrit(problem=dahlquist_multilevel_structure_3, tol=1e-10).solve()
# Option 4: Mix options 2 and 3
dahlquist_lvl_0 = Dahlquist(t_start=0, t_stop=5, nt=101)
dahlquist_lvl_1 = Dahlquist(
t_interval=dahlquist_lvl_0.t[::2]) # Using t from the upper level.
dahlquist_lvl_2 = Dahlquist(t_start=0, t_stop=5, nt=26)
dahlquist_multilevel_structure_4 = [
dahlquist_lvl_0, dahlquist_lvl_1, dahlquist_lvl_2
]
Mgrit(problem=dahlquist_multilevel_structure_4, tol=1e-10).solve()
def main():
# Create Dahlquist's test problem with 101 time steps in the interval [0, 5]
dahlquist = Dahlquist(t_start=0, t_stop=5, nt=101)
# Construct a two-level multigrid hierarchy for the test problem using a coarsening factor of 2
dahlquist_multilevel_structure = simple_setup_problem(problem=dahlquist,
level=2,
coarsening=2)
# Set up the MGRIT solver for the test problem
mgrit = Mgrit(
problem=dahlquist_multilevel_structure, # Problem structure
transfer=None, # Spatial grid transfer. Automatically set if None.
max_iter=10, # Maximum number of iterations (default: 100)
tol=1e-10, # Stopping tolerance (default: 1e-7)
nested_iteration=
True, # Use (True) or do not use (False) nested iterations
# (default: True)
cf_iter=1, # Number of CF relaxations (default: 1)
cycle_type='V', # multigrid cycling type (default: 'V'):
# 'V' -> V-cycles
# 'F' -> F-cycles
comm_time=MPI.
COMM_WORLD, # Time communicator (default: MPI.COMM_WORLD)
comm_space=MPI.
COMM_NULL, # Space communicator (default: MPI.COMM_NULL)
weight_c=1, # C - relaxation weight (default: 1)
logging_lvl=20, # Logging level (default: 20):
# 10: Debug -> Runtime of all components
# 20: Info -> Info per iteration + summary
# 30: None -> No information
output_fcn=None, # Function for saving solution values to file
# (default: None)
output_lvl=1, # Output level (default: 1):
# 0 -> output_fcn is never called
# 1 -> output_fcn is called at the end of the simulation
# 2 -> output_fcn is called after each MGRIT iteration
t_norm=2, # Temporal norm
# 1 -> One-norm
# 2 -> Two-norm
# 3 -> Infinity-norm
random_init_guess=
False # Use (True) or do not use (False) random initial guess
# for all unknowns (default: False)
)
# Solve the test problem
return mgrit.solve()
def main():
# Define output function that writes the solution to a file
def output_fcn(self):
# Set path to solution
path = 'results/' + 'dahlquist'
# Create path if not existing
pathlib.Path(path).mkdir(parents=True, exist_ok=True)
# Save solution to file; here, we just have a single solution value at each time point.
# Useful member variables of MGRIT solver:
# - self.t[0] : local fine-grid (level 0) time interval
# - self.index_local[0] : indices of local fine-grid (level 0) time interval
# - self.u[0] : fine-grid (level 0) solution values
np.save(path + '/dahlquist',
[self.u[0][i].get_values() for i in self.index_local[0]
]) # Solution values at local time points
# Create Dahlquist's test problem with 101 time steps in the interval [0, 5]
dahlquist = Dahlquist(t_start=0, t_stop=5, nt=101)
# Construct a two-level multigrid hierarchy for the test problem using a coarsening factor of 2
dahlquist_multilevel_structure = simple_setup_problem(problem=dahlquist,
level=2,
coarsening=2)
# Set up the MGRIT solver for the test problem and set the output function
mgrit = Mgrit(problem=dahlquist_multilevel_structure,
output_fcn=output_fcn)
# Solve the test problem
info = mgrit.solve()
# Plot the solution (Note: modifications necessary if more than one process is used for the simulation!)
t = np.linspace(dahlquist.t_start, dahlquist.t_end, dahlquist.nt)
sol = np.load('results/dahlquist/dahlquist.npy')
plt.plot(t, sol)
plt.xlabel('t')
plt.ylabel('u(t)')
plt.show()
def test_dahlquist_constructor_exception():
"""
Test constructor
"""
with pytest.raises(Exception):
Dahlquist(t_start=0, t_stop=1, nt=11, method='unknown')
def test_dahlquist_constructor_tr():
"""
Test constructor
"""
dahlquist = Dahlquist(t_start=0, t_stop=1, nt=11, method='TR')
np.testing.assert_equal('TR', dahlquist.method)