def main():
# Split the communicator into space and time communicator
comm_world = MPI.COMM_WORLD
comm_x, comm_t = split_communicator(comm_world, 2)
# Define spatial domain
# The domain is a 10x10 square with periodic boundary conditions in each direction.
n = 20
mesh = PeriodicSquareMesh(n, n, 10, comm=comm_x)
# Set up the problem
diffusion0 = Diffusion2D(mesh=mesh,
kappa=0.1,
comm_space=comm_x,
t_start=0,
t_stop=10,
nt=17)
diffusion1 = Diffusion2D(mesh=mesh,
kappa=0.1,
comm_space=comm_x,
t_start=0,
t_stop=10,
nt=9)
# Setup three-level MGRIT solver with the space and time communicators and
# solve the problem
mgrit = Mgrit(problem=[diffusion0, diffusion1],
comm_time=comm_t,
comm_space=comm_x)
info = mgrit.solve()
def run_mgrit(nt, space_procs, coarsening, freq=1, a=1.0, t_start=0, t_stop=1, cycle='V'):
size = MPI.COMM_WORLD.Get_size()
comm_x, comm_t = split_communicator(MPI.COMM_WORLD, space_procs)
nx = ny = 65
dmda_coarse = PETSc.DMDA().create([nx, ny], stencil_width=1, comm=comm_x)
dmda_fine = dmda_coarse.refine()
t_interval = np.linspace(t_start, t_stop, nt)
time_procs = int(size / space_procs)
problem = [HeatPetsc(dmda=dmda_fine, comm_x=comm_x, freq=freq, a=a, t_interval=t_interval)]
for i in range(0, len(coarsening)):
problem.append(HeatPetsc(dmda=dmda_fine, comm_x=comm_x, freq=freq, a=a,
t_interval=t_interval[::np.prod(coarsening[:i + 1], dtype=int)]))
nested_iteration = True if len(coarsening) > 0 else False
if cycle == 'V':
mgrit = Mgrit(problem=problem, comm_time=comm_t, comm_space=comm_x, nested_iteration=nested_iteration)
else:
mgrit = Mgrit(problem=problem, comm_time=comm_t, comm_space=comm_x, nested_iteration=nested_iteration,
cycle_type='F', cf_iter=0)
info = mgrit.solve()
return info['time_setup'], info['time_solve'], info['time_setup'] + info['time_solve']
def main():
def output_fcn(self):
# Set path to solution
path = 'results/petsc'
# Create path if not existing
pathlib.Path(path).mkdir(parents=True, exist_ok=True)
# Save solution with corresponding time point to file
np.save(path + '/petsc' + str(self.comm_time_rank) + str(self.comm_space_rank),
[[[self.t[0][i], self.comm_space_rank, self.u[0][i].get_values().getArray()] for i in
self.index_local[0]]])
# Split the communicator into space and time communicator
comm_world = MPI.COMM_WORLD
comm_x, comm_t = split_communicator(comm_world, 4)
# Create PETSc DMDA grids
nx = 129
ny = 129
dmda_coarse = PETSc.DMDA().create([nx, ny], stencil_width=1, comm=comm_x)
dmda_fine = dmda_coarse.refine()
# Set up the problem
heat_petsc_0 = HeatPetsc(dmda=dmda_fine, comm_x=comm_x, freq=1, a=1.0, t_start=0, t_stop=1, nt=33)
heat_petsc_1 = HeatPetsc(dmda=dmda_coarse, comm_x=comm_x, freq=1, a=1.0, t_interval=heat_petsc_0.t[::2])
heat_petsc_2 = HeatPetsc(dmda=dmda_coarse, comm_x=comm_x, freq=1, a=1.0, t_interval=heat_petsc_1.t[::2])
# Setup three-level MGRIT solver with the space and time communicators and
# solve the problem
mgrit = Mgrit(problem=[heat_petsc_0, heat_petsc_1, heat_petsc_2],
transfer=[GridTransferPetsc(fine_prob=dmda_fine, coarse_prob=dmda_coarse), GridTransferCopy()],
comm_time=comm_t, comm_space=comm_x, output_fcn=output_fcn)
info = mgrit.solve()
import time
if comm_t.Get_rank() == 0:
time.sleep(1)
sol = []
path = 'results/petsc/'
for filename in os.listdir(path):
data = np.load(path + filename, allow_pickle=True).tolist()[0]
sol += data
sol = [item for item in sol if item[1] == comm_x.Get_rank()]
sol.sort(key=lambda tup: tup[0])
u_e = heat_petsc_0.u_exact(t=heat_petsc_0.t[-1]).get_values().getArray()
diff = sol[-1][2] - u_e
print('Difference at time point', heat_petsc_0.t[-1], ':',
np.linalg.norm(diff, np.inf), '(space rank',comm_x.Get_rank() , ')')
def run_timestepping(nt, space_procs, freq=1, a=1.0, t_start=0, t_stop=1):
comm_x, comm_t = split_communicator(MPI.COMM_WORLD, space_procs)
nx = ny = 65
dmda_coarse = PETSc.DMDA().create([nx, ny], stencil_width=1, comm=comm_x)
dmda_fine = dmda_coarse.refine()
t_interval = np.linspace(t_start, t_stop, nt)
heat_petsc_0 = HeatPetsc(dmda=dmda_fine, comm_x=comm_x, freq=freq, a=a, t_interval=t_interval)
import time
start = time.time()
sol = heat_petsc_0.vector_t_start
for i in range(1, len(heat_petsc_0.t)):
sol = heat_petsc_0.step(u_start=sol, t_start=heat_petsc_0.t[i - 1], t_stop=heat_petsc_0.t[i])
info = {'time_setup': 0, 'time_solve': time.time() - start}
return info['time_setup'], info['time_solve'], info['time_setup'] + info['time_solve']
