def gen_vector(self,v=None):
"""
Generate/initialize a dolfin generic vector to be compatible with the size of dof.
"""
if v is None:
vec = df.Vector(self.mpi_comm,self.dim) # dofs not aligned to function.vector() in parallel
# vec = df.Function(self.V).vector()
vec.zero()
else:
if type(v) in (df.Vector,df.PETScVector):
vec = df.Vector(v)
elif type(v) is np.ndarray:
vec = df.Vector(self.mpi_comm,len(v))
# vec = df.Function(self.V).vector()
# vec[:]=np.array(v)
# import pydevd; pydevd.settrace()
dofmap = self.V.dofmap()
dof_first, dof_last = dofmap.ownership_range()
unowned = dofmap.local_to_global_unowned()
dofs = filter(lambda dof: dofmap.local_to_global_index(dof) not in unowned, range(dof_first,dof_last))
vec.set_local(v[list(dofs)]); #vec.apply('insert')
else:
df.warning('Unknown type.')
vec=None
return vec
def filter_values(values, operator):
"""
Remove inf's and nan's, and apply operator to each value in
values. Return sorted array of nonzero values, and the number
of zeroes.
"""
values = array(values)
# Remove infs and nans
upper_bound = ascot_parameters["inf"]
values = values[where(abs(values) < upper_bound)]
if any(abs(values) > 1.e8):
warning(
"Some eigenvalues are larger than 1.e8. Consider checking your inner products!"
)
# Replace small (possibly negative numbers) by zero!
is_nonzero = abs(values) >= ascot_parameters["eps"]
zeros = values[abs(values) < ascot_parameters["eps"]]
values = values[where(is_nonzero)]
# Apply operator (sqrt) if indicated
values = array(list(map(operator, values)))
# Sort values
values.sort()
return values, sum(is_nonzero == False)
def collapse(x):
"""Compute an explicit matrix representation of an operator. For example,
given a block_ mul object M=A*B, collapse(M) performs the actual matrix
multiplication.
"""
# Since _collapse works recursively, this method is a user-visible wrapper
# to print timing, and to check input/output arguments.
from time import time
from dolfin import EpetraMatrix, info, warning
T = time()
res = _collapse(x)
if getattr(res, 'transposed', False):
# transposed matrices will normally be converted to a non-transposed
# one by matrix multiplication or addition, but if the transpose is the
# outermost operation then this doesn't work.
warning('Transposed matrix returned from collapse() -- this matrix can be used for multiplications, '
+ 'but not (for example) as input to ML. Try to convert from (A*B)^T to B^T*A^T in your call.')
from block.block_compose import block_transpose
return block_transpose(EpetraMatrix(res.M))
info('computed explicit matrix representation %s in %.2f s'%(str(res),time()-T))
result = EpetraMatrix(res.M)
# Sanity check. Cannot trust EpetraExt.Multiply always, it seems.
from block import block_vec
v = x.create_vec()
block_vec([v]).randomize()
xv = x*v
err = (xv-result*v).norm('l2')/(xv).norm('l2')
if (err > 1e-3):
raise RuntimeError('collapse computed wrong result; ||(a-a\')x||/||ax|| = %g'%err)
return result
def update_functional(self, s):
"""
Update the adjoint RHS associated with the functional at the end of timestep
s.
"""
if not isinstance(s, int) or s < 0:
raise InvalidArgumentException("s must be a non-negative integer")
if not isinstance(self.__functional, TimeFunctional):
return
a_rhs = OrderedDict()
for f_dep in self.__functional.dependencies(s):
if is_static_coefficient(f_dep):
pass
elif isinstance(f_dep, dolfin.Function):
a_x = self.__a_map[f_dep]
a_rhs[a_x] = self.__functional.derivative(f_dep, s)
elif isinstance(f_dep, dolfin.Constant):
pass
else:
raise DependencyException("Invalid dependency")
self.__a_L_rhs = [None for i in xrange(len(self.__a_x))]
for a_x in a_rhs:
if not a_x in self.__a_keys:
dolfin.warning("Missing functional dependency %s" % a_x.name())
else:
self.__a_L_rhs[self.__a_keys[a_x]] = a_rhs[a_x]
return
def update_functional(self, s):
"""
Update the adjoint RHS associated with the functional at the end of timestep
s.
"""
if not isinstance(s, int) or s < 0:
raise InvalidArgumentException("s must be a non-negative integer")
if not isinstance(self.__functional, TimeFunctional):
return
a_rhs = OrderedDict()
for f_dep in self.__functional.dependencies(s):
if is_static_coefficient(f_dep):
pass
elif isinstance(f_dep, dolfin.Function):
a_x = self.__a_map[f_dep]
a_rhs[a_x] = self.__functional.derivative(f_dep, s)
elif isinstance(f_dep, dolfin.Constant):
pass
else:
raise DependencyException("Invalid dependency")
self.__a_L_rhs = [None for i in range(len(self.__a_x))]
for a_x in a_rhs:
if not a_x in self.__a_keys:
dolfin.warning("Missing functional dependency %s" % a_x.name())
else:
self.__a_L_rhs[self.__a_keys[a_x]] = a_rhs[a_x]
return
def _as_petscmat(self):
if df.has_petsc4py():
from petsc4py import PETSc
mat = PETSc.Mat().createPython(df.as_backend_type(self.prior.M).mat().getSizes(), comm = self.prior.mpi_comm)
# mat = PETSc.Mat().createPython(self.dim, comm = self.prior.mpi_comm)
mat.setPythonContext(self)
return df.PETScMatrix(mat)
else:
df.warning('Petsc4py not installed: cannot generate PETScMatrix with specified size!')
pass
def copy(obj):
"""Return a deep copy of the object"""
if hasattr(obj, 'copy'):
return obj.copy()
else:
import copy
try:
return copy.deepcopy(obj)
except TypeError:
from dolfin import warning
warning(
"Don't know how to make a deep copy of (%d,%d), making shallow copy"
% (i, j))
return copy.copy(obj)
def matvec(self, b):
from time import time
from block.block_vec import block_vec
from dolfin import log, info, Progress
TRACE = 13 # dolfin.TRACE
T = time()
# If x and initial_guess are block_vecs, some of the blocks may be
# scalars (although they are normally converted to vectors by bc
# application). To be sure, call allocate() on them.
if isinstance(b, block_vec):
# Create a shallow copy to call allocate() on, to avoid changing the caller's copy of b
b = block_vec(len(b), b.blocks)
b.allocate(self.A, dim=0)
if self.initial_guess:
# Most (all?) solvers modify x, so make a copy to avoid changing
# the caller's copy of x
from block.block_util import copy
x = copy(self.initial_guess)
if isinstance(x, block_vec):
x.allocate(self.A, dim=1)
else:
x = self.A.create_vec(dim=1)
x.zero()
try:
log(TRACE, self.__class__.__name__+' solve of '+str(self.A))
if self.B != 1.0:
log(TRACE, 'Using preconditioner: '+str(self.B))
progress = Progress(self.name, self.maxiter)
if self.tolerance < 0:
tolerance = -self.tolerance
relative = True
else:
tolerance = self.tolerance
relative = False
x = self.method(self.B, self.AR, x, b, tolerance=tolerance,
relativeconv=self.relativeconv, maxiter=self.maxiter,
progress=progress, callback=self.callback,
**self.kwargs)
del progress # trigger final printout
except Exception, e:
from dolfin import warning
warning("Error solving " + self.name)
raise
def timestep_range(T, dt):
"""Return a matching time step range for given end time and time
step. Note that the time step may be adjusted so that it matches
the given end time."""
# Compute range
ds = dt
n = ceil(T / dt)
t_range = linspace(0, T, n + 1)[1:]
dt = t_range[0]
# Warn about changing time step
if ds != dt:
warning("Changing time step from %g to %g" % (ds, dt))
return dt, t_range
def timestep_range(T, dt):
"""Return a matching time step range for given end time and time
step. Note that the time step may be adjusted so that it matches
the given end time."""
# Compute range
ds = dt
n = ceil(T / dt)
t_range = linspace(0, T, n + 1)[1:]
dt = t_range[0]
# Warn about changing time step
if ds != dt:
warning("Changing time step from %g to %g" % (ds, dt))
return dt, t_range
def gen_vector(self, v=None):
"""
Generate/initialize a dolfin generic vector to be compatible with the size of dof.
"""
if v is None:
vec = df.Vector(self.mpi_comm, self.dim)
vec.zero()
else:
if type(v) is df.Vector:
vec = df.Vector(v)
elif type(v) is np.ndarray:
vec = df.Vector(self.mpi_comm, len(v))
vec[:] = np.array(v)
else:
df.warning('Unknown type.')
vec = None
return vec
def XDMFTempSeries(path, V, first=0, last=None):
'''
Read in the temp series of functions in V from XDMF file. If V is not
a function space then a finite element has to be provided for constructing
the space on the recovered mesh.
'''
# NOTE: in 2017.2.0 fenics only stores vertex values so CG1 functions
# is what we go for
_, ext = os.path.splitext(path)
assert ext == '.xdmf'
tree = ET.parse(path)
domain = list(tree.getroot())[0]
grid = list(domain)[0]
times = [] # Only collect time stamps so that we access in right order
h5_file = '' # Consistency of piece as VisualisationVector ...
for item in grid:
_, __, time, attrib = list(item)
time = time.attrib['Value']
times.append(time)
piece = list(attrib)[0]
h5_file_, fdata = piece.text.split(':/')
assert not h5_file or h5_file == h5_file_
h5_file = h5_file_
times = times[slice(first, last, None)]
# We read visualization vector from this
h5_file = os.path.join(os.path.dirname(os.path.abspath(path)), h5_file)
if not isinstance(V, FunctionSpace):
warning('Setting up P1 space on the recovered mesh')
cell_type = V.cell() # Dangerously assuming this is a UFL element
mesh = read_h5_mesh(h5_file, cell_type)
V = FunctionSpace(mesh, V)
V = get_P1_space(V)
functions = read_h5_function(h5_file, times, V)
ft_pairs = zip(functions, map(float, times))
return TempSeries(ft_pairs)
def rand_aux(self, cov='I'):
"""
Generate random vector: _v ~ N(0,_K), _K = I + Nu_r * (D_r-I_r) * Nu_r'
"""
noise = dl.Vector()
self.model.prior.init_vector(noise, "noise")
hp.random.Random.normal(noise, 1., True)
_v = self.model.model_stat.generate_vector(hp.PARAMETER)
_v_help = dl.Vector(_v)
self.model.whtprior.sample(noise, _v_help)
if cov is 'I':
_v[:] = _v_help
elif cov is 'K':
self.rtK(_v_help, _v)
else:
dl.warning('Wrong covariance specification!')
pass
return _v
def apply(self, a):
# Manual application of bcs
if isinstance(a, dolfin.Matrix):
A = a
# Modif A: zero bc row & set diagonal to 1
A.ident_local(self.dof_set)
A.apply("insert")
elif isinstance(a, dolfin.GenericVector):
b = a
# Modif b: entry in the bc row is taken from bc_f
bc_values = self.bc_f.vector().array()
b_values = b.array()
b_values[self.dof_set] = bc_values[self.dof_set]
b.set_local(b_values)
b.apply("insert")
else:
dolfin.warning("Could not apply Point BC.")
def test_stability(forms, inner_products, spaces, bcs=None):
"""
Test Babuska-Brezzi stability for a variational problem specified
by (a set of) forms, inner products and a discretization spaces
parameterized over a mesh family.
"""
if ascot_parameters["check_continuity"]:
info("Checking continuity of form")
continuous = test_continuity(forms, inner_products, spaces)
if not continuous.is_stable():
warning(
"The form does not seems to be bounded!. Check your inner products!"
)
if is_saddle_point(forms):
return _test_brezzi_stability(forms, inner_products, spaces, bcs)
return _test_babuska_stability(forms, inner_products, spaces, bcs)
def compute_signs(self, AA, bb):
self.signs = [None]*len(self)
bb.allocate(AA, dim=0)
for i in range(len(self)):
if not self[i]:
# No BC on this block, sign doesn't matter
continue
if numpy.isscalar(AA[i,i]):
xAx = AA[i,i]
else:
# Do not use a constant vector, as that may be in the null space
# before boundary conditions are applied
x = AA[i,i].create_vec(dim=1)
ran = numpy.random.random(x.local_size())
x.set_local(ran)
Ax = AA[i,i]*x
xAx = x.inner(Ax)
if xAx == 0:
from dolfin import warning
warning("block_bc: zero or semi-definite block (%d,%d), using sign +1"%(i,i))
self.signs[i] = -1 if xAx < 0 else 1
dolfin.info('Calculated signs of diagonal blocks:' + str(self.signs))
def PVDTempSeries(path, V=None, first=0, last=None):
'''
Read in the temp series of functions in V from PVD file. If V is not
a function space then a finite element has to be provided for constructing
the space on the recovered mesh.
'''
_, ext = os.path.splitext(path)
assert ext == '.pvd'
tree = ET.parse(path)
collection = list(tree.getroot())[0]
path = os.path.dirname(os.path.abspath(path))
# Read in paths/timestamps for VTUs. NOTE: as thus is supposed to be serial
# assert part 0
vtus, times = [], []
for dataset in collection:
assert dataset.attrib['part'] == '0'
vtus.append(os.path.join(path, dataset.attrib['file']))
times.append(float(dataset.attrib['timestep']))
vtus, times = vtus[slice(first, last,
None)], times[slice(first, last, None)]
# path.vtu -> function. But vertex values!!!!
if not isinstance(V, FunctionSpace):
warning('Setting up P1 space on the recovered mesh')
cell_type = V.cell() # Dangerously assuming this is a UFL element
mesh = read_vtu_mesh(vtus[0], cell_type)
V = FunctionSpace(mesh, V)
V = get_P1_space(V)
functions = read_vtu_function(vtus, V)
ft_pairs = zip(functions, times)
return TempSeries(ft_pairs)
def compute_signs(self, AA, bb):
self.signs = [None] * len(self)
bb.allocate(AA, dim=0)
for i in range(len(self)):
if not self[i]:
# No BC on this block, sign doesn't matter
continue
if numpy.isscalar(AA[i, i]):
xAx = AA[i, i]
else:
# Do not use a constant vector, as that may be in the null space
# before boundary conditions are applied
x = AA[i, i].create_vec(dim=1)
ran = numpy.random.random(x.local_size())
x.set_local(ran)
Ax = AA[i, i] * x
xAx = x.inner(Ax)
if xAx == 0:
from dolfin import warning
warning(
"block_bc: zero or semi-definite block (%d,%d), using sign +1"
% (i, i))
self.signs[i] = -1 if xAx < 0 else 1
dolfin.info('Calculated signs of diagonal blocks:' + str(self.signs))
def dolfin_to_carpfile(mesh, basename, markers=None, \
vert_fields=None, cell_fields=None):
"""
NOT DEBUGGED:
Write carp mesh and fields to file from dolfin data
mesh : dolfin.Mesh
The dolfin.mesh which should be written to file
basename : str
Basename of file which all data will be written to
markers : dict (optional)
A dict of name to markers of facet booundaries contained in the mesh
vert_fields : dict (optional)
A dict between named vertex field data and dolfin Functions
cell_fields : dict (optional)
A dict between named cell field data and dolfin Functions
"""
import dolfin as d
import numpy as np
boundary = d.CompiledSubDomain("on_boundary")
d.warning("This function is not tested...")
boundary_facets = d.FacetFunction("size_t", mesh, 0)
boundary.mark(boundary_facets, 1)
num_boundary_facets = np.sum(boundary_facets.array() == 1)
with open(basename + ".pts", "w") as f:
f.write("{0}\n".format(mesh.num_vertices()))
[f.write("{0:.10f} {1:.10f} {2:.10f}\n".format(*coord)) \
for coord in mesh.coordinates()]
with open(basename + ".elem", "w") as f:
f.write("{0}\n".format(mesh.num_cells()))
[f.write("Tt {0} {1} {2} {3} 0\n".format(*cell)) \
for cell in mesh.cells()]
with open(basename + ".surf", "w") as f:
f.write("{0}\n".format(num_boundary_facets))
[f.write("Tr {0} {1} {2}\n".format(*facet.entities(0))) \
for facet in d.SubsetIterator(boundary_facets, 1)]
# If generating mapping between vertices and boundaries
if markers:
# Get the facet markers
facet_markers = mesh.domains().facet_domains(mesh)
# Iterate over markers
for boundary_name, marker in markers.items():
vertices = set()
for face in SubsetIterator(facet_markers, marker):
vertices.update(face.entities(0))
with open(basename + "_" + boundary_name + ".vtx", "w") as f:
f.write("{0:d}\nintra \n".format(int(len(vertices))))
[f.write("{0}\n".format(vert)) for vert in vertices]
# Apex node...
#with open(basename+"_apex.vtx", "w") as f:
# f.write("{0:d}\nintra \n".format(1))
# f.write("{0:d}\n".format((apex_point.array()==1).nonzero()[0][0]))
# If outputing vertex fields
if vert_fields:
# Get dof mapping
dofs_to_vert, vectordofs_to_vert, vectordofs_to_subvert = \
dofs_to_verts(mesh)
# Iterate over the passed fields
for field_name, func in vert_fields.items():
values = func.vector().array()
# If scalar field
if mesh.num_vertices() == len(dofs):
reordered_values = values[dofs_to_vert]
# Write the field to file
with open(basename + "_" + field_name + ".dat", "w") as f:
[
f.write("{0:.10f}\n".format(value))
for value in reordered_values
]
# If vector field
elif mesh.num_vertices() == 3 * len(dofs):
raise NotImplementedError
else:
raise ValueError("Field and mesh do not match: " + field_name)
from collections import namedtuple
import numpy as np
import dolfin as df
try:
import mshr
except ImportError:
df.warning('mshr is not installed')
geometry = namedtuple("geometry", "mesh, ffun, markers")
if df.__version__.startswith('20'):
# Year based versioning
DOLFIN_VERSION_MAJOR = float(df.__version__.split('.')[0])
else:
DOLFIN_VERSION_MAJOR = float('.'.join(df.__version__.split('.')[:2]))
def mpi_comm_world():
if DOLFIN_VERSION_MAJOR >= 2018:
return df.MPI.comm_world
else:
return df.mpi_comm_world()
def value_size(obj):
if DOLFIN_VERSION_MAJOR >= 2018:
value_shape = obj.value_shape()
if len(value_shape) == 0:
return 1
else:
return [0]
else:
return obj.value_size()
def solve(self):
"""
Solve the equation
"""
x, pre_assembly_parameters = self.x(), self.pre_assembly_parameters()
if not self.__initial_guess is None and not self.__initial_guess is x:
x.assign(self.__initial_guess)
if self.is_linear():
bcs, linear_solver = self.bcs(), self.linear_solver()
if isinstance(self.__a, dolfin.GenericMatrix):
L = assemble(self.__L, copy = len(bcs) > 0)
enforce_bcs(L, bcs)
linear_solver.solve(x.vector(), L)
elif self.__a.rank() == 2:
a = assemble(self.__a, copy = len(bcs) > 0)
L = assemble(self.__L, copy = len(bcs) > 0)
apply_bcs(a, bcs, L = L, symmetric_bcs = pre_assembly_parameters["equations"]["symmetric_boundary_conditions"])
linear_solver.set_operator(a)
linear_solver.solve(x.vector(), L)
else:
assert(self.__a.rank() == 1)
assert(linear_solver is None)
a = assemble(self.__a, copy = False)
L = assemble(self.__L, copy = False)
assert(L.local_range() == a.local_range())
x.vector().set_local(L.array() / a.array())
x.vector().apply("insert")
enforce_bcs(x.vector(), bcs)
elif self.solver_parameters().get("nonlinear_solver", "newton") == "newton":
# Newton solver, intended to have near identical behaviour to the Newton
# solver supplied with DOLFIN. See
# http://fenicsproject.org/documentation/tutorial/nonlinear.html for
# further details.
default_parameters = dolfin.NewtonSolver.default_parameters()
solver_parameters = self.solver_parameters()
if "newton_solver" in solver_parameters:
parameters = solver_parameters["newton_solver"]
else:
parameters = {}
linear_solver = self.linear_solver()
atol = default_parameters["absolute_tolerance"]
rtol = default_parameters["relative_tolerance"]
max_its = default_parameters["maximum_iterations"]
omega = default_parameters["relaxation_parameter"]
err = default_parameters["error_on_nonconvergence"]
r_def = default_parameters["convergence_criterion"]
for key in parameters.keys():
if key == "absolute_tolerance":
atol = parameters[key]
elif key == "convergence_criterion":
r_def = parameters[key]
elif key == "error_on_nonconvergence":
err = parameters[key]
elif key == "maximum_iterations":
max_its = parameters[key]
elif key == "relative_tolerance":
rtol = parameters[key]
elif key == "relaxation_parameter":
omega = parameters[key]
elif key in ["linear_solver", "preconditioner", "lu_solver", "krylov_solver"]:
pass
elif key in ["method", "report"]:
raise NotImplementedException("Unsupported Newton solver parameter: %s" % key)
else:
raise ParameterException("Unexpected Newton solver parameter: %s" % key)
eq, bcs, hbcs = self.eq(), self.bcs(), self.hbcs()
a, L = self.__a, self.__L
x_name = x.name()
x = x.vector()
enforce_bcs(x, bcs)
dx = self.__dx
if not isinstance(linear_solver, dolfin.GenericLUSolver):
dx.zero()
if r_def == "residual":
l_L = assemble(L, copy = len(hbcs) > 0)
enforce_bcs(l_L, hbcs)
r_0 = l_L.norm("l2")
it = 0
if r_0 >= atol:
l_a = assemble(a, copy = len(hbcs) > 0)
apply_bcs(l_a, hbcs, symmetric_bcs = pre_assembly_parameters["equations"]["symmetric_boundary_conditions"])
linear_solver.set_operator(l_a)
linear_solver.solve(dx, l_L)
x.axpy(omega, dx)
it += 1
atol = max(atol, r_0 * rtol)
while it < max_its:
l_L = assemble(L, copy = len(hbcs) > 0)
enforce_bcs(l_L, hbcs)
r = l_L.norm("l2")
if r < atol:
break
l_a = assemble(a, copy = len(hbcs) > 0)
apply_bcs(l_a, hbcs, symmetric_bcs = pre_assembly_parameters["equations"]["symmetric_boundary_conditions"])
linear_solver.set_operator(l_a)
linear_solver.solve(dx, l_L)
x.axpy(omega, dx)
it += 1
elif r_def == "incremental":
l_a = assemble(a, copy = len(hbcs) > 0)
l_L = assemble(L, copy = len(hbcs) > 0)
apply_bcs(l_a, hbcs, L = l_L, symmetric_bcs = pre_assembly_parameters["equations"]["symmetric_boundary_conditions"])
linear_solver.set_operator(l_a)
linear_solver.solve(dx, l_L)
x.axpy(omega, dx)
it = 1
r_0 = dx.norm("l2")
if r_0 >= atol:
atol = max(atol, rtol * r_0)
while it < max_its:
l_a = assemble(a, copy = len(hbcs) > 0)
l_L = assemble(L, copy = len(hbcs) > 0)
apply_bcs(l_a, hbcs, L = l_L, symmetric_bcs = pre_assembly_parameters["equations"]["symmetric_boundary_conditions"])
linear_solver.set_operator(l_a)
linear_solver.solve(dx, l_L)
x.axpy(omega, dx)
it += 1
if dx.norm("l2") < atol:
break
else:
raise ParameterException("Invalid convergence criterion: %s" % r_def)
if it == max_its:
if err:
raise StateException("Newton solve for %s failed to converge after %i iterations" % (x_name, it))
else:
dolfin.warning("Newton solve for %s failed to converge after %i iterations" % (x_name, it))
# dolfin.info("Newton solve for %s converged after %i iterations" % (x_name, it))
else:
problem = dolfin.NonlinearVariationalProblem(self.eq().lhs - self.eq().rhs, x, bcs = self.bcs(), J = self.J())
nl_solver = dolfin.NonlinearVariationalSolver(problem)
nl_solver.parameters.update(self.solver_parameters())
nl_solver.solve()
return
# This is the most fragile component of the package so be advised that
# these ARE NOT GENERAL PURPOSE READEDERS
from dolfin import Function, dof_to_vertex_map, warning, Mesh, MeshEditor
import xml.etree.ElementTree as ET
from itertools import dropwhile
from mpi4py import MPI
import numpy as np
try:
import h5py
except ImportError:
warning('H5Py missing')
assert MPI.COMM_WORLD.size == 1, 'No parallel (for your own good)'
def data_reordering(V):
'''Reshaping/reordering data read from files'''
# HDF5/VTK store 3d vectors and 3d tensor so we need to chop the data
# also reorder as in 2017.2.0 only(?) vertex values are dumped
if V.ufl_element().value_shape() == ():
dof2v = dof_to_vertex_map(V)
reorder = lambda a: a[dof2v]
return reorder
Vi = V.sub(0).collapse()
dof2v = dof_to_vertex_map(Vi)
from collections import namedtuple
import numpy as np
import dolfin as df
try:
import mshr
except ImportError:
df.warning("mshr is not installed")
geometry = namedtuple("geometry", "mesh, ffun, markers")
if df.__version__.startswith("20"):
# Year based versioning
DOLFIN_VERSION_MAJOR = float(df.__version__.split(".")[0])
else:
try:
DOLFIN_VERSION_MAJOR = float(".".join(df.__version__.split(".")[:2]))
except:
DOLFIN_VERSION_MAJOR = 1.6
def mpi_comm_world():
if DOLFIN_VERSION_MAJOR >= 2018:
return df.MPI.comm_world
else:
return df.mpi_comm_world()
def value_size(obj):
if DOLFIN_VERSION_MAJOR >= 2018:
value_shape = obj.value_shape()
def trace_mat_no_restrict(V, TV, trace_mesh=None, tag_data=None):
'''The first cell connected to the facet gets to set the values of TV'''
mesh = V.mesh()
if trace_mesh is None: trace_mesh = TV.mesh()
fdim = trace_mesh.topology().dim()
# None means all
if tag_data is None:
tag_data = (MeshFunction('size_t', trace_mesh,
trace_mesh.topology().dim(), 0), set((0, )))
trace_mesh_subdomains, tags = tag_data
# Init/extract the mapping
try:
assert get_entity_map(mesh, trace_mesh, trace_mesh_subdomains, tags)
except (AssertionError, IndexError):
warning('Using non-conforming trace')
# So non-conforming matrix returns PETSc.Mat
return nonconforming_trace_mat(V, TV)
# We can get it
mapping = trace_mesh.parent_entity_map[mesh.id()][
fdim] # Map cell of TV to cells of V
mesh.init(fdim, fdim + 1)
f2c = mesh.topology()(fdim, fdim + 1) # Facets of V to cell of V
# The idea is to evaluate TV's degrees of freedom at basis functions
# of V
Tdmap = TV.dofmap()
TV_dof = DegreeOfFreedom(TV)
dmap = V.dofmap()
V_basis_f = FEBasisFunction(V)
# Only look at tagged cells
trace_cells = itertools.chain(*[
itertools.imap(operator.methodcaller('index'),
SubsetIterator(trace_mesh_subdomains, tag))
for tag in tags
])
# Rows
visited_dofs = [False] * TV.dim()
# Column values
dof_values = np.zeros(V_basis_f.elm.space_dimension(), dtype='double')
with petsc_serial_matrix(TV, V) as mat:
for trace_cell in trace_cells:
# We might
TV_dof.cell = trace_cell
trace_dofs = Tdmap.cell_dofs(trace_cell)
# Figure out the dofs of V to use here. Does not matter which
# cell of the connected ones we pick
cell = f2c(mapping[trace_cell])[0]
V_basis_f.cell = cell
dofs = dmap.cell_dofs(cell)
for local_T, dof_T in enumerate(trace_dofs):
if visited_dofs[dof_T]:
continue
else:
visited_dofs[dof_T] = True
# Define trace dof
TV_dof.dof = local_T
# Eval at V basis functions
for local, dof in enumerate(dofs):
# Set which basis foo
V_basis_f.dof = local
dof_values[local] = TV_dof.eval(V_basis_f)
# Can fill the matrix now
col_indices = np.array(dofs, dtype='int32')
# Insert
mat.setValues([dof_T], col_indices, dof_values,
PETSc.InsertMode.INSERT_VALUES)
return mat
import dolfin
import ffc
import instant
import numpy
import types
import ufl
from .embedded_cpp import *
from .versions import *
__all__ = []
# Only versions 1.5.x and 1.6.x have been tested.
if dolfin_version() < (1, 5, 0) or dolfin_version() >= (1, 7, 0):
dolfin.warning("DOLFIN version %s not supported" % dolfin.__version__)
if ufl_version() < (1, 5, 0) or ufl_version() >= (1, 7, 0):
dolfin.warning("UFL version %s not supported" % ufl.__version__)
if ffc_version() < (1, 5, 0) or ffc_version() >= (1, 7, 0):
dolfin.warning("FFC version %s not supported" % ffc.__version__)
if instant_version() < (1, 5, 0) or instant_version() >= (1, 7, 0):
dolfin.warning("Instant version %s not supported" % instant.__version__)
# DOLFIN patches.
if dolfin_version() < (1, 1, 0):
__all__ += \
[
"GenericLinearSolver",
"GenericLUSolver",
"FacetFunction",
"MeshFunction",
def expand_expr(expr):
"""
Recursively expand the supplied Expr into the largest possible Sum.
"""
if not isinstance(expr, ufl.expr.Expr):
raise InvalidArgumentException("expr must be an Expr")
if isinstance(expr, ufl.algebra.Sum):
terms = []
for term in expr.operands():
terms += expand_expr(term)
return terms
elif isinstance(expr, ufl.algebra.Product):
ops = expr.operands()
fact1 = ops[0]
fact2 = ops[1]
for op in ops[2:]:
fact2 *= op
fact1_terms = expand_expr(fact1)
fact2_terms = expand_expr(fact2)
terms = []
for term1 in fact1_terms:
for term2 in fact2_terms:
terms.append(term1 * term2)
return terms
elif isinstance(expr, ufl.indexed.Indexed):
ops = expr.operands()
assert(len(ops) == 2)
return [ufl.indexed.Indexed(term, ops[1]) for term in expand_expr(ops[0])]
elif isinstance(expr, ufl.tensors.ComponentTensor):
ops = expr.operands()
assert(len(ops) == 2)
return [ufl.tensors.ComponentTensor(term, ops[1]) for term in expand_expr(ops[0])]
elif isinstance(expr, ufl.algebra.Division):
ops = expr.operands()
assert(len(ops) == 2)
return [ufl.algebra.Division(term, ops[1]) for term in expand_expr(ops[0])]
elif isinstance(expr, ufl.restriction.PositiveRestricted):
ops = expr.operands()
assert(len(ops) == 1)
return [ufl.restriction.PositiveRestricted(term) for term in expand_expr(ops[0])]
elif isinstance(expr, ufl.restriction.NegativeRestricted):
ops = expr.operands()
assert(len(ops) == 1)
return [ufl.restriction.NegativeRestricted(term) for term in expand_expr(ops[0])]
elif isinstance(expr, ufl.differentiation.Grad):
ops = expr.operands()
assert(len(ops) == 1)
return [ufl.differentiation.Grad(term) for term in expand_expr(ops[0])]
elif isinstance(expr, (ufl.tensoralgebra.Dot,
ufl.tensoralgebra.Inner,
ufl.differentiation.CoefficientDerivative,
ufl.differentiation.VariableDerivative)):
return expand_expr(expand(expr))
# Expr types white-list. These cannot be expanded.
elif isinstance(expr, (ufl.constantvalue.ConstantValue,
ufl.argument.Argument,
dolfin.Expression,
dolfin.Function,
dolfin.Constant,
ufl.geometry.Circumradius,
ufl.algebra.Abs,
ufl.geometry.FacetNormal,
ufl.mathfunctions.Sqrt,
ufl.classes.Variable,
ufl.mathfunctions.Exp,
ufl.algebra.Power,
ufl.indexing.MultiIndex,
ufl.classes.Label)):
return [expr]
# Expr types grey-list. It might be possible to expand these, but just ignore
# them at present.
elif isinstance(expr, (ufl.tensors.ListTensor,
ufl.classes.Conditional,
ufl.indexsum.IndexSum)):
return [expr]
else:
dolfin.warning("Expr type %s not expanded by expand_expr" % expr.__class__)
return [expr]
def nonconforming_trace_mat(V, T):
'''
Matrix taking function f from d dim space V to g in (d-1) space T.
T(f) ~ g should hold.
'''
# For this to work I only make sure that function values are the same
assert V.dolfin_element().value_rank() == T.dolfin_element().value_rank()
assert V.ufl_element().value_shape() == T.ufl_element().value_shape()
# I want to evaluate T degrees of freedom at V basis functions, i.e.
# L^T_k{phi^V_l}. The picture is
#
# ------
# \ /\
# ===\==/==\====T
# \/----\
#
# and thus is assume that each dof of T space (row) will involve
# collisions with several cells/basis function of V space
mesh = V.mesh() # The (d-1)trace mesh
tree = mesh.bounding_box_tree()
limit = mesh.topology().size_global(mesh.topology().dim())
Tdm = T.dofmap()
elm_T = T.element()
# Colliding cells with trace dofs
collisions = []
for Tdof_x in T.tabulate_dof_coordinates().reshape((T.dim(), -1)):
cs = tree.compute_entity_collisions(Point(*Tdof_x))
if any(c >= limit for c in cs):
warning('Some colliding cells not found')
cs = filter(lambda c: c < limit, cs)
collisions.append(cs)
# So we fill rows by checking basis functions of on the isected cells
Vdm = V.dofmap()
elm_V = V.element()
V_basis_function = FEBasisFunction(V)
T_degree_of_freedom = DegreeOfFreedom(T)
visited_dofs = [False]*T.dim()
with petsc_serial_matrix(T, V) as mat:
for Tcell in range(T.mesh().num_cells()):
# Set for this cell
T_degree_of_freedom.cell = Tcell
Tdofs = Tdm.cell_dofs(Tcell)
for local_T, Tdof in enumerate(Tdofs):
# Seen the row?
if visited_dofs[Tdof]: continue
visited_dofs[Tdof] = True
# Set to current dof
T_degree_of_freedom.dof = local_T
col_indices, col_values = [], []
# Now all the V cells and their basis functions
for c in collisions[Tdof]:
# Set the dof cell
V_basis_function.cell = c
Vdofs = Vdm.cell_dofs(c)
# Columns
for local_V, Vdof in enumerate(Vdofs):
if Vdof in col_indices:
continue
# Set as basis_function
V_basis_function.dof = local_V
# Evaluate trace dof at basis function
dof_value = T_degree_of_freedom.eval(V_basis_function)
col_indices.append(Vdof)
col_values.append(dof_value)
# Can fill the matrix row
col_indices = np.array(col_indices, dtype='int32')
col_values = np.array(col_values)
mat.setValues([Tdof], col_indices, col_values, PETSc.InsertMode.INSERT_VALUES)
return mat
import dolfin
import ffc
import instant
import numpy
import types
import ufl
from embedded_cpp import *
from versions import *
__all__ = []
# Only versions 1.2.x and 1.3.x have been tested.
if dolfin_version() < (1, 2, 0) or dolfin_version() >= (1, 5, 0):
dolfin.warning("DOLFIN version %s not supported" % dolfin.__version__)
if ufl_version() < (1, 2, 0) or ufl_version() >= (1, 5, 0):
dolfin.warning("UFL version %s not supported" % ufl.__version__)
if ffc_version() < (1, 2, 0) or ffc_version() >= (1, 5, 0):
dolfin.warning("FFC version %s not supported" % ffc.__version__)
if instant_version() < (1, 2, 0) or instant_version() >= (1, 5, 0):
dolfin.warning("Instant version %s not supported" % instant.__version__)
# DOLFIN patches.
if dolfin_version() < (1, 1, 0):
__all__ += \
[
"GenericLinearSolver",
"GenericLUSolver",
"FacetFunction",
"MeshFunction",
def nonconforming_trace_mat(V, T):
'''
Matrix taking function f from d dim space V to g in (d-1) space T.
T(f) ~ g should hold.
'''
# For this to work I only make sure that function values are the same
assert V.ufl_element().value_shape() == T.ufl_element().value_shape()
# I want to evaluate T degrees of freedom at V basis functions, i.e.
# L^T_k{phi^V_l}. The picture is
#
# ------
# \ /\
# ===\==/==\====T
# \/----\
#
# and thus is assume that each dof of T space (row) will involve
# collisions with several cells/basis function of V space. However
# here we only snap to the first one
mesh = V.mesh() # The (d-1)trace mesh
tree = mesh.bounding_box_tree()
limit = mesh.num_entities_global(mesh.topology().dim())
Tdm = T.dofmap()
elm_T = T.element()
# Colliding cells with trace dofs
collisions = []
for Tdof_x in T.tabulate_dof_coordinates().reshape((T.dim(), -1)):
c = tree.compute_first_entity_collision(df.Point(*Tdof_x))
# Contained?
c >= limit and df.warning('Some colliding cells not found')
collisions.append(c)
# So we fill rows by checking basis functions of on the isected cells
Vdm = V.dofmap()
elm_V = V.element()
V_basis_function = FEBasisFunction(V)
T_degree_of_freedom = DegreeOfFreedom(T)
X_T = T.tabulate_dof_coordinates().reshape((T.dim(), -1))
X_V = V.tabulate_dof_coordinates().reshape((V.dim(), -1))
visited_dofs = np.zeros(T.dim(), dtype=bool)
col_values = np.zeros(V_basis_function.elm.space_dimension(),
dtype='double')
with petsc_serial_matrix(T, V) as mat:
for Tcell in range(T.mesh().num_cells()):
# Set for this cell
T_degree_of_freedom.cell = Tcell
Tdofs = Tdm.cell_dofs(Tcell)
for local_T, Tdof in enumerate(Tdofs):
# Seen the row?
if visited_dofs[Tdof]: continue
visited_dofs[Tdof] = True
# Set to current dof
T_degree_of_freedom.dof = local_T
# Now all the V cells and their basis functions
c = collisions[Tdof]
# If we have no reasonable cell leave the row empty
if c >= limit: continue
# Set the dof cell
V_basis_function.cell = c
Vdofs = np.array(Vdm.cell_dofs(c),
dtype='int32') # These are columns
# Fill column
for local_V, Vdof in enumerate(Vdofs):
# Set as basis_function
V_basis_function.dof = local_V
# Evaluate trace dof at basis function
dof_value = T_degree_of_freedom.eval(V_basis_function)
col_values[local_V] = dof_value
mat.setValues([Tdof], Vdofs, col_values,
PETSc.InsertMode.INSERT_VALUES)
return mat
def cbc_warning(msg):
"Raise warning on master process."
if on_master_process():
warning(msg)
def expand_expr(expr):
"""
Recursively expand the supplied Expr into the largest possible Sum.
"""
if not isinstance(expr, ufl.core.expr.Expr):
raise InvalidArgumentException("expr must be an Expr")
if isinstance(expr, ufl.algebra.Sum):
terms = []
for term in expr.operands():
terms += expand_expr(term)
return terms
elif isinstance(expr, ufl.algebra.Product):
ops = expr.operands()
fact1 = ops[0]
fact2 = ops[1]
for op in ops[2:]:
fact2 *= op
fact1_terms = expand_expr(fact1)
fact2_terms = expand_expr(fact2)
terms = []
for term1 in fact1_terms:
for term2 in fact2_terms:
terms.append(term1 * term2)
return terms
elif isinstance(expr, ufl.indexed.Indexed):
ops = expr.operands()
assert(len(ops) == 2)
return [ufl.indexed.Indexed(term, ops[1]) for term in expand_expr(ops[0])]
elif isinstance(expr, ufl.tensors.ComponentTensor):
ops = expr.operands()
assert(len(ops) == 2)
return [ufl.tensors.ComponentTensor(term, ops[1]) for term in expand_expr(ops[0])]
elif isinstance(expr, ufl.algebra.Division):
ops = expr.operands()
assert(len(ops) == 2)
return [ufl.algebra.Division(term, ops[1]) for term in expand_expr(ops[0])]
elif isinstance(expr, ufl.restriction.PositiveRestricted):
ops = expr.operands()
assert(len(ops) == 1)
return [ufl.restriction.PositiveRestricted(term) for term in expand_expr(ops[0])]
elif isinstance(expr, ufl.restriction.NegativeRestricted):
ops = expr.operands()
assert(len(ops) == 1)
return [ufl.restriction.NegativeRestricted(term) for term in expand_expr(ops[0])]
elif isinstance(expr, ufl.differentiation.Grad):
ops = expr.operands()
assert(len(ops) == 1)
return [ufl.differentiation.Grad(term) for term in expand_expr(ops[0])]
elif isinstance(expr, (ufl.tensoralgebra.Dot,
ufl.tensoralgebra.Inner,
ufl.differentiation.CoefficientDerivative,
ufl.differentiation.VariableDerivative)):
return expand_expr(expand(expr))
# Expr types white-list. These cannot be expanded.
elif isinstance(expr, (ufl.constantvalue.ConstantValue,
ufl.argument.Argument,
dolfin.Expression,
dolfin.Function,
dolfin.Constant,
ufl.geometry.Circumradius,
ufl.algebra.Abs,
ufl.geometry.FacetNormal,
ufl.mathfunctions.Sqrt,
ufl.classes.Variable,
ufl.mathfunctions.Exp,
ufl.algebra.Power,
ufl.indexing.MultiIndex,
ufl.classes.Label)):
return [expr]
# Expr types grey-list. It might be possible to expand these, but just ignore
# them at present.
elif isinstance(expr, (ufl.tensors.ListTensor,
ufl.classes.Conditional,
ufl.indexsum.IndexSum)):
return [expr]
else:
dolfin.warning("Expr type %s not expanded by expand_expr" % expr.__class__)
return [expr]
def trace_mat_no_restrict(V, TV, trace_mesh=None):
'''The first cell connected to the facet gets to set the values of TV'''
mesh = V.mesh()
if trace_mesh is None: trace_mesh = TV.mesh()
fdim = trace_mesh.topology().dim()
# Init/extract the mapping
try:
assert get_entity_map(mesh, trace_mesh)
except AssertionError:
warning('Using non-conforming trace')
return nonconforming_trace_mat(V, TV)
# We can get it
mapping = trace_mesh.parent_entity_map[mesh.id()][fdim] # Map cell of TV to cells of V
mesh.init(fdim, fdim+1)
f2c = mesh.topology()(fdim, fdim+1) # Facets of V to cell of V
# The idea is to evaluate TV's degrees of freedom at basis functions
# of V
Tdmap = TV.dofmap()
TV_dof = DegreeOfFreedom(TV)
dmap = V.dofmap()
V_basis_f = FEBasisFunction(V)
# Rows
visited_dofs = [False]*TV.dim()
# Column values
dof_values = np.zeros(V_basis_f.elm.space_dimension(), dtype='double')
with petsc_serial_matrix(TV, V) as mat:
for trace_cell in range(TV.mesh().num_cells()):
TV_dof.cell = trace_cell
trace_dofs = Tdmap.cell_dofs(trace_cell)
# Figure out the dofs of V to use here. Does not matter which
# cell of the connected ones we pick
cell = f2c(mapping[trace_cell])[0]
V_basis_f.cell = cell
dofs = dmap.cell_dofs(cell)
for local_T, dof_T in enumerate(trace_dofs):
if visited_dofs[dof_T]:
continue
else:
visited_dofs[dof_T] = True
# Define trace dof
TV_dof.dof = local_T
# Eval at V basis functions
for local, dof in enumerate(dofs):
# Set which basis foo
V_basis_f.dof = local
dof_values[local] = TV_dof.eval(V_basis_f)
# Can fill the matrix now
col_indices = np.array(dofs, dtype='int32')
# Insert
mat.setValues([dof_T], col_indices, dof_values, PETSc.InsertMode.INSERT_VALUES)
return mat
def matvec(self, b):
from time import time
from block.block_vec import block_vec
from dolfin import info, Progress
from ffc.log import log
TRACE = 13 # dolfin.TRACE
T = time()
# If x and initial_guess are block_vecs, some of the blocks may be
# scalars (although they are normally converted to vectors by bc
# application). To be sure, call allocate() on them.
if isinstance(b, block_vec):
# Create a shallow copy to call allocate() on, to avoid changing the caller's copy of b
b = block_vec(len(b), b.blocks)
b.allocate(self.A, dim=0)
if self.initial_guess:
# Most (all?) solvers modify x, so make a copy to avoid changing
# the caller's copy of x
from block.block_util import copy
x = copy(self.initial_guess)
if isinstance(x, block_vec):
x.allocate(self.A, dim=1)
else:
x = self.A.create_vec(dim=1)
x.zero()
try:
log(TRACE, self.__class__.__name__ + ' solve of ' + str(self.A))
if self.B != 1.0:
log(TRACE, 'Using preconditioner: ' + str(self.B))
progress = Progress(self.name, self.maxiter)
if self.tolerance < 0:
tolerance = -self.tolerance
relative = True
else:
tolerance = self.tolerance
relative = False
x = self.method(self.B,
self.AR,
x,
b,
tolerance=tolerance,
relativeconv=self.relativeconv,
maxiter=self.maxiter,
progress=progress,
callback=self.callback,
**self.kwargs)
del progress # trigger final printout
except Exception as e:
from dolfin import warning
warning("Error solving " + self.name)
raise
x, self.residuals, self.alphas, self.betas = x
if self.tolerance == 0:
msg = "done"
elif self.converged:
msg = "converged"
else:
msg = "NOT CONV."
if self.show == 1:
info('%s %s [iter=%2d, time=%.2fs, res=%.1e]' \
% (self.name, msg, self.iterations, time()-T, self.residuals[-1]))
elif self.show >= 2:
info('%s %s [iter=%2d, time=%.2fs, res=%.1e, true res=%.1e]' \
% (self.name, msg, self.iterations, time()-T, self.residuals[-1], (self.A*x-b).norm('l2')))
if self.show == 3:
from dolfin import MPI
if MPI.rank(None) == 0:
try:
from matplotlib import pyplot
pyplot.figure('%s convergence (show=3)' % self.name)
pyplot.semilogy(self.residuals)
pyplot.show(block=True)
except:
pass
if self.R is not None:
x = self.R * x
if self.retain_guess:
self.initial_guess = x
if not self.converged and self.nonconvergence_is_fatal:
raise RuntimeError('Not converged')
return x
def trace_mat_no_restrict(V, TV, trace_mesh=None):
'''The first cell connected to the facet gets to set the values of TV'''
mesh = V.mesh()
if trace_mesh is None: trace_mesh = TV.mesh()
fdim = trace_mesh.topology().dim()
# Init/extract the mapping
try:
assert get_entity_map(mesh, trace_mesh)
except AssertionError:
warning('Using non-conforming trace')
return nonconforming_trace_mat(V, TV)
# We can get it
mapping = trace_mesh.parent_entity_map[mesh.id()][
fdim] # Map cell of TV to cells of V
mesh.init(fdim, fdim + 1)
f2c = mesh.topology()(fdim, fdim + 1) # Facets of V to cell of V
# The idea is to evaluate TV's degrees of freedom at basis functions
# of V
Tdmap = TV.dofmap()
TV_dof = DegreeOfFreedom(TV)
dmap = V.dofmap()
V_basis_f = FEBasisFunction(V)
# Rows
visited_dofs = [False] * TV.dim()
# Column values
dof_values = np.zeros(V_basis_f.elm.space_dimension(), dtype='double')
with petsc_serial_matrix(TV, V) as mat:
for trace_cell in range(TV.mesh().num_cells()):
TV_dof.cell = trace_cell
trace_dofs = Tdmap.cell_dofs(trace_cell)
# Figure out the dofs of V to use here. Does not matter which
# cell of the connected ones we pick
cell = f2c(mapping[trace_cell])[0]
V_basis_f.cell = cell
dofs = dmap.cell_dofs(cell)
for local_T, dof_T in enumerate(trace_dofs):
if visited_dofs[dof_T]:
continue
else:
visited_dofs[dof_T] = True
# Define trace dof
TV_dof.dof = local_T
# Eval at V basis functions
for local, dof in enumerate(dofs):
# Set which basis foo
V_basis_f.dof = local
dof_values[local] = TV_dof.eval(V_basis_f)
# Can fill the matrix now
col_indices = np.array(dofs, dtype='int32')
# Insert
mat.setValues([dof_T], col_indices, dof_values,
PETSc.InsertMode.INSERT_VALUES)
return mat
def test_stokes_noflow(gamma, Re, nu_interp, postprocessor):
#set_log_level(WARNING)
basename = postprocessor.basename
label = "{}_{}_gamma_{}_Re_{:.0e}".format(basename, nu_interp, gamma, Re)
c = postprocessor.get_coefficients()
c[r"\nu_1"] = c[r"\rho_1"] / Re
c[r"\nu_2"] = c[r"r_visc"] * c[r"\nu_1"]
c[r"\nu_1"] /= c[r"\rho_0"] * c[r"V_0"] * c[r"L_0"]
c[r"\nu_2"] /= c[r"\rho_0"] * c[r"V_0"] * c[r"L_0"]
cc = wrap_coeffs_as_constants(c)
nu = eval("nu_" + nu_interp) # choose viscosity interpolation
for level in range(1, 4):
mesh, boundary_markers, pinpoint, periodic_bnd = create_domain(level)
periodic_bnd = None
W = create_mixed_space(mesh, periodic_boundary=periodic_bnd)
bcs = create_bcs(W,
boundary_markers,
periodic_boundary=periodic_bnd,
pinpoint=pinpoint)
phi = create_fixed_vfract(mesh, c)
# Create forms
a, L = create_forms(W, rho(phi, cc), nu(phi, cc), c[r"g_a"],
boundary_markers, gamma)
# Solve problem
w = df.Function(W)
A, b = df.assemble_system(a, L, bcs)
solver = df.LUSolver("mumps")
df.PETScOptions.set("fieldsplit_u_mat_mumps_icntl_14", 500)
solver.set_operator(A)
try:
solver.solve(w.vector(), b)
except:
df.warning("Ooops! Something went wrong: {}".format(
sys.exc_info()[0]))
continue
# Pre-process results
v, p = w.split(True)
v.rename("v", "velocity")
p.rename("p", "pressure")
V_dv = df.FunctionSpace(mesh, "DG",
W.sub(0).ufl_element().degree() - 1)
div_v = df.project(df.div(v), V_dv)
div_v.rename("div_v", "velocity-divergence")
D_22 = df.project(v.sub(1).dx(1), V_dv)
p_h = create_hydrostatic_pressure(mesh, cc)
#p_ref = df.project(p_h, W.sub(1).ufl_element())
p_ref = df.project(
p_h,
df.FunctionSpace(mesh, df.FiniteElement("CG", mesh.ufl_cell(), 4)))
v_errL2, v_errH10, div_errL2, p_errL2 = compute_errornorms(
v, div_v, p, p_ref)
if nu_interp[:2] == "PW":
V_nu = df.FunctionSpace(mesh, "DG", phi.ufl_element().degree())
else:
V_nu = phi.function_space()
nu_0 = df.project(nu(phi, cc), V_nu)
T_22 = df.project(2.0 * nu(phi, cc) * v.sub(1).dx(1), V_nu)
# Save results
make_cut = postprocessor._make_cut
rs = dict(ndofs=W.dim(),
level=level,
h=mesh.hmin(),
r_dens=c[r"r_dens"],
r_visc=c[r"r_visc"],
gamma=gamma,
Re=Re,
nu_interp=nu_interp)
rs[r"$v_2$"] = make_cut(v.sub(1))
rs[r"$p$"] = make_cut(p)
rs[r"$\phi$"] = make_cut(phi)
rs[r"$D_{22}$"] = make_cut(D_22)
rs[r"$T_{22}$"] = make_cut(T_22)
rs[r"$\nu$"] = make_cut(nu_0)
rs[r"$||\mathbf{v} - \mathbf{v}_h||_{L^2}$"] = v_errL2
rs[r"$||\nabla (\mathbf{v} - \mathbf{v}_h)||_{L^2}$"] = v_errH10
rs[r"$||\mathrm{div} \mathbf{v}_h||_{L^2}$"] = div_errL2
rs[r"$||\mathbf{p} - \mathbf{p}_h||_{L^2}$"] = p_errL2
print(label, level)
# Send to posprocessor
comm = mesh.mpi_comm()
rank = df.MPI.rank(comm)
postprocessor.add_result(rank, rs)
# Plot results obtained in the last round
outdir = os.path.join(postprocessor.outdir, "XDMFoutput")
with df.XDMFFile(os.path.join(outdir, "v.xdmf")) as file:
file.write(v, 0.0)
with df.XDMFFile(os.path.join(outdir, "p.xdmf")) as file:
file.write(p, 0.0)
with df.XDMFFile(os.path.join(outdir, "phi.xdmf")) as file:
file.write(phi, 0.0)
with df.XDMFFile(os.path.join(outdir, "div_v.xdmf")) as file:
file.write(div_v, 0.0)
# Save results into a binary file
filename = "results_{}.pickle".format(label)
postprocessor.save_results(filename)
# Flush plots as we now have data for all level values
postprocessor.pop_items(["level", "h"])
postprocessor.flush_plots()
# Cleanup
df.set_log_level(df.INFO)
gc.collect()
def trace_mat_no_restrict(V, TV, trace_mesh=None, tag_data=None):
'''The first cell connected to the facet gets to set the values of TV'''
mesh = V.mesh()
if trace_mesh is None: trace_mesh = TV.mesh()
fdim = trace_mesh.topology().dim()
# None means all
if tag_data is None:
try:
marking_function = trace_mesh.marking_function
tag_data = (marking_function, set(marking_function.array()))
except AttributeError:
tag_data = (MeshFunction('size_t', trace_mesh,
trace_mesh.topology().dim(), 0), set(
(0, )))
trace_mesh_subdomains, tags = tag_data
# Init/extract the mapping
try:
assert get_entity_map(mesh, trace_mesh, trace_mesh_subdomains, tags)
except (AssertionError, IndexError):
warning('Using non-conforming trace')
# So non-conforming matrix returns PETSc.Mat
return nonconforming_trace_mat(V, TV)
if V.ufl_element().family() == 'HDiv Trace':
assert V.ufl_element().degree() == 0
# In this case
return DLT_trace_mat(V, TV, trace_mesh=trace_mesh, tag_data=tag_data)
# We can get it
mapping = trace_mesh.parent_entity_map[mesh.id()][
fdim] # Map cell of TV to cells of V
mesh.init(fdim, fdim + 1)
f2c = mesh.topology()(fdim, fdim + 1) # Facets of V to cell of V
# The idea is to evaluate TV's degrees of freedom at basis functions of V
Tdmap = TV.dofmap()
TV_dof = DegreeOfFreedom(TV)
dmap = V.dofmap()
V_basis_f = FEBasisFunction(V)
# Only look at tagged cells
trace_cells = list(
itertools.chain(*[
map(operator.methodcaller('index'),
SubsetIterator(trace_mesh_subdomains, tag)) for tag in tags
]))
ndofs_elm, nbasis_elm = TV_dof.elm.space_dimension(
), V_basis_f.elm.space_dimension()
local_values = np.zeros((nbasis_elm, ndofs_elm))
if len(trace_cells) > 10_000:
print(f'Trace mat {TV.ufl_element()} -> {V.ufl_element()}')
trace_cells = tqdm.tqdm(trace_cells, total=len(trace_cells))
rows, cols, values = [], [], []
# DG spaces don't share rows between cells so we take advantage of
# this in special branch
if TV.ufl_element().family() == 'Discontinuous Lagrange':
for trace_cell in trace_cells:
TV_dof.cell = trace_cell
# Many rows at once
trace_dofs = Tdmap.cell_dofs(trace_cell)
# Figure out the dofs of V to use here. Does not matter which
# cell of the connected ones we pick
cell = f2c(mapping[trace_cell])[0]
V_basis_f.cell = cell
# Columns for the rows
dofs = dmap.cell_dofs(cell)
for local, dof in enumerate(dofs):
# Set which basis foo
V_basis_f.dof = local
# Get all rows at once
local_values[local][:] = TV_dof.eval_dofs(V_basis_f)
# Indices for the filled piece
rows_ = np.tile(trace_dofs, nbasis_elm)
cols_ = np.repeat(dofs, ndofs_elm)
rows.extend(rows_)
cols.extend(cols_)
values.extend(local_values.flat)
# FIXME: Othewise we need to take care of duplicate entrieselse:
else:
needs_fill = np.ones(TV.dim(), dtype=bool)
for trace_cell in trace_cells:
TV_dof.cell = trace_cell
# Many rows at once
trace_dofs = Tdmap.cell_dofs(trace_cell)
# Don't add duplicates
unseen = needs_fill[trace_dofs] # Some will be true and
# For the future
needs_fill[trace_dofs[unseen]] = False
# Figure out the dofs of V to use here. Does not matter which
# cell of the connected ones we pick
cell = f2c(mapping[trace_cell])[0]
V_basis_f.cell = cell
# Columns for the rows
dofs = dmap.cell_dofs(cell)
for local, dof in enumerate(dofs):
# Set which basis foo
V_basis_f.dof = local
# Get all rows at once
local_values[local][:] = TV_dof.eval_dofs(V_basis_f)
# Indices for the filled piece
rows_ = np.tile(trace_dofs[unseen], nbasis_elm)
cols_ = np.repeat(dofs, sum(unseen))
rows.extend(rows_)
cols.extend(cols_)
values.extend(local_values[:, unseen].flat)
mat = csr_matrix((values, (rows, cols)), shape=(TV.dim(), V.dim()))
return PETSc.Mat().createAIJ(comm=PETSc.COMM_WORLD,
size=mat.shape,
csr=(mat.indptr, mat.indices, mat.data))