def __init__(self, model, config):
"""
Initialize solver. Initialize all of the physics classes specified
as 'on' in the config object.
"""
self.model = model
self.config = config
self.config['mode'] = 'transient'
# initialize velocity solver :
if self.config['velocity']['on']:
if self.config['velocity']['approximation'] == 'fo':
self.velocity_instance = VelocityBP(model, config)
elif self.config['velocity']['approximation'] == 'stokes':
self.velocity_instance = VelocityStokes(model, config)
else:
print "Please choose 'fo' or 'stokes'. "
# initialized enthalpy solver :
if self.config['enthalpy']['on']:
self.enthalpy_instance = Enthalpy(model, config)
# initialize age solver :
if self.config['age']['on']:
self.age_instance = Age(model, config)
# initialize surface climate solver :
if self.config['surface_climate']['on']:
self.surface_climate_instance = SurfaceClimate(model, config)
# initialize free surface solver :
if config['free_surface']['on']:
self.surface_instance = FreeSurface(model, config)
self.M_prev = 1.0
# Set up files for logging time dependent solutions to paraview files.
if config['log']:
self.file_U = File(self.config['output_path'] + 'U.pvd')
self.file_T = File(self.config['output_path'] + 'T.pvd')
self.file_S = File(self.config['output_path'] + 'S.pvd')
self.file_a = File(self.config['output_path'] + 'age.pvd')
self.dheight = []
self.mass = []
self.t_log = []
self.step_time = []
self.M_prev = 1.0
def __init__(self, space_name, variable_name, function_space):
# Define initial interface values
self.interface_new = Function(function_space)
self.interface_old = Function(function_space)
# Define initial values for time loop
self.new = Function(function_space)
self.old = Function(function_space)
# Create arrays of empty functions and iterations
self.array = []
self.iterations = []
# Create pvd files
self.pvd = File(f"solutions/{space_name}/pvd/{variable_name}.pvd")
# Remember space
self.function_space = function_space
# Remember space and variable names
self.space_name = space_name
self.variable_name = variable_name
# Create HDF5 counter
self.HDF5_counter = 0
def gen_rect_mesh(nx, ny, xmin, xmax, ymin, ymax, outfile, direction='right'):
mesh = RectangleMesh(MPI.COMM_SELF,
Point(xmin, ymin),
Point(xmax, ymax),
nx, ny, direction)
File(MPI.COMM_SELF, outfile) << mesh
def write_one_file(self, name, data, extension='.pvd'): """ Save a single file of FEniCS Function <data> named <name> to the DataOutput instance's directory. Extension may be '.xml' or '.pvd'. """ s = "::: writing file %s :::" % (name + extension) print_text(s, self.color) file_handle = File(self.directory + name + extension) file_handle << data
def distribute_mesh(mesh):
"""Distribute a local copy of a mesh
Required argument:
mesh: a sequential copy of the mesh to be distributed. Only the
copy on the rank 0 process is used. This mesh will be distribuetd
among all processes connected to MPI.COMM_WORLD so that it can be
used for FEniCS computations.
Return value: the distributed mesh
"""
scomm = MPI.COMM_SELF
wcomm = MPI.COMM_WORLD
gmesh = gather_mesh(mesh)
if wcomm.rank == 0:
assert (gmesh.mpi_comm().size == 1) # check it's sequential
with tempfile.TemporaryDirectory() as td:
meshfile = os.path.join(td, 'mesh.xml')
logGATHER('writing ' + meshfile)
File(MPI.COMM_SELF, meshfile) << gmesh
logGATHER('broadcasting meshfile')
meshfile = wcomm.bcast(meshfile, root=0)
try:
with open(meshfile, 'r') as mf: # rank 0
dmesh = fe.Mesh(wcomm, meshfile)
logGATHER('dmesh', dmesh)
except FileNotFoundError:
logGATHER('meshfile', meshfile, 'not found')
wcomm.Barrier() # wait for everyone to read it
logGATHER('destroying temp directory')
# context manager destroyed, temp dir gets deleted
else:
meshfile = None
logGATHER('receiving broadcast meshfile')
meshfile = wcomm.bcast(meshfile, root=0)
logGATHER('meshfile', meshfile)
try:
with open(meshfile, 'r') as mf: # rank != 0
dmesh = fe.Mesh(wcomm, meshfile)
logGATHER('dmesh', dmesh)
except FileNotFoundError:
logGATHER('meshfile', meshfile, 'not found')
wcomm.Barrier()
return (dmesh)
# apply Dirichlet boundary condition on coupling interface
bcs.append(precice.create_coupling_dirichlet_boundary_condition(V))
a, L = lhs(F), rhs(F)
# Time-stepping
u_np1 = Function(V)
F_known_u = u_np1 * v / dt * dx + alpha * dot(grad(u_np1),
grad(v)) * dx - u_n * v / dt * dx
u_np1.rename("T", "")
t = 0
u_D.t = t + precice._precice_tau
assert (dt == precice._precice_tau)
file_out = File("Solid/VTK/%s.pvd" % solver_name)
while precice.is_coupling_ongoing():
# Compute solution
solve(a == L, u_np1, bcs)
# Dirichlet problem obtains flux from solution and sends flux on boundary to Neumann problem
fluxes = fluxes_from_temperature_full_domain(F_known_u, V, k)
is_converged = precice.advance(fluxes, dt)
if is_converged:
# Update previous solution
if abs(t % dt_out) < 10e-5 or abs(
t % dt_out
) < 10e-5: # just a very complicated way to only produce output if t is a multiple of dt_out
t = 0
# reference solution at t=0
u_ref = interpolate(u_D, V)
u_ref.rename("reference", " ")
# mark mesh w.r.t ranks
mesh_rank = MeshFunction("size_t", mesh, mesh.topology().dim())
if problem is ProblemType.NEUMANN:
mesh_rank.set_all(MPI.rank(MPI.comm_world) + 4)
else:
mesh_rank.set_all(MPI.rank(MPI.comm_world) + 0)
mesh_rank.rename("myRank", "")
# Generating output files
temperature_out = File("out/%s.pvd" % precice.get_participant_name())
ref_out = File("out/ref%s.pvd" % precice.get_participant_name())
error_out = File("out/error%s.pvd" % precice.get_participant_name())
ranks = File("out/ranks%s.pvd" % precice.get_participant_name())
# output solution and reference solution at t=0, n=0
n = 0
print('output u^%d and u_ref^%d' % (n, n))
temperature_out << u_n
ref_out << u_ref
ranks << mesh_rank
error_total, error_pointwise = compute_errors(u_n, u_ref, V)
error_out << error_pointwise
# set t_1 = t_0 + dt, this gives u_D^1
u_np1.rename("Source-Data", "")
elif args.drain:
u_n.rename("Drain-Data", "")
u_np1.rename("Drain-Data", "")
t = 0
mesh_rank = MeshFunction("size_t", mesh, mesh.topology().dim())
if args.source:
mesh_rank.set_all(MPI.rank(MPI.comm_world) + 4)
else:
mesh_rank.set_all(MPI.rank(MPI.comm_world) + 0)
mesh_rank.rename("myRank", "")
# Generating output files
solution_out = File("output/%s.pvd" % precice.get_participant_name())
ranks = File("output/ranks%s.pvd" % precice.get_participant_name())
# output solution and reference solution at t=0, n=0
n = 0
print('output u^%d and u_ref^%d' % (n, n))
solution_out << u_n
ranks << mesh_rank
while precice.is_coupling_ongoing():
# write checkpoint
if precice.is_action_required(precice.action_write_iteration_checkpoint()):
precice.store_checkpoint(u_n, t, n)
read_data = precice.read_data()
# apply constant Dirichlet boundary condition at bottom edge
# apply Dirichlet boundary condition on coupling interface
bcs = [
DirichletBC(V, coupling_expression, coupling_boundary),
DirichletBC(V, u_D, bottom_boundary)
]
a, L = lhs(F), rhs(F)
# Time-stepping
u_np1 = Function(V)
t = 0
u_D.t = t + dt
# mark mesh w.r.t ranks
ranks = File("Solid/VTK/ranks%s.pvd.pvd" % precice.get_participant_name())
mesh_rank = MeshFunction("size_t", mesh, mesh.topology().dim())
mesh_rank.set_all(MPI.rank(MPI.comm_world))
mesh_rank.rename("myRank", "")
ranks << mesh_rank
# Create output file
file_out = File("Solid/VTK/%s.pvd" % precice.get_participant_name())
file_out << u_n
print("output vtk for time = {}".format(float(t)))
n = 0
fluxes = Function(V_g)
fluxes.rename("Fluxes", "")
nx = 50
ny = 50
nz = 10
model = Model()
model.generate_uniform_mesh(nx,
ny,
nz,
xmin=0,
xmax=L,
ymin=0,
ymax=L,
generate_pbcs=True)
Surface = Expression('- x[0] * tan(alpha)',
alpha=alpha,
element=model.Q.ufl_element())
Bed = Expression( '- x[0] * tan(alpha) - 1000.0 + 500.0 * ' \
+ ' sin(2*pi*x[0]/L) * sin(2*pi*x[1]/L)',
alpha=alpha, L=L, element=model.Q.ufl_element())
File('./results_A_BP/' + 'B.pvd') << interpolate(Bed, model.Q)
model.set_geometry(Surface, Bed, deform=True)
model.set_parameters(IceParameters())
model.calculate_boundaries()
model.initialize_variables()
F = SteadySolver(model, config)
F.solve()
# the finite-element mesh used :
mesh = UnitSquareMesh(n_x, n_x)
# initialize the model :
grid_model = GridModel(mesh, out_dir, verbose=False)
# create the main model to perform MPM calculations :
model = Model(out_dir, grid_model, dt, verbose=False)
# add the materials to the model :
model.add_material(disk1)
model.add_material(disk2)
# files for saving grid variables :
m_file = File(out_dir + '/m.pvd')
u_file = File(out_dir + '/u.pvd')
a_file = File(out_dir + '/a.pvd')
f_file = File(out_dir + '/f.pvd')
# callback function saves result :
def cb_ftn():
if model.iter % save_int == 0:
model.retrieve_cpp_grid_m()
model.retrieve_cpp_grid_U3()
model.retrieve_cpp_grid_f_int()
model.retrieve_cpp_grid_a3()
grid_model.save_pvd(grid_model.m, 'm', f=m_file, t=model.t)
grid_model.save_pvd(grid_model.U3, 'U3', f=u_file, t=model.t)
grid_model.save_pvd(grid_model.a3, 'a3', f=a_file, t=model.t)
def makeSaveMonitor(self, prefix=None):
"""Make a saveMonitor for use as a TS monitor
Note that makesaveMonitor is not itself a monitor
function. It returns a callable that can be used as a save
monitor. Typical usage:
(saveMonitor, closer) = ts.makeSaveMonitor(prefix='solution')
ts.setMonitor(save_Monitor)
ts.solve()
...
closer()
Optional keyword argument:
prefix=None: The filename prefix to use for the saved
files (may begin with a file path. If not provided,
the prefix is "solution' prepended to a string
produced by the uuid function uuid4.
"""
if not prefix:
prefix = 'solution' + str(uuid4()) + '_'
#
# save basic info about FunctionSpace
#
fsname = prefix + 'rank' + str(self.comm.rank) + '_fsinfo.h5'
if not hasattr(self, 'remap'):
self.lmesh = gather_mesh(self.ksdg.mesh)
logTS('makeSaveMonitor: self.lmesh', self.lmesh)
self.remap = dofremap(self.ksdg, gathered_mesh=self.lmesh)
logTS('makeSaveMonitor: self.remap', self.remap)
if hasattr(self.ksdg, 'omesh'):
self.omesh = gather_mesh(self.ksdg.omesh)
if self.comm.rank == 0:
logTS('self.lmesh.mpi_comm().size', self.lmesh.mpi_comm().size)
lmeshf = File(MPI.COMM_SELF, prefix + '_mesh.xml.gz')
lmeshf << self.lmesh
logTS('self.lmesh saved')
if hasattr(self, 'omesh'):
logTS('self.omesh.mpi_comm().size', self.omesh.mpi_comm().size)
omeshf = File(MPI.COMM_SELF, prefix + '_omesh.xml.gz')
omeshf << self.omesh
logTS('self.omesh saved')
try:
scomm = fe.mpi_comm_self()
except AttributeError:
scomm = MPI.COMM_SELF
fsf = HDF5File(scomm, fsname, 'w')
fs = self.ksdg.sol.function_space()
fsf.write(self.ksdg.sol, 'sol')
fsf.write(self.ksdg.mesh, 'mesh')
if self.comm.rank == 0:
fsf.write(self.lmesh, 'lmesh')
fsf.close()
fsf = h5py.File(fsname, 'r+')
fsf['/mpi/rank'] = self.comm.rank
fsf['/mpi/size'] = self.comm.size
if self.comm.rank == 0:
fsf['remap'] = self.remap
if hasattr(self.ksdg, 'srhos'):
rhofss = [rho.function_space() for rho in self.ksdg.srhos]
else:
rhofss = [self.ksdg.srho.function_space()]
if hasattr(self.ksdg, 'sUs'):
Ufss = [U.function_space() for U in self.ksdg.sUs]
else:
Ufss = [self.ksdg.sU.function_space()]
dofmap = fs.dofmap()
fsinfo = {}
fsf['degree'] = self.ksdg.degree
if hasattr(self.ksdg, 'nelements'):
fsf['nelements'] = self.ksdg.nelements
if hasattr(self.ksdg, 'periodic'):
fsf['periodic'] = self.ksdg.periodic
else:
fsf['periodic'] = False
if hasattr(self.ksdg, 'ligands'):
fsf['ligands'] = pickle.dumps(self.ksdg.ligands, protocol=0)
else:
fsf['ligands'] = False
if hasattr(self.ksdg, 'param_names'):
fsf['param_names'] = pickle.dumps(self.ksdg.param_names,
protocol=0)
else:
fsf['param_names'] = pickle.dumps([], protocol=0)
if hasattr(self.ksdg, 'param_funcs'):
try:
dillfunc = dill.dumps(self.ksdg.param_funcs, protocol=0)
fsf['param_funcs'] = np.void(dillfunc)
#
# retrieve using fsf['param_funcs'].tobytes()
#
except ValueError as e:
traceback.print_exc()
fsf['param_funcs'] = dill.dumps([], protocol=0)
else:
fsf['param_funcs'] = dill.dumps([], protocol=0)
if hasattr(self.ksdg, 'params0'):
fsf['params0'] = pickle.dumps(self.ksdg.params0, protocol=0)
else:
fsf['params0'] = pickle.dumps({}, protocol=0)
dim = self.ksdg.dim
fsf['dim'] = dim
try:
fsf['ghost_mode'] = self.ksdg.mesh.ghost_mode()
except AttributeError:
pass
fsf['off_process_owner'] = dofmap.off_process_owner()
owneddofs = dofmap.ownership_range()
fsf['ownership_range'] = owneddofs
logFSINFO('owneddofs', owneddofs)
ltgu = np.zeros(len(dofmap.local_to_global_unowned()), dtype=int)
ltgu[:] = dofmap.local_to_global_unowned()
fsf['local_to_global_unowned'] = ltgu
ltgi = np.zeros(owneddofs[1] - owneddofs[0], dtype=int)
logFSINFO('np.array(dofmap.dofs())', np.array(dofmap.dofs()))
logFSINFO(
'dofmap local_to_global_indexes', *owneddofs,
np.array(
[dofmap.local_to_global_index(d) for d in range(*owneddofs)]))
logFSINFO(
'dofmap local_to_global_indexes', 0, owneddofs[1] - owneddofs[0],
np.array([
dofmap.local_to_global_index(d)
for d in range(owneddofs[1] - owneddofs[0])
]))
ltgi = np.array(
np.array(
[dofmap.local_to_global_index(d) for d in range(*owneddofs)]))
fsf['local_to_global_index'] = ltgi
fsf['tabulate_local_to_global_dofs'] = dofmap.tabulate_local_to_global_dofs(
)
logFSINFO('tabulate_local_to_global_dofs',
dofmap.tabulate_local_to_global_dofs())
# fsf['shared_nodes'] = dofmap.shared_nodes()
try:
fsf['neighbours'] = repr(dofmap.neighbours())
except (AttributeError, TypeError):
pass
try:
fsf['dofmap_str'] = dofmap.str(True)
except (AttributeError, TypeError):
fsf['dofmap_str'] = repr(dofmap)
try:
fsf['dofmap_id'] = dofmap.id()
except (AttributeError, TypeError):
pass
try:
fsf['dofmap_label'] = dofmap.label()
except (AttributeError, TypeError):
pass
try:
fsf['dofmap_name'] = dofmap.name()
except (AttributeError, TypeError):
pass
try:
fsf['max_cell_dimension'] = dofmap.max_cell_dimension()
except (AttributeError, TypeError):
pass
try:
fsf['max_element_dofs'] = dofmap.max_element_dofs()
except (AttributeError, TypeError):
pass
try:
fsf['dofmap_parameters'] = list(dofmap.parameters.iteritems())
except (AttributeError, TypeError):
try:
fsf['dofmap_parameters'] = list(dofmap.parameters.items())
except (AttributeError, TypeError):
pass
try:
fsf['dofmap_thisown'] = dofmap.thisown
except (AttributeError, TypeError):
pass
try:
fsf['is_view'] = dofmap.is_view()
except (AttributeError, TypeError):
pass
for d in range(dim + 1):
fsf['entity_closure_dofs' + str(d)] = \
dofmap.entity_closure_dofs(self.ksdg.mesh, d)
fsf['entity_dofs' + str(d)] = \
dofmap.entity_dofs(self.ksdg.mesh, d)
fsf['dofcoords'] = np.reshape(fs.tabulate_dof_coordinates(), (-1, dim))
try:
fsf['block_size'] = dofmap.block_size()
except (AttributeError, TypeError):
pass
try:
fsf['dofs'] = dofmap.dofs()
except (AttributeError, TypeError):
pass
for i in range(len(rhofss)):
fsf['rho_dofs/' + str(i)] = rhofss[i].dofmap().dofs()
for i in range(len(Ufss)):
fsf['U_dofs/' + str(i)] = Ufss[i].dofmap().dofs()
dofspercell = dofmap.cell_dofs(0).size
ncells = self.ksdg.mesh.cells().shape[0]
celldofs = np.zeros((ncells, dofspercell), dtype=np.int)
for cell in range(ncells):
celldofs[cell] = dofmap.cell_dofs(cell)
fsf['cell_dofs'] = celldofs
fsf.close()
logTS('creating KSDGTimeSeries')
tsname = prefix + '_ts.h5'
if self.comm.rank == 0:
tsf = KSDGTimeSeries(tsname, 'w')
tsf.close()
def closeSaveMonitor():
if self.comm.rank == 0:
tsf.close()
def saveMonitor(ts, k, t, u):
#
# make a local copy of the dof vector
#
# logTS('saveMonitor entered')
psol = fe.as_backend_type(self.ksdg.sol.vector()).vec()
u.copy(psol)
self.ksdg.sol.vector().apply('insert')
lu = self.ksdg.sol.vector().gather_on_zero()
if ts.comm.rank == 0:
lu = lu[self.remap]
#
# reopen and close every time, so file valid after abort
#
tsf = KSDGTimeSeries(tsname, 'r+')
tsf.store(lu, t, k=k)
tsf.close()
return (saveMonitor, closeSaveMonitor)
from fenics import FunctionSpace, interpolate, File
from utils import reference_data, exact_kepler
# get initial data and mesh for a Kelper problem with
# energy H=-1.5 (elliptic orbit) and initial momentum L=0.5.
H = -1.5
L = 0.5
(_, _, gexp, mesh) = reference_data(H=H, L=L, mesh_type='unstructured',
mesh_size=24, padding=0.07)
(q0, p0, T, S, (c, a, b), sol, t2s) = exact_kepler(H, L)
g = interpolate(gexp, FunctionSpace(mesh, "Regge", 1))
File("plots/kepler_metric.pvd") << g
F += precice.create_coupling_neumann_boundary_condition(v)
a, L = lhs(F), rhs(F)
# Time-stepping
u_np1 = Function(V)
F_known_u = u_np1 * v * dx + dt * dot(grad(u_np1),
grad(v)) * dx - (u_n + dt * f) * v * dx
u_np1.rename("Temperature", "")
t = 0
# reference solution at t=0
u_e = interpolate(u_D, V)
u_e.rename("reference", " ")
file_out = File("out/%s.pvd" % solver_name)
ref_out = File("out/ref%s.pvd" % solver_name)
# output solution and reference solution at t=0, n=0
n = 0
print('output u^%d and u_ref^%d' % (n, n))
file_out << u_n
ref_out << u_e
# set t_1 = t_0 + dt, this gives u_D^1
u_D.t = t + precice._precice_tau
assert (dt == precice._precice_tau)
while precice.is_coupling_ongoing():
# Compute solution u^n+1, use bcs u_D^n+1, u^n and coupling bcs
Forces_x, Forces_y = precice.create_force_boundary_condition(V)
a_form = lhs(res)
L_form = rhs(res)
# Prepare for time-stepping
t = 0.0
n = 0
time = []
u_tip = []
time.append(0.0)
u_tip.append(0.0)
E_ext = 0
displacement_out = File("Solid/FSI-S/u_fsi.pvd")
u_n.rename("Displacement", "")
u_np1.rename("Displacement", "")
displacement_out << u_n
# time loop for coupling
while precice.is_coupling_ongoing():
A, b = assemble_system(a_form, L_form, bc)
b_forces = b.copy(
) # b is the same for every iteration, only forces change
for ps in Forces_x:
ps.apply(b_forces)
for ps in Forces_y:
u = TrialFunction(V)
v = TestFunction(V)
F = u * v / dt * dx + alpha * dot(grad(u), grad(v)) * dx - u_n * v / dt * dx
# apply Dirichlet boundary condition on coupling interface
bcs.append(precice.create_coupling_dirichlet_boundary_condition(V))
a, L = lhs(F), rhs(F)
# Time-stepping
u_np1 = Function(V)
F_known_u = u_np1 * v / dt * dx + alpha * dot(grad(u_np1), grad(v)) * dx - u_n * v / dt * dx
t = 0
u_D.t = t + dt
file_out = File("Solid/VTK/%s.pvd" % precice._solver_name)
n=0
while precice.is_coupling_ongoing():
# Compute solution
solve(a == L, u_np1, bcs)
# Dirichlet problem obtains flux from solution and sends flux on boundary to Neumann problem
fluxes = fluxes_from_temperature_full_domain(F_known_u, V, k)
t, n, precice_timestep_is_complete, precice_dt = precice.advance(fluxes, u_np1, u_n, t, dt, n)
dt = np.min([fenics_dt, precice_dt]) # todo we could also consider deciding on time stepping size inside the adapter
if precice_timestep_is_complete:
if abs(t % dt_out) < 10e-5 or abs(t % dt_out) < 10e-5: # just a very complicated way to only produce output if t is a multiple of dt_out
# parameters for Time-Stepping
t = 0.0
n = 0
time = []
u_tip = []
time.append(0.0)
u_tip.append(0.0)
E_ext = 0
# mark mesh w.r.t ranks
mesh_rank = MeshFunction("size_t", mesh, mesh.topology().dim())
mesh_rank.set_all(MPI.rank(MPI.comm_world) + 0)
mesh_rank.rename("myRank", "")
displacement_out = File("Solid/FSI-S/u_fsi.pvd")
ranks = File("Solid/FSI-S/ranks%s.pvd" % precice.get_participant_name())
u_n.rename("Displacement", "")
u_np1.rename("Displacement", "")
displacement_out << u_n
ranks << mesh_rank
while precice.is_coupling_ongoing():
if precice.is_action_required(
precice.action_write_iteration_checkpoint()): # write checkpoint
precice.store_checkpoint(u_n, t, n)
# read data from preCICE and get a new coupling expression
read_data = precice.read_data()
# Prepare for time-stepping
#parameters for Time-Stepping
#T = 1.0
t = 0.0
n = 0
time = []
u_tip = []
time.append(0.0)
u_tip.append(0.0)
E_ext = 0
if Case is StructureCase.DUMMY2D:
displacement_out = File("Solid/Dummy2DOut/u_2dd.pvd")
elif Case is StructureCase.DUMMY3D:
displacement_out = File("Solid/Dummy3DOut/u_3dd.pvd")
elif Case is StructureCase.OPENFOAM:
displacement_out = File("Solid/FSI-S/u_fsi.pvd")
elif Case is StructureCase.RFERENCE:
displacement_out = File("Reference/u_ref.pvd")
displacement_out << u_n
#time loop for coupling
if Case is not StructureCase.RFERENCE:
from utils import plot_mesh, exact_kepler
from mshr import Circle, generate_mesh
from sympy2fenics import sympy2exp
# exact kepler orbit
H = -1.5
L = 0.5
(q0, p0, _, S, (c, a, b), _, _) = exact_kepler(H, L)
# symbolic computation for the jacobi metric for schwarzschild geodesics
x, y = sympy.var('x[0], x[1]')
E, m, M = sympy.var('E, m, M')
r = sympy.sqrt(x * x + y * y)
g = E**2 - m**2 + 2 * M * m**2 / r
f = 1 / (1 - 2 * M / r)
ds = f * g / r**2 * sympy.Matrix(
((f * x**2 + y**2, (f - 1) * x * y), ((f - 1) * x * y, x**2 + f * y**2)))
# choose parameters so that the schwarzschild solution is close to the kelper
# the most import parameter is M.
M = 0.0025
m = 1.0 / M**0.5
E = (2.0 * H + m**2)**0.5
gexp = Expression(sympy2exp(ds), E=E, m=m, M=M, degree=8)
# build a large enough domain
domain = Circle(Point(c), b + 0.45)
mesh = generate_mesh(domain, 32)
g = interpolate(gexp, FunctionSpace(mesh, "Regge", 1))
File("plots/schwarzschild_jacobi_metric.pvd") << g
# residual
a_np1 = update_a(du, u_n, v_n, a_n, ufl=True)
v_np1 = update_v(a_np1, u_n, v_n, a_n, ufl=True)
res = m(avg(a_n, a_np1, alpha_m), v) + k(avg(u_n, du, alpha_f), v)
a_form = lhs(res)
L_form = rhs(res)
# parameters for Time-Stepping
t = 0.0
n = 0
E_ext = 0
displacement_out = File("output/u_fsi.pvd")
u_n.rename("Displacement", "")
u_np1.rename("Displacement", "")
displacement_out << u_n
while precice.is_coupling_ongoing():
if precice.is_action_required(
precice.action_write_iteration_checkpoint()): # write checkpoint
precice.store_checkpoint(u_n, t, n)
# read data from preCICE and get a new coupling expression
read_data = precice.read_data()
# Update the point sources on the coupling boundary with the new read data
def solve(self):
r"""
Perform the optimization.
First, we define functions that return the objective function and Jacobian.
These are passed to scipy's fmin_l_bfgs_b, which is a python wrapper for the
Fortran code of Nocedal et. al.
The functions are needed to make the calculation of the search direction
and update of search point take place globally, across all proccessors,
rather than on a per-processor basis.
We also specify bounds:
:Condition:
.. math::
\beta_{2} > 0
"""
model = self.model
config = self.config
def get_global(m):
"""
Takes a distributed object and returns a numpy array that
contains all global values.
"""
if type(m) == float:
return array(m)
# return a numPy array of values or single value of Constant :
if type(m) == Constant:
a = p = zeros(m.value_size())
m.eval(a, p)
return a
# return a numPy array of values of a FEniCS function :
elif type(m) in (function.Function, functions.function.Function):
m_v = m.vector()
m_a = DoubleArray(m.vector().size())
try:
m.vector().gather(m_a, arange(m_v.size(), dtype='intc'))
return array(m_a.array())
except TypeError:
return m.vector().gather(arange(m_v.size(), dtype='intc'))
# The following type had to be added to the orginal function so that
# it could accomodate the return from the adjoint system solve.
elif type(m) == cpp.la.Vector:
m_a = DoubleArray(m.size())
try:
m.gather(m_a, arange(m.size(), dtype='intc'))
return array(m_a.array())
except TypeError:
return m.gather(arange(m.size(), dtype='intc'))
else:
raise TypeError, 'Unknown parameter type %s.' % str(type(m))
def set_local_from_global(m, m_global_array):
"""
Sets the local values of the distrbuted object m to the values contained
in the global array m_global_array.
"""
# This had to be changed, because the dolfin-adjoint constant.Constant is
# different from the constant of dolfin.
if type(m) == Constant:
if m.rank() == 0:
m.assign(m_global_array[0])
else:
m.assign(Constant(tuple(m_global_array)))
elif type(m) in (function.Function, functions.function.Function):
begin, end = m.vector().local_range()
m_a_local = m_global_array[begin:end]
m.vector().set_local(m_a_local)
m.vector().apply('insert')
else:
raise TypeError, 'Unknown parameter type'
def I(c_array, *args):
"""
Solve forward model with given control, calculate objective function
"""
n = len(c_array) / len(config['adjoint']['control_variable'])
for ii, c in enumerate(config['adjoint']['control_variable']):
set_local_from_global(c, c_array[ii * n:(ii + 1) * n])
self.forward_model.solve()
I = assemble(
self.adjoint_instance.I) #FIXME: ISMIP_HOM inverse C fails
return I
def J(c_array, *args):
"""
Solve adjoint model, calculate gradient
"""
# dolfin.adjoint method:
n = len(c_array) / len(config['adjoint']['control_variable'])
for ii, c in enumerate(config['adjoint']['control_variable']):
set_local_from_global(c, c_array[ii * n:(ii + 1) * n])
self.adjoint_instance.solve()
# This is not the best place for this, but we leave it here for now
# so that we can see the impact of every line search update on the
# variables of interest.
Js = []
for JJ in self.adjoint_instance.J:
Js.extend(get_global(assemble(JJ)))
Js = array(Js)
# FIXME: project and extrude ruin the output for paraview, we just
# save when finished for now.
U = project(as_vector([model.u, model.v, model.w]))
dSdt = project(- (model.u*model.S.dx(0) + model.v*model.S.dx(1)) \
+ model.w + model.adot)
file_b_pvd << model.extrude(model.beta2, 3, 2)
file_u_pvd << U
file_dSdt_pvd << dSdt
return Js
#===========================================================================
# Set up file I/O
path = config['output_path']
file_b_pvd = File(path + 'beta2.pvd')
file_u_pvd = File(path + 'U.pvd')
file_dSdt_pvd = File(path + 'dSdt.pvd')
# Switching over to the parallel version of the optimization that is found
# in the dolfin-adjoint optimize.py file:
maxfun = config['adjoint']['max_fun']
bounds_list = config['adjoint']['bounds']
beta_0 = []
for mm in config['adjoint']['control_variable']:
beta_0.extend(get_global(mm))
beta_0 = array(beta_0)
# Shut up all processors but the first one.
if MPI.rank(mpi_comm_world()) != 0:
iprint = -1
else:
iprint = 1
b = []
# convert bounds to an array of tuples and serialize it in parallel environ.
for bounds in bounds_list:
bounds_arr = []
for i in range(2):
if type(bounds[i]) == int or type(bounds[i]) == float:
bounds_arr.append(bounds[i] *
ones(model.beta2.vector().size()))
else:
bounds_arr.append(get_global(bounds[i]))
b.append(array(bounds_arr).T)
bounds = vstack(b)
print bounds
# minimize I with initial guess beta_0 and gradient J :
mopt, f, d = fmin_l_bfgs_b(I,
beta_0,
fprime=J,
bounds=bounds,
maxfun=maxfun,
iprint=iprint)
n = len(mopt) / len(config['adjoint']['control_variable'])
for ii, c in enumerate(config['adjoint']['control_variable']):
set_local_from_global(c, mopt[ii * n:(ii + 1) * n])
# apply constant Dirichlet boundary condition at bottom edge
# apply Dirichlet boundary condition on coupling interface
bcs = [
DirichletBC(V, coupling_expression, coupling_boundary),
DirichletBC(V, u_D, bottom_boundary)
]
a, L = lhs(F), rhs(F)
# Time-stepping
u_np1 = Function(V)
t = 0
u_D.t = t + dt
# mark mesh w.r.t ranks
ranks = File("output/ranks%s.pvd.pvd" % precice.get_participant_name())
mesh_rank = MeshFunction("size_t", mesh, mesh.topology().dim())
mesh_rank.set_all(MPI.rank(MPI.comm_world))
mesh_rank.rename("myRank", "")
ranks << mesh_rank
# Create output file
file_out = File("output/%s.pvd" % precice.get_participant_name())
file_out << u_n
print("output vtk for time = {}".format(float(t)))
n = 0
fluxes = Function(V_g)
fluxes.rename("Fluxes", "")
def solve(self):
"""
Solve the problem using a Picard iteration, evaluating the velocity,
enthalpy, surface mass balance, temperature boundary condition, and
the age equation. Turn off any solver by editing the appropriate config
dict entry to "False". If config['coupled']['on'] is "False", solve only
once.
"""
model = self.model
config = self.config
T0 = config['velocity']['T0']
outpath = config['output_path']
# Set the initial Picard iteration (PI) parameters
# L_\infty norm in velocity between iterations
inner_error = inf
# number of iterations
counter = 0
# previous velocity for norm calculation
u_prev = project(model.u, model.Q).vector().array()
# set an inner tolerance for PI
inner_tol = config['coupled']['inner_tol']
max_iter = config['coupled']['max_iter']
# Initialize a temperature field for visc. calc.
if config['velocity']['use_T0']:
model.T.vector().set_local(T0 *
ones(len(model.T.vector().array())))
if not config['coupled']['on']: max_iter = 1
# Perform a Picard iteration until the L_\infty norm of the velocity
# difference is less than tolerance
while inner_error > inner_tol and counter < max_iter:
# Solve surface mass balance and temperature boundary condition
if config['surface_climate']['on']:
self.surface_climate_instance.solve()
# Solve velocity
if config['velocity']['on']:
self.velocity_instance.solve()
U = project(as_vector([model.u, model.v, model.w]))
if config['log']:
File(outpath + 'U.pvd') << U
# if the velocity solve is full-stokes, save pressure too :
if config['velocity']['approximation'] == 'stokes':
File(outpath + 'P.pvd') << model.P
print_min_max(U, 'U')
# Solve enthalpy (temperature, water content)
if config['enthalpy']['on']:
self.enthalpy_instance.solve()
if config['log']:
File(outpath + 'T.pvd') << model.T # save temperature
File(outpath + 'Mb.pvd') << model.Mb # save melt rate
File(outpath + 'W.pvd') << model.W # save water content
print_min_max(model.T, 'T')
# Calculate L_infinity norm
if config['coupled']['on']:
u_new = project(model.u, model.Q).vector().array()
diff = (u_prev - u_new)
inner_error = diff.max()
u_prev = u_new
counter += 1
print 'Picard iteration %i (max %i) done: r = %.3e (tol %.3e)' \
% (counter, max_iter, inner_error, inner_tol)
# Solve age equation
if config['age']['on']:
self.age_instance.solve()
if config['log']:
File(outpath + 'age.pvd') << model.age # save age
def solve_flem(model_space, physical_space, flow, u_n, mesh, V, bc, dt,
num_steps, out_time, plot, statistics, name):
"""
Solve for landscape evolution
This function does hte hard work. First the model domain is created. Then we loop through time and solve the
diffusion equation to solve for landscape evolution. Output can be saved as vtk files at every "out_time" specified.
Plots using fenics inbuilt library can be visualised at every "plot_time"
This function returns a 1d numpy array of time, sediment flux and if statistics is turned on a 2d numpy array of
the final wavelength of the landscape.
:param model_space: list of domain variables, [lx,ly,res]
:param physical_space: list of physical parameters, [kappa, c, nexp, alpha, U]
:param flow: 0 = MFD node-to-node; 1 = MFD cell-to-cell; 2 = SD node-to-node; 3 = SD cell-to-cell
:param u_n: elevation function
:param mesh: dolphyn mesh
:param V: fenics functionspace
:param bc: boundary conditions
:param dt: time step size in years
:param num_steps: number of time steps
:param out_time: time steps to output vtk files (0=none)
:param plot: plot sediment flux (0=off,1=on)
:param statistics: output statistics of landscape (0=off,1=on)
:param name: directory name for output vtk files
:return: sed_flux, time, wavelength
"""
# Domain dimensions
lx = model_space[0]
ly = model_space[1]
# Physical parameters
kappa = physical_space[0] # diffusion coefficient
c = physical_space[1] # discharge transport coefficient
nexp = physical_space[2] # discharge exponent
alpha = physical_space[3] # precipitation rate
De = c * pow(alpha * ly, nexp) / kappa
uamp = physical_space[4] * ly / kappa # uplift
dt = dt * kappa / (ly * ly) # time step size
sed_flux = np.zeros(num_steps) # array to store sediment flux
time = np.zeros(num_steps)
# Define variational problem
u = TrialFunction(V)
v = TestFunction(V)
f = Constant(uamp)
# 0 = MFD node-to-node; 1 = MFD cell-to-cell; 2 = SD node-to-node; 3 = SD cell-to-cell
if flow == 0:
q_n = mfd_nodenode(mesh, V, u_n, De, nexp)
if flow == 1:
q_n = mfd_cellcell(mesh, V, u_n, De, nexp)
if flow == 2:
q_n = sd_nodenode(mesh, V, u_n, De, nexp)
if flow == 3:
q_n = sd_cellcell(mesh, V, u_n, De, nexp)
F = u * v * dx + dt * q_n * dot(grad(u),
grad(v)) * dx - (u_n + dt * f) * v * dx
a, L = lhs(F), rhs(F)
# Solution and sediment flux
u = Function(V)
q_s = Expression('u0 + displ - u1',
u0=u_n,
displ=Constant(uamp * dt),
u1=u,
degree=2)
# Iterate
t = 0
i = 0
for n in range(num_steps):
# This needs to become an option!
# Double rain fall
# if n == 501:
# alpha = 2
# De = c*pow(alpha*ly,nexp)/kappa
# Update current time
t += dt
# Compute solution
solve(a == L, u, bc)
# Calculate sediment flux
sed_flux[i] = assemble(q_s * dx(mesh))
time[i] = t
i += 1
# Update previous solution
u_n.assign(u)
# Update flux
# 0 = MFD node-to-node; 1 = MFD cell-to-cell; 2 = SD node-to-node; 3 = SD cell-to-cell
if flow == 0:
q = mfd_nodenode(mesh, V, u_n, De, nexp)
if flow == 1:
q = mfd_cellcell(mesh, V, u_n, De, nexp)
if flow == 2:
q = sd_nodenode(mesh, V, u_n, De, nexp)
if flow == 3:
q = sd_cellcell(mesh, V, u_n, De, nexp)
q_n.assign(q)
# Output solutions
if out_time != 0:
if np.mod(n, out_time) == 0:
filename = '%s/u_solution_%d.pvd' % (name, n)
vtkfile = File(filename)
vtkfile << u
filename = '%s/q_solution_%d.pvd' % (name, n)
vtkfile = File(filename)
vtkfile << q
# Post processing
if plot != 0:
plt.plot(time * 1e-6 * ly * ly / kappa,
sed_flux / dt * kappa,
'k',
linewidth=2)
plt.xlabel('Time (Myr)')
plt.ylabel('Sediment Flux (m^2/yr)')
sedname = '%s/sed_flux_%d.svg' % (name, model_space[2])
plt.savefig(sedname, format='svg')
plt.clf()
if out_time != 0:
# Output last elevation
filename = '%s/u_solution_%d_%d.pvd' % (name, model_space[2], n)
vtkfile = File(filename)
u.rename("elv", "elevation")
vtkfile << u
# Output last water flux
filename = '%s/q_solution_%d_%d.pvd' % (name, model_space[2], n)
vtkfile = File(filename)
q.rename("flx", "flux")
vtkfile << q
# Calculate valley spacing from peak to peak in water flux
tol = 0.001 # avoid hitting points outside the domain
y = np.linspace(0 + tol, 1 - tol, 100)
x = np.linspace(0.01, lx / ly - 0.01, 20)
wavelength = np.zeros(len(x))
if statistics != 0:
i = 0
for ix in x:
points = [(ix, y_) for y_ in y] # 2D points
q_line = np.array([q(point) for point in points])
indexes = peakutils.indexes(q_line, thres=0.05, min_dist=5)
if len(indexes) > 1:
wavelength[i] = sum(np.diff(y[indexes])) / (len(indexes) - 1)
else:
wavelength[i] = 0
i += 1
if plot != 0:
plt.plot(y * 1e-3 * ly, q_line * kappa / ly, 'k', linewidth=2)
plt.plot(y[indexes] * 1e-3 * ly, q_line[indexes] * kappa / ly,
'+r')
plt.xlabel('Distance (km)')
plt.ylabel('Water Flux (m/yr)')
watername = '%s/water_flux_spacing_%d.svg' % (name, model_space[2])
plt.savefig(watername, format='svg')
plt.clf()
return sed_flux, time, wavelength
# there are two ways to do this: either via the project() method or the interpolate() method;
# projecy() is very popular, but since we have a closed form solution here we want to use interpolate()
# in order to recover the exact solution within machine-error precision
# Define variational problem
u = TrialFunction(V)
v = TestFunction(V)
f = Constant(0)
F = u * v * dx + dt * dot(grad(u), grad(v)) * dx - (u_n + dt * f) * v * dx
# in general, we manually define the bilinear form a(:, :) containing the unknown solution u and
# the right-hand-side term L(:) with known terms, however this might be difficult in complicated expressions,
# therefore we can rely on the following synthax of FEniCS that computes a and L automatically
a, L = lhs(F), rhs(F)
# Create VTK file for saving solution
vtkfile = File('../../outputs/heat_gaussian/solution.pvd')
# !!!DEVELOPER WARNING!!! change the location to save if you need to, but do not pollute the rest of repo
# the the outputs directory is set to be ignored by git, so you won't be able to pull or push any file within!
# this file will keep a ledger of all files generated during execution, which can be later viewed with ParaView
# Time-stepping
u = Function(V)
t = 0
for n in range(num_steps):
t += dt # Update current time
solve(a == L, u, bc) # Compute solution
vtkfile << (u, t) # Save to file
u_n.assign(u)
# this is important as we want to keep track of the previous solution in the backward Euler schema
# notice that we should not assign u_n = u as this would prevent us from considering u_n and u as
if problem is ProblemType.NEUMANN:
# apply Neumann boundary condition on coupling interface, modify weak form correspondingly
F += precice.create_coupling_neumann_boundary_condition(v)
a, L = lhs(F), rhs(F)
# Time-stepping
u_np1 = Function(V)
u_np1.rename("Temperature", "")
t = 0
# reference solution at t=0
u_ref = interpolate(u_D, V)
u_ref.rename("reference", " ")
temperature_out = File("out/%s.pvd" % precice.get_solver_name())
ref_out = File("out/ref%s.pvd" % precice.get_solver_name())
error_out = File("out/error%s.pvd" % precice.get_solver_name())
# output solution and reference solution at t=0, n=0
n = 0
print('output u^%d and u_ref^%d' % (n, n))
temperature_out << u_n
ref_out << u_ref
error_total, error_pointwise = compute_errors(u_n, u_ref, V)
error_out << error_pointwise
# set t_1 = t_0 + dt, this gives u_D^1
u_D.t = t + dt(
0) # call dt(0) to evaluate FEniCS Constant. Todo: is there a better way?
def write_mesh_to_file(self, filename):
# Output mesh
File(filename) << self.new_mesh