def store_mesh(self,
mesh: dolfin.Mesh,
cell_domains: dolfin.MeshFunction = None,
facet_domains: dolfin.MeshFunction = None) -> None:
"""Save the mesh, and cellfunction and facet function if provided."""
with dolfin.XDMFFile(mesh.mpi_comm(),
str(self._casedir / "mesh.xdmf")) as meshfile:
meshfile.write(mesh)
# if cell_domains is not None:
# meshfile.write(cell_domains, "cell_domains")
# if facet_domains is not None:
# meshfile.write(facet_domains, "facet_domains")
if cell_domains is not None:
with df.XDMFFile(mesh.mpi_comm(),
str(self._casedir /
"cell_function.xdmf")) as cf_file:
cf_file.write(mesh)
cf_file.write(cell_domains)
if facet_domains is not None:
with df.XDMFFile(mesh.mpi_comm(),
str(self._casedir /
"facet_function.xdmf")) as ff_file:
ff_file.write(mesh)
ff_file.write(facet_domains)
def readmesh(mesh_file):
''' read HDF5 or DOLFIN XML mesh '''
# TODO: exceptions, files exist?
from dolfin import Mesh, MeshFunction, CellFunction, HDF5File, \
FacetFunction
tmp = mesh_file.split('/')[-1].split('.')
mesh_type = tmp[-1]
mesh_name = '.'.join(tmp[0:-1])
if mesh_type == 'xml':
mesh = Mesh(mesh_file)
rank = mesh.mpi_comm().Get_rank()
try:
subdomains = MeshFunction("size_t", mesh,
mesh_name+"_physical_region.xml")
except:
if rank == 0:
print('no subdomain file found (%s)' %
(mesh_name+"_physical_region.xml"))
subdomains = CellFunction("size_t", mesh)
try:
boundaries = MeshFunction("size_t", mesh,
mesh_name+"_facet_region.xml")
except:
if rank == 0:
print('no boundary file found (%s)' %
(mesh_name+"_physical_region.xml"))
boundaries = FacetFunction("size_t", mesh)
elif mesh_type == 'h5':
mesh = Mesh()
rank = mesh.mpi_comm().Get_rank()
hdf = HDF5File(mesh.mpi_comm(), mesh_file, "r")
hdf.read(mesh, "/mesh", False)
subdomains = CellFunction("size_t", mesh)
boundaries = FacetFunction("size_t", mesh)
if hdf.has_dataset('subdomains'):
hdf.read(subdomains, "/subdomains")
else:
if rank == 0:
print('no <subdomains> datasets found in file %s' % mesh_file)
if hdf.has_dataset('boundaries'):
hdf.read(boundaries, "/boundaries")
else:
if rank == 0:
print('no <boundaries> datasets found in file %s' % mesh_file)
elif mesh_type in ['xdmf', 'xmf']:
import sys
sys.exit('XDMF not supported yet. Use HDF5 instead!')
else:
import sys
sys.exit('mesh format not recognized. try XML (serial) or HDF5')
# NOTE http://fenicsproject.org/qa/5337/importing-marked-mesh-for-parallel-use
# see file xml2xdmf.py
return mesh, subdomains, boundaries
def make_mesh(coordinates, cells, tdim, gdim):
'''Mesh by MeshEditor from vertices and cells'''
mesh = Mesh()
# FEniCS 2017
try:
assert mesh.mpi_comm().tompi4py().size == 1
# FEniCS 2018
except AttributeError:
assert mesh.mpi_comm().size == 1
coordinates.shape = (np.prod(coordinates.shape), )
cells.shape = (np.prod(cells.shape), )
fill_mesh(coordinates, cells, tdim, gdim, mesh)
return mesh
def __init__(self,
mesh: df.Mesh,
time: df.Constant,
M_i: tp.Union[df.Expression, tp.Dict[int, df.Expression]],
I_s: tp.Union[df.Expression, tp.Dict[int,
df.Expression]] = None,
v_: df.Function = None,
cell_domains: df.MeshFunction = None,
facet_domains: df.MeshFunction = None,
parameters: df.Parameters = None) -> None:
super().__init__(mesh,
time,
M_i,
I_s=I_s,
v_=v_,
cell_domains=cell_domains,
facet_domains=facet_domains,
parameters=parameters)
# Create variational forms
self._timestep = df.Constant(self.parameters["default_timestep"])
self._lhs, self._rhs, self._prec = self.variational_forms(
self._timestep)
# Preassemble left-hand side (will be updated if time-step changes)
self._lhs_matrix = df.assemble(self._lhs)
self._rhs_vector = df.Vector(mesh.mpi_comm(), self._lhs_matrix.size(0))
self._lhs_matrix.init_vector(self._rhs_vector, 0)
# Create linear solver (based on parameter choices)
self._linear_solver = self._create_linear_solver()
def convert(msh_file, h5_file):
'''Temporary version of convert from msh to h5'''
root, _ = os.path.splitext(msh_file)
assert os.path.splitext(msh_file)[1] == '.msh'
assert os.path.splitext(h5_file)[1] == '.h5'
# Get the xml mesh
xml_file = '.'.join([root, 'xml'])
subprocess.call(['dolfin-convert %s %s' % (msh_file, xml_file)], shell=True)
# Success?
assert os.path.exists(xml_file)
mesh = Mesh(xml_file)
out = HDF5File(mesh.mpi_comm(), h5_file, 'w')
out.write(mesh, 'mesh')
info('Mesh has %d cells' % mesh.num_cells())
info('Mesh size %g %g' % (mesh.hmin(), mesh.hmax()))
outputs = [mesh]
# Save ALL data as facet_functions
names = ('surfaces', 'volumes')
for name, region in zip(names, ('facet_region.xml', 'physical_region.xml')):
r_xml_file = '_'.join([root, region])
f = MeshFunction('size_t', mesh, r_xml_file)
out.write(f, name)
outputs.append(f)
return outputs
def convert(msh_file):
'''Temporary version of convertin from msh to h5'''
root, _ = os.path.splitext(msh_file)
assert os.path.splitext(msh_file)[1] == '.msh'
# Get the xml mesh
xml_file = '.'.join([root, 'xml'])
# Convert to XML
convert2xml(msh_file, xml_file)
# Success?
assert os.path.exists(xml_file)
mesh = Mesh(xml_file)
h5_file = '.'.join([root, 'h5'])
out = HDF5File(mesh.mpi_comm(), h5_file, 'w')
out.write(mesh, 'mesh')
# Save ALL data as facet_functions
data_sets = ('curves', 'surfaces', 'volumes')
regions = ('curve_region.xml', 'facet_region.xml', 'volume_region.xml')
for data_set, region in zip(data_sets, regions):
r_xml_file = '_'.join([root, region])
if os.path.exists(r_xml_file):
f = MeshFunction('size_t', mesh, r_xml_file)
out.write(f, data_set)
# And clean
os.remove(r_xml_file)
# and clean
os.remove(xml_file)
return h5_file
def convert(msh_file, h5_file):
'''Convert msh file to h5_file'''
root, _ = os.path.splitext(msh_file)
assert os.path.splitext(msh_file)[1] == '.msh'
assert os.path.splitext(h5_file)[1] == '.h5'
# Get the xml mesh
xml_file = '.'.join([root, 'xml'])
subprocess.call(['dolfin-convert %s %s' % (msh_file, xml_file)],
shell=True)
# Success?
assert os.path.exists(xml_file)
mesh = Mesh(xml_file)
out = HDF5File(mesh.mpi_comm(), h5_file, 'w')
out.write(mesh, 'mesh')
for region in ('facet_region.xml', ):
name, _ = region.split('_')
r_xml_file = '_'.join([root, region])
f = MeshFunction('size_t', mesh, r_xml_file)
out.write(f, name)
# Sucess?
assert os.path.exists(h5_file)
return mesh
def load_mesh(filename, subdir="mesh", use_partition_from_file=False):
""" Loads the mesh specified by the argument filename. """
info_cyan("Loading mesh: " + filename)
mesh = Mesh()
h5file = HDF5File(mesh.mpi_comm(), filename, "r")
h5file.read(mesh, subdir, use_partition_from_file)
h5file.close()
return mesh
def make_mesh(coordinates, cells, tdim, gdim):
'''Mesh by MeshEditor from vertices and cells'''
mesh = Mesh()
assert mesh.mpi_comm().tompi4py().size == 1
fill_mesh(coordinates.flatten(), cells.flatten(), tdim, gdim, mesh)
return mesh
def load_mesh(filename):
""" Loads in the mesh specified by the argument filename. """
info_cyan("Loading mesh: " + filename)
mesh = Mesh()
h5file = HDF5File(mesh.mpi_comm(), filename, "r")
h5file.read(mesh, "mesh", False)
h5file.close()
return mesh
def make_mesh(coordinates, cells, tdim, gdim, mesh=None):
'''Mesh by MeshEditor from vertices and cells'''
if mesh is None:
mesh = Mesh()
assert mesh.mpi_comm().size == 1
module.fill_mesh(coordinates.flatten(), cells.flatten(), tdim, gdim, mesh)
return mesh
def make_mesh(coordinates, cells, tdim, gdim, mesh=None):
'''Mesh by MeshEditor from vertices and cells'''
if mesh is None:
mesh = Mesh()
assert mesh.mpi_comm().size == 1
module.fill_mesh(coordinates.flatten(), cells.flatten(), tdim, gdim, mesh)
return mesh
def read_h5(h5Path):
mesh = Mesh()
hdf = HDF5File(mesh.mpi_comm(), h5Path, 'r')
hdf.read(mesh, '/mesh', False)
subdomains = MeshFunction('size_t', mesh, 3)
boundaries = MeshFunction('size_t', mesh, 2)
hdf.read(subdomains, '/subdomains')
hdf.read(boundaries, '/boundaries')
return mesh, subdomains, boundaries
def store_mesh(self,
mesh: dolfin.Mesh,
cell_domains: dolfin.MeshFunction = None,
facet_domains: dolfin.MeshFunction = None) -> None:
"""Save the mesh, and cellfunction and facet function if provided."""
filename = self.casedir / Path("mesh.hdf5")
with dolfin.HDF5File(mesh.mpi_comm(), str(filename), "w") as meshfile:
meshfile.write(mesh, "/Mesh")
if cell_domains is not None:
meshfile.write(cell_domains, "/CellDomains")
if facet_domains is not None:
meshfile.write(facet_domains, "/FacetDomains")
def load_h5_mesh(h5_file, scale_factor=None):
'''Unpack to mesh, volumes and surfaces'''
mesh = Mesh()
h5 = HDF5File(mesh.mpi_comm(), h5_file, 'r')
h5.read(mesh, 'mesh', False)
# Convert units
if scale_factor is not None:
assert scale_factor > 0, "Scale factor must be a positive real number!"
mesh.coordinates()[:] *= scale_factor
surfaces = MeshFunction('size_t', mesh, mesh.topology().dim() - 1)
h5.read(surfaces, 'surfaces')
volumes = MeshFunction('size_t', mesh, mesh.topology().dim())
h5.read(volumes, 'volumes')
return mesh, volumes, surfaces
def as_pvd(h5_file):
'''Store facet and cell function for pvd'''
root, ext = os.path.splitext(h5_file)
mesh = Mesh()
hdf = HDF5File(mesh.mpi_comm(), h5_file, 'r')
hdf.read(mesh, '/mesh', False)
facet_markers = FacetFunction('size_t', mesh)
hdf.read(facet_markers, '/facet_markers')
cell_markers = CellFunction('size_t', mesh)
hdf.read(cell_markers, '/cell_markers')
File(root + 'facets' + '.pvd') << facet_markers
File(root + 'volumes' + '.pvd') << cell_markers
return True
def convert(msh_file, h5_file, save_mvc=False):
'''Temporary version of convertin from msh to h5'''
root, _ = os.path.splitext(msh_file)
assert os.path.splitext(msh_file)[1] == '.msh'
assert os.path.splitext(h5_file)[1] == '.h5'
# Get the xml mesh
xml_file = '.'.join([root, 'xml'])
subprocess.call(['dolfin-convert %s %s' % (msh_file, xml_file)], shell=True)
# Success?
assert os.path.exists(xml_file)
mesh = Mesh(xml_file)
out = HDF5File(mesh.mpi_comm(), h5_file, 'w')
out.write(mesh, 'mesh')
print('Mesh has %d cells' % mesh.num_cells())
print('Mesh size %g %g' % (mesh.hmin(), mesh.hmax()))
# Save ALL data as facet_functions
names = ('surfaces', 'volumes')
if not save_mvc:
for name, region in zip(names, ('facet_region.xml', 'physical_region.xml')):
r_xml_file = '_'.join([root, region])
f = MeshFunction('size_t', mesh, r_xml_file)
print('%d %s with 1' % (sum(1 for _ in SubsetIterator(f, 1)), name))
out.write(f, name)
return True
for name, region in zip(names, ('facet_region.xml', 'physical_region.xml')):
r_xml_file = '_'.join([root, region])
f = MeshFunction('size_t', mesh, r_xml_file)
# With mesh value collection we only store nonzero tags
mvc = MeshValueCollection('size_t', mesh, f.dim())
# Fill
fill_mvc_from_mf(f, mvc)
# And save
out.write(mvc, name)
return True
for (nx, dt, pres, store_step) in zip(nx_list, dt_list, pres_list, storestep_list):
if comm.Get_rank() == 0:
print("Starting computation with grid resolution " + str(nx))
# Compute num steps till completion
num_steps = np.rint(Tend / float(dt))
# Generate mesh
mesh = Mesh("./../../meshes/circle_0.xml")
n = nx
while n > 1:
mesh = refine(mesh)
n /= 2
output_field = XDMFFile(mesh.mpi_comm(), outdir + "psi_h_nx" + str(nx) + ".xdmf")
# Velocity and initial condition
V = VectorFunctionSpace(mesh, "DG", 3)
uh = Function(V)
uh.assign(Expression(("-Uh*x[1]", "Uh*x[0]"), Uh=Uh, degree=3))
psi0_expression = GaussianPulse(
center=(xc, yc), sigma=float(sigma), U=[Uh, Uh], time=0.0, height=1.0, degree=3
)
# Generate particles
x = RandomCircle(Point(x0, y0), r).generate([pres, pres])
s = np.zeros((len(x), 1), dtype=np.float_)
# Initialize particles with position x and scalar property s at the mesh
class FBVP:
def __init__(self, mesh_name, parameters, alpha_range=None):
# LOAD MESH AND PARAMETERS
self.parameters = parameters
self.mesh_name = mesh_name
if not alpha_range:
self.alpha_range = parameters.alpha_range
else:
self.alpha_range = alpha_range
mesh_path = self.parameters.get_mesh_path()
self.mesh = Mesh()
with XDMFFile(mesh_path) as f:
f.read(self.mesh)
print(f'Mesh size= {self.mesh.hmax()}')
# dimension of approximation space
self.dim = len(self.mesh.coordinates())
print(f'Dimension of solution space is {self.dim}')
self.V = FunctionSpace(self.mesh, 'CG', 1) # CG = P1
self.coords = self.mesh.coordinates()[dof_to_vertex_map(self.V)]
self.T = self.parameters.T # final time
self.w = TrialFunction(self.V)
self.u = TestFunction(self.V)
#######################################################################
# CONTROL SET CREATION
self.control_set = np.linspace(self.alpha_range[0],
self.alpha_range[1],
self.parameters.control_set_size)
self.control_set_size = len(self.control_set)
print(f'Discretized control set has size {self.control_set_size}')
#######################################################################
# BOUNDARY CONDITIONS
parameters.set_boundary_conditions(self.mesh)
self.boundary_markers = MeshFunction('size_t', self.mesh, 1)
self.boundary_markers.set_all(4) # pylint: disable=no-member
for i, omega in self.parameters.omegas.items():
omega.mark(self.boundary_markers, i)
self.ds = Measure('ds',
domain=self.mesh,
subdomain_data=self.boundary_markers)
self.dirichlet_bcs = [
DirichletBC(self.V, parameters.RHS_bound[j], self.boundary_markers,
j) for j in self.parameters.regions["Dirichlet"]
]
# Get indices of dirichlet and robin dofs
self.dirichlet_nodes_list = set()
self.dirichlet_nodes_dict = {}
for j in self.parameters.regions["Dirichlet"]:
bc = DirichletBC(self.V, Constant(0), self.boundary_markers, j)
self.dirichlet_nodes_list |= set(bc.get_boundary_values().keys())
self.dirichlet_nodes_dict[j] = list(
bc.get_boundary_values().keys())
self.robin_nodes_list = set()
self.robin_nodes_dict = {}
for j in self.parameters.regions["Robin"]:
bc = DirichletBC(self.V, Constant(0), self.boundary_markers, j)
self.robin_nodes_list |= set(bc.get_boundary_values().keys())
self.robin_nodes_dict[j] = list(bc.get_boundary_values().keys())
bc = DirichletBC(self.V, Constant(0), 'on_boundary')
self.boundary_nodes_list = bc.get_boundary_values().keys()
self.robint_nodes_list = set()
self.robint_nodes_dict = {}
for j in self.parameters.regions["RobinTime"]:
bc = DirichletBC(self.V, Constant(0), self.boundary_markers, j)
self.robint_nodes_list |= set(bc.get_boundary_values().keys())
self.robint_nodes_dict[j] = list(bc.get_boundary_values().keys())
#######################################################################
# ASSEMBLY
time_start = time.process_time()
self.assemble_diagonal_matrix() # auxilliary generic diagonal matrix
# used for vector*matrix multiplication of dolfin matrices
self.assemble_lumpedmm() # lumped mass matrix
# which serves the role of identity operator
self.assemble_laplacian() # discrete laplacian
self.ad_data_path = f'out/{self.parameters.experiment}'
Path(self.ad_data_path).mkdir(parents=True, exist_ok=True)
self.timesteps = self.parameters.get_number_of_timesteps()
self.assemble_HJBe() # assembly of explicit operators
self.assemble_HJBi() # assembly of implicit operators
self.assemble_RHS() # assembly of forcing term
print('Final time assembly complete')
print(f'Assembly took {time.process_time() - time_start} seconds')
print('===========================================================')
def assemble_diagonal_matrix(self):
print("Assembling auxilliary diagonal matrix")
""" Operator assembled to get the right sparameterssity pattern
(non-zero terms can only exist on diagonal)
"""
mesh3 = UnitIntervalMesh(self.dim)
V3 = FunctionSpace(mesh3, "DG", 0)
wid = TrialFunction(V3)
uid = TestFunction(V3)
self.diag_matrix = assemble(uid * wid * dx)
self.diag_matrix.zero()
def assemble_lumpedmm(self):
""" Assembly lumped mass matrix - equal to 0 on robin boundary since
there is no time derivative there.
"""
print("Assembling lumped mass matrix")
mass_form = self.w * self.u * dx
mass_action_form = action(mass_form, Constant(1))
self.MM_terms = assemble(mass_action_form)
for n in self.robint_nodes_list:
self.MM_terms[n] = 1.0
for n in self.robin_nodes_list:
self.MM_terms[n] = 0.0
self.mass_matrix = assemble(mass_form)
self.mass_matrix.zero()
self.mass_matrix.set_diagonal(self.MM_terms)
self.scipy_mass_matrix = toscipy(self.mass_matrix)
def assemble_laplacian(self):
print("Assembling laplacians")
# laplacian discretisation
self.laplacian = assemble(dot(grad(self.w), grad(self.u)) * dx)
def assemble_HJBe(self, t=None):
""" Assembly explicit operator for every control in the control set,
then apply artificial diffusion to all of them. Note that artificial
diffusion is calculated differently on the boundary nodes.
"""
self.explicit_matrices = np.empty(self.control_set_size, dtype=object)
self.explicit_diffusion = np.empty([self.control_set_size, self.dim])
diagonal_vector = Vector(self.mesh.mpi_comm(), self.dim)
global_min_timestep = float('inf')
# Create explicit operator for each control in control set
for k, alpha in enumerate(self.control_set):
if k % 10 == 0:
print(f'Assembling explicit matrix under control {k}'
f' out of {self.control_set_size}')
# coefficients in the interior
advection_x = self.parameters.adv_x(alpha)
advection_y = self.parameters.adv_y(alpha)
reaction = self.parameters.lin(alpha)
if t is not None:
advection_x.t = t
advection_y.t = t
reaction.t = t
# Discretize PDE (set values on boundary rows to zero)
b = np.array([advection_x, advection_y])
E_interior_form = (np.dot(b, grad(self.w)) +
reaction * self.w) * self.u * dx
explicit_matrix = assemble(E_interior_form)
set_zero_rows(explicit_matrix, self.boundary_nodes_list)
# Calculate diffusion necessary to make explicit operator monotone
min_diffusion = np.zeros(explicit_matrix.size(0))
for rows, row_num in getrows(explicit_matrix,
self.laplacian,
ignore=self.boundary_nodes_list):
min_diffusion[row_num] = calc_ad(rows, row_num)
self.explicit_diffusion[k] = min_diffusion
discrete_diffusion = apply_ad(self.laplacian, min_diffusion)
explicit_matrix += discrete_diffusion
for j in self.parameters.regions['RobinTime']:
self.set_directional_derivative(
explicit_matrix,
region=j,
nodes=self.robint_nodes_dict[j],
control=alpha,
time=t)
explicit_matrix.get_diagonal(diagonal_vector)
current_min_timestep = get_min_timestep(
diagonal_vector, self.MM_terms,
self.dirichlet_nodes_list | self.robin_nodes_list)
global_min_timestep = min(current_min_timestep,
global_min_timestep)
self.explicit_matrices[k] = toscipy(explicit_matrix)
#######################################################################
min_timesteps = int(self.T / global_min_timestep) + 1
if not self.timesteps or self.timesteps < min_timesteps:
self.timesteps = min_timesteps
try:
filename = (f'meshes/{self.parameters.domain}/'
f'Mvalues-{self.parameters.experiment}.json')
with open(filename, 'r') as f:
min_timesteps_dict = json.load(f)
except FileNotFoundError:
min_timesteps_dict = {}
min_timesteps_dict[self.parameters.mesh_name] = self.timesteps
with open(filename, 'w') as f:
json.dump(min_timesteps_dict, f)
self.timestep_size = self.T / self.timesteps # time step size
self.parameters.calculate_save_interval()
self.explicit_matrices = self.timestep_size * self.explicit_matrices - \
np.repeat(self.scipy_mass_matrix, self.control_set_size)
print('Checking if the explicit operators satisfy'
' monotonicity conditions')
for explicit_matrix in self.explicit_matrices:
explicit_check(explicit_matrix, self.dirichlet_nodes_list)
def assemble_RHS(self, t=None):
"""Assemble right hand side of the FBVP
"""
print('Assembling RHS')
self.forcing_terms = np.empty([self.control_set_size, self.dim])
for i, alpha in enumerate(self.control_set):
rhs = self.parameters.RHSt(alpha)
if t is not None:
rhs.t = t
# Initialise forcing term
F = np.array(assemble(rhs * self.u * dx)[:])
for j in self.parameters.regions['RobinTime']:
rhs = self.parameters.RHS_bound[j](alpha)
if t is not None:
rhs.t = t
bc = DirichletBC(self.V, rhs, self.boundary_markers, j)
vals = bc.get_boundary_values()
F[list(vals.keys())] = list(vals.values())
for j in self.parameters.regions['Robin']:
rhs = self.parameters.RHS_bound[j](alpha)
if t is not None:
rhs.t = t
bc = DirichletBC(self.V, rhs, self.boundary_markers, j)
vals = bc.get_boundary_values()
F[list(vals.keys())] = list(vals.values())
self.forcing_terms[i] = self.timestep_size * F
def assemble_HJBi(self, t=None):
""" Assembly matrix discretizing second order terms after diffusion
moved to the explicit operator is subtracted. Whenever amount of
diffusion used to make some row of an explicit operator monotonic
exceeds the amount of natural diffusion at that node we call it
artificial diffusion. In such case, this row of the implicit operator
is multiplied by zero
"""
print('Assembling implicit operators')
self.implicit_matrices = []
remaining_diffusion = Function(self.V)
max_art_dif = 0.0
max_art_dif_loc = None
diffusion_matrix = self.diag_matrix.copy()
for explicit_diffusion, alpha in \
zip(self.explicit_diffusion, self.control_set):
diffusion = self.parameters.diffusion(alpha)
if t is not None:
diffusion.t = t
diff = interpolate(diffusion, self.V).vector()
if not np.all(diff >= 0):
raise Exception("Choose non-negative diffusion")
diff_vec = np.array([
diff[i] if i not in self.boundary_nodes_list else 0.0
for i in range(self.dim)
])
artificial_diffusion = explicit_diffusion - diff_vec
if np.amax(artificial_diffusion) > max_art_dif:
max_art_dif = np.amax(artificial_diffusion)
max_art_dif_loc = self.coords[np.argmax(artificial_diffusion)]
# discretise second order terms
remaining_diffusion.vector()[:] = np.maximum(
-artificial_diffusion, [0] * self.dim)
diffusion_matrix.set_diagonal(remaining_diffusion.vector())
implicit_matrix = matmult(diffusion_matrix, self.laplacian)
for j in self.parameters.regions['Robin']:
self.set_directional_derivative(implicit_matrix,
region=j,
nodes=self.robin_nodes_dict[j],
control=alpha,
time=t)
self.implicit_matrices.append(self.timestep_size *
implicit_matrix + self.mass_matrix)
self.scipy_implicit_matrices = [
toscipy(mat) for mat in self.implicit_matrices
]
print('Checking if the implicit operators satisfy'
' monotonicity conditions')
for implicit_matrix in self.scipy_implicit_matrices:
implicit_check(implicit_matrix)
with open(self.ad_data_path + '/ad.txt', 'a') as f:
time_str = f' at time {t}\n' if t is not None else '\n'
f.write(f'For mesh {self.mesh_name} max value of artificial'
' diffusion coefficient was'
f' {max_art_dif} at {max_art_dif_loc}' + time_str)
def set_directional_derivative(self,
operator,
region,
nodes,
control,
time=None):
if region in self.parameters.regions['Robin']:
adv_x = self.parameters.robin_adv_x[region](control)
adv_y = self.parameters.robin_adv_y[region](control)
lin = self.parameters.robin_lin[region](control)
elif region in self.parameters.regions['RobinTime']:
adv_x = self.parameters.robint_adv_x[region](control)
adv_y = self.parameters.robint_adv_y[region](control)
lin = self.parameters.robint_lin[region](control)
if time is not None:
adv_x.t = time
adv_y.t = time
lin.t = time
b = (interpolate(adv_x, self.V), interpolate(adv_y, self.V))
c = interpolate(lin, self.V)
for n in nodes:
# node coordinates
x = self.coords[n]
# evaluate advection at robin node
b_x = np.array([b[0].vector()[n], b[1].vector()[n]])
# denominator used to calculate directional derivative
if np.linalg.norm(b_x) > 1:
lamb = 0.1 * self.mesh.hmin() / np.linalg.norm(b_x)
else:
lamb = 0.1 * self.mesh.hmin()
# position of first node of the stencil
x_prev = x - lamb * b_x
# Find cell containing first node of stencil and get its
# dof/vertex coordinates
try:
cell_ind = self.mesh.bounding_box_tree(
).compute_entity_collisions(Point(x_prev))[0]
except IndexError:
i = 16
while i > 2:
# sometimes Fenics does not detect nodes if boundary is
# parallel to the boundary advection due to rounding errors
# so try different precisions just to be sure
try:
cell_ind = self.mesh.bounding_box_tree(
).compute_entity_collisions(Point(np.round(x_prev,
i)))[0]
break
except IndexError:
i -= 1
else:
raise Exception(
"Boundary advection outside tangential cone")
cell_vertices = self.mesh.cells()[cell_ind]
cell_dofs = vertex_to_dof_map(self.V)[cell_vertices]
cell_coords = self.mesh.coordinates()[cell_vertices]
# calculate weigth of each vertex in the cell (using
# barycentric coordinates)
A = np.vstack((cell_coords.T, np.ones(3)))
rhs = np.append(x_prev, np.ones(1))
weights = np.linalg.solve(A, rhs)
weights = [w if w > 1e-14 else 0 for w in weights]
dof_to_weight = dict(zip(cell_dofs, weights))
# calculate directional derivative at each node using
# weights to interpolate value of numerical solution at
# x_prev
row = operator.getrow(n)
indices = row[0]
data = row[1]
for dof in cell_dofs:
pos = np.where(indices == dof)[0][0]
if dof != n:
data[pos] = -dof_to_weight[dof] / lamb
else:
c_n = c.vector()[dof]
# make sure reaction term is positive adding artificial
# constant if necessary
if region in self.parameters.regions['Robin']:
c_n = max(c_n, min(lamb, 1E-8))
data[pos] = (1 - dof_to_weight[dof]) / lamb + c_n
operator.set([data], [n], indices)
operator.apply('insert')
for (nx, dt, pres, store_step) in zip(nx_list, dt_list, pres_list,
storestep_list):
if comm.Get_rank() == 0:
print("Starting computation with grid resolution " + str(nx))
# Compute num steps till completion
num_steps = np.rint(Tend / float(dt))
# Generate mesh
mesh = Mesh("./../../meshes/circle_0.xml")
n = nx
while n > 1:
mesh = refine(mesh)
n /= 2
output_field = XDMFFile(mesh.mpi_comm(),
outdir + "psi_h_nx" + str(nx) + ".xdmf")
# Velocity and initial condition
V = VectorFunctionSpace(mesh, "DG", 3)
uh = Function(V)
uh.assign(Expression(("-Uh*x[1]", "Uh*x[0]"), Uh=Uh, degree=3))
psi0_expression = GaussianPulse(center=(xc, yc),
sigma=float(sigma),
U=[Uh, Uh],
time=0.0,
height=1.0,
degree=3)
# Generate particles
def create_slice(basemesh, point, normal, closest_region=False, crinkle_clip=False):
"""Create a slicemesh from a basemesh.
:param basemesh: Mesh to slice
:param point: Point in slicing plane
:param normal: Normal to slicing plane
:param closest_region: Set to True to extract disjoint region closest to specified point
:param crinkle_clip: Set to True to return mesh of same topological dimension as basemesh
.. note::
Only 3D-meshes currently supported for slicing.
.. warning::
Slice-instances are intended for visualization only, and may produce erronous
results if used for computations.
"""
assert basemesh.geometry().dim() == 3, "Can only slice 3D-meshes."
P = np.array([point[0], point[1], point[2]], dtype=np.double)
# Create unit normal
n = np.array([normal[0],normal[1], normal[2]])
n = n/np.linalg.norm(n)
#self.n = Constant((n[0], n[1], n[2]))
# Calculate the distribution of vertices around the plane
# (sign of np.dot(p-P, n) determines which side of the plane p is on)
vsplit = np.dot(basemesh.coordinates()-P, n)
# Count each cells number of vertices on the "positive" side of the plane
# Only cells with vertices on both sides of the plane intersect the plane
operator = np.less
npos = np.sum(vsplit[basemesh.cells()] < 0, 1)
intersection_cells = basemesh.cells()[(npos > 0) & (npos < 4)]
if len(intersection_cells) == 0:
# Try to put "zeros" on other side of plane
# FIXME: handle cells with vertices exactly intersecting the plane in a more robust manner.
operator = np.greater
npos = np.sum(vsplit[basemesh.cells()] > 0, 1)
#cell_indices = (npos > 0) & (npos < 4)
intersection_cells = basemesh.cells()[(npos > 0) & (npos < 4)]
if crinkle_clip:
cf = CellFunction("size_t", basemesh)
cf.set_all(0)
cf.array()[(npos>0) & (npos<4)] = 1
mesh = create_submesh(basemesh, cf, 1)
else:
def add_cell(cells, cell):
# Split cell into triangles
for i in xrange(len(cell)-2):
cells.append(cell[i:i+3])
cells = []
index = 0
indexes = {}
for c in intersection_cells:
a = operator(vsplit[c], 0)
positives = c[np.where(a==True)[0]]
negatives = c[np.where(a==False)[0]]
cell = []
for pp_ind in positives:
pp = basemesh.coordinates()[pp_ind]
for pn_ind in negatives:
pn = basemesh.coordinates()[pn_ind]
if (pp_ind, pn_ind) not in indexes:
# Calculate intersection point with the plane
d = np.dot(P-pp, n)/np.dot(pp-pn, n)
ip = pp+(pp-pn)*d
indexes[(pp_ind, pn_ind)] = (index, ip)
index += 1
cell.append(indexes[(pp_ind, pn_ind)][0])
add_cell(cells, cell)
MPI.barrier(mpi_comm_world())
# Assign global indices
# TODO: Assign global indices properly
dist = distribution(index)
global_idx = sum(dist[:MPI.rank(mpi_comm_world())])
vertices = {}
for idx, p in indexes.values():
vertices[idx] = (global_idx, p)
global_idx += 1
global_num_cells = MPI.sum(mpi_comm_world(), len(cells))
global_num_vertices = MPI.sum(mpi_comm_world(), len(vertices))
mesh = Mesh()
# Return empty mesh if no intersections were found
if global_num_cells == 0:
mesh_editor = MeshEditor()
mesh_editor.open(mesh, "triangle", 2, 3)
mesh_editor.init_vertices(0)
mesh_editor.init_cells(0)
mesh_editor.close()
else:
# Distribute mesh if empty on any processors
cells, vertices = distribute_meshdata(cells, vertices)
# Build mesh
mesh_editor = MeshEditor()
mesh_editor.open(mesh, "triangle", 2, 3)
mesh_editor.init_vertices(len(vertices))
mesh_editor.init_cells(len(cells))
for index, cell in enumerate(cells):
mesh_editor.add_cell(index, cell[0], cell[1], cell[2])
for local_index, (global_index, coordinates) in vertices.items():
mesh_editor.add_vertex_global(int(local_index), int(global_index), coordinates)
mesh_editor.close()
mesh.topology().init(0, len(vertices), global_num_vertices)
mesh.topology().init(2, len(cells), global_num_cells)
if closest_region and mesh.size_global(0) > 0:
assert MPI.size(mpi_comm_world())==1, "Extract closest region does not work in parallel"
regions = compute_connectivity(mesh)
i,d = mesh.bounding_box_tree().compute_closest_entity(Point(P))
if d == MPI.min(mesh.mpi_comm(), d):
v = regions[int(i)]
else:
v = 0
v = MPI.max(mesh.mpi_comm(), v)
mesh = create_submesh(mesh, regions, v)
return mesh
class FBVP:
def __init__(self,
mesh_name,
parameters,
alpha_range=None,
beta_range=None):
# DEFINE MESH AND PARAMETERS
self.parameters = parameters
self.mesh_name = mesh_name
if not alpha_range:
self.alpha_range = parameters.alpha_range
else:
self.alpha_range = alpha_range
if not beta_range:
self.beta_range = parameters.beta_range
else:
self.beta_range = alpha_range
meshname = \
f'meshes/{parameters.domain}/{parameters.domain}_{self.mesh_name}.xdmf'
self.mesh = Mesh()
with XDMFFile(meshname) as f:
f.read(self.mesh)
print(f'Mesh size= {self.mesh.hmax()}')
# dimension of approximation space
self.dim = len(self.mesh.coordinates())
print(f'Dimension of solution space is {self.dim}')
self.V = FunctionSpace(self.mesh, 'CG', 1) # CG = P1
self.coords = self.mesh.coordinates()[dof_to_vertex_map(self.V)]
# self.t_V = FunctionSpace(self.t_mesh, 'CG', 1)
self.T = self.parameters.T # final time
self.w = TrialFunction(self.V)
self.u = TestFunction(self.V)
#######################################################################
# CONTROL SET CREATION
self.ctrset_alpha = np.linspace(self.alpha_range[0],
self.alpha_range[1],
parameters.alpha_size)
self.ctrset_beta = np.linspace(self.beta_range[0], self.beta_range[1],
parameters.beta_size)
self.csize_alpha = len(self.ctrset_alpha)
self.csize_beta = len(self.ctrset_beta)
print(f'Discretized control set has size'
f' {self.csize_alpha * self.csize_beta}')
#######################################################################
# BOUNDARY CONDITIONS
parameters.set_boundary_conditions(self.mesh)
self.boundary_markers = MeshFunction('size_t', self.mesh, 1)
self.boundary_markers.set_all(99) # pylint: disable=no-member
for i, omega in self.parameters.omegas.items():
omega.mark(self.boundary_markers, i)
self.ds = Measure('ds',
domain=self.mesh,
subdomain_data=self.boundary_markers)
self.dirichlet_bcs = [
DirichletBC(self.V, parameters.RHS_bound[i], self.boundary_markers,
i) for i in parameters.omegas
]
# Get indices of dirichlet and dofs
self.boundary_nodes_list = \
DirichletBC(self.V, Constant('0.0'),
'on_boundary').get_boundary_values().keys()
#######################################################################
# ASSEMBLY
time_start = time.process_time()
self.assemble_diagonal_matrix() # auxilliary generic diagonal matrix
# used for vector*matrix multiplication of dolfin matrices
self.assemble_lumpedmm() # assembly lumped mass matrix
# which serves the role of identity operator
self.assemble_laplacian() # assembly of discrete laplacian
self.ad_data_path = f'out/{parameters.experiment}'
Path(self.ad_data_path).mkdir(parents=True, exist_ok=True)
# FIXME: value of timestep required to impose monotonity may be
# different at different times, at this moment code assumes that
# it won't be smaller than in case t=T
self.timesteps = parameters.get_number_of_timesteps()
self.assemble_HJBe() # assembly of explicit operators
self.assemble_HJBi() # assembly of implicit operators
self.assemble_RHS() # assembly of forcing term
print('Final time assembly complete')
print(f'Assembly took {time.process_time() - time_start} seconds')
print('===========================================================')
def assemble_diagonal_matrix(self):
print("Assembling auxilliary diagonal matrix")
""" Operator assembled to get the right sparsity pattern
(non-zero terms can only exist on diagonal)
"""
mesh3 = UnitIntervalMesh(self.dim)
V3 = FunctionSpace(mesh3, "DG", 0)
wid = TrialFunction(V3)
uid = TestFunction(V3)
self.diag_matrix = assemble(uid * wid * dx)
self.diag_matrix.zero()
def assemble_lumpedmm(self):
""" Assembly lumped mass matrix - plays role of identity matrix
"""
print("Assembling lumped mass matrix")
mass_form = self.w * self.u * dx
self.mass_matrix = assemble(mass_form)
mass_action_form = action(mass_form, Constant(1))
self.MM_terms = assemble(mass_action_form)
self.mass_matrix.zero()
self.mass_matrix.set_diagonal(self.MM_terms)
self.scipy_mass_matrix = toscipy(self.mass_matrix)
def assemble_laplacian(self):
print("Assembling laplacians")
# laplacian discretisation
self.laplacian = assemble(dot(grad(self.w), grad(self.u)) * dx)
def assemble_HJBe(self, t=None):
""" Assembly explicit operator for every control in the control set,
then apply artificial diffusion to all of them. Note that artificial
diffusion is calculated differently on the boundary nodes.
"""
self.explicit_matrices = np.empty([self.csize_beta, self.csize_alpha],
dtype=object)
self.explicit_diffusion = np.empty([self.csize_beta, self.csize_alpha],
dtype=object)
diag_vector = Vector(self.mesh.mpi_comm(), self.dim)
global_min_timestep = float('inf')
# Create explicit operator for each control in control set
for ind_a, a in enumerate(self.ctrset_alpha):
for ind_b, b in enumerate(self.ctrset_beta):
if (ind_a * self.csize_beta + ind_b) % 10 == 0:
print(f'Assembling explicit matrix under control '
f'{ind_a*self.csize_beta + ind_b} out of '
f'{self.csize_alpha*self.csize_beta}')
# coefficients in the interior
advection_x = self.parameters.adv_x(a, b)
advection_y = self.parameters.adv_y(a, b)
reaction = self.parameters.lin(a, b)
if t is not None:
advection_x.t = t
advection_y.t = t
reaction.t = t
# Discretize PDE (set values on boundary rows to zero)
b = np.array([advection_x, advection_y])
E_int_form = (np.dot(b, grad(self.w)) +
reaction * self.w) * self.u * dx
explicit_matrix = assemble(E_int_form)
# Calculate nodewise minimum diffusion required to
# impose monotonicity
min_diffusion = [0] * explicit_matrix.size(0)
for rows, row_num in getrows(explicit_matrix,
self.laplacian,
ignore=self.boundary_nodes_list):
min_diffusion[row_num] = calc_ad(rows, row_num)
self.explicit_diffusion[ind_b][ind_a] = min_diffusion
diffusion_matrix = apply_ad(self.laplacian, min_diffusion)
explicit_matrix += diffusion_matrix
explicit_matrix.get_diagonal(diag_vector)
current_min_timestep = get_min_timestep(
diag_vector, self.MM_terms, self.boundary_nodes_list)
global_min_timestep = min(current_min_timestep,
global_min_timestep)
self.explicit_matrices[ind_b][ind_a] = toscipy(explicit_matrix)
#######################################################################
min_timesteps = int(self.T / global_min_timestep) + 1
if not self.timesteps or self.timesteps < min_timesteps:
self.timesteps = min_timesteps
try:
filename = (f'meshes/{self.parameters.domain}/'
f'Mvalues-{self.parameters.experiment}.json')
with open(filename, 'r') as f:
min_timesteps_dict = json.load(f)
except FileNotFoundError:
min_timesteps_dict = {}
min_timesteps_dict[self.parameters.mesh_name] = self.timesteps
with open(filename, 'w') as f:
json.dump(min_timesteps_dict, f)
self.timestep_size = self.T / self.timesteps # time step size
self.parameters.calculate_save_interval()
self.explicit_matrices = [[
self.timestep_size * E - self.scipy_mass_matrix for E in Elist
] for Elist in self.explicit_matrices]
print('Checking if the explicit operators satisfy'
' monotonicity conditions')
for matrix_list in self.explicit_matrices:
for matrix in matrix_list:
explicit_check(matrix, self.boundary_nodes_list)
def assemble_RHS(self, t=None):
"""Assemble right hand side of the FBVP
"""
print('Assembling RHS')
self.forcing_terms = np.empty(
[self.csize_beta, self.csize_alpha, self.dim])
for ind_a, alpha in enumerate(self.ctrset_alpha):
for ind_b, beta in enumerate(self.ctrset_beta):
rhs = self.parameters.RHSt(alpha, beta)
if t is not None:
rhs.t = t
# Initialise forcing term
F = np.array(assemble(rhs * self.u * dx)[:])
self.forcing_terms[ind_b][ind_a] = self.timestep_size * F
def assemble_HJBi(self, t=None):
""" Assembly matrix discretizing second order terms after diffusion
moved to the explicit operator is subtracted. Whenever amount of
diffusion used to make some row of an explicit operator monotonic
exceeds the amount of natural diffusion at that node we call it
artificial diffusion. In such case, this row of the implicit operator
is multiplied by zero
"""
print('Assembling implicit operators')
self.implicit_matrices = np.empty([self.csize_beta, self.csize_alpha],
dtype=object)
remaining_diffusion = Function(self.V)
max_art_dif = 0.0
max_art_dif_loc = None
diffusion_matrix = self.diag_matrix.copy()
for ind_a, alpha in enumerate(self.ctrset_alpha):
for ind_b, beta in enumerate(self.ctrset_beta):
# TODO: Include assert making sure that diffusion is
# non-negative on all of the internal nodes
diffusion = self.parameters.diffusion(alpha, beta)
if t is not None:
diffusion.t = t
diff = interpolate(diffusion, self.V).vector()
if not np.all(diff >= 0):
raise Exception("Choose non-negative diffusion")
diff_vec = np.array([
diff[i] if i not in self.boundary_nodes_list else 0.0
for i in range(self.dim)
])
artdif = self.explicit_diffusion[ind_b][ind_a] - diff_vec
if np.amax(artdif) > max_art_dif:
max_art_dif = np.amax(artdif)
max_art_dif_loc = self.coords[np.argmax(artdif)]
# discretise second order terms
remaining_diffusion.vector()[:] = np.maximum(
-artdif, [0] * self.dim)
diffusion_matrix.set_diagonal(remaining_diffusion.vector())
Iab = matmult(diffusion_matrix, self.laplacian)
self.implicit_matrices[ind_b][ind_a] = self.timestep_size * \
Iab + self.mass_matrix
self.scipy_implicit_matrices = [[toscipy(mat) for mat in Ialist]
for Ialist in self.implicit_matrices]
print('Checking if the implicit operators satisfy'
' monotonicity conditions')
for matrix_list in self.scipy_implicit_matrices:
for matrix in matrix_list:
implicit_check(matrix)
with open(self.ad_data_path + '/ad.txt', 'a') as f:
time_str = f' at time {t}\n' if t is not None else '\n'
f.write(f'For mesh {self.mesh_name} max value of artificial'
' diffusion coefficient was'
f' {max_art_dif} at {max_art_dif_loc}' + time_str)
def __init__(
self,
time: df.Constant,
mesh: df.Mesh,
conductivity: Dict[int, df.Expression],
conductivity_ratio: Dict[int, df.Expression],
cell_function: df.MeshFunction,
cell_tags: CellTags,
interface_function: df.MeshFunction,
interface_tags: InterfaceTags,
parameters: CoupledMonodomainParameters,
neumann_boundary_condition: Dict[int, df.Expression] = None,
v_prev: df.Function = None,
surface_to_volume_factor: Union[float, df.Constant] = None,
membrane_capacitance: Union[float, df.Constant] = None,
) -> None:
self._time = time
self._mesh = mesh
self._conductivity = conductivity
self._cell_function = cell_function
self._cell_tags = cell_tags
self._interface_function = interface_function
self._interface_tags = interface_tags
self._parameters = parameters
if surface_to_volume_factor is None:
surface_to_volume_factor = df.constant(1)
if membrane_capacitance is None:
membrane_capacitance = df.constant(1)
self._chi_cm = df.Constant(surface_to_volume_factor) * df.Constant(
membrane_capacitance)
if neumann_boundary_condition is None:
self._neumann_boundary_condition: Dict[int, df.Expression] = dict()
else:
self._neumann_boundary_condition = neumann_boundary_condition
if not set(conductivity.keys()) == set(conductivity_ratio.keys()):
raise ValueError(
"intracellular conductivity and lambda does not have natching keys."
)
self._lambda = conductivity_ratio
# Function spaces
self._function_space = df.FunctionSpace(mesh, "CG", 1)
# Test and trial and previous functions
self._v_trial = df.TrialFunction(self._function_space)
self._v_test = df.TestFunction(self._function_space)
self._v = df.Function(self._function_space)
if v_prev is None:
self._v_prev = df.Function(self._function_space)
else:
# v_prev is shipped from an odesolver.
self._v_prev = v_prev
_cell_tags = set(self._cell_tags)
_cell_function_values = set(self._cell_function.array())
if not _cell_tags <= _cell_function_values.union({None}):
msg = f"Cell function does not contain {_cell_tags - _cell_function_values}"
raise ValueError(msg)
_interface_tags = set(self._interface_tags)
_interface_function_values = {
*set(self._interface_function.array()), None
}
if not _interface_tags <= _interface_function_values.union({None}):
msg = f"interface function does not contain {_interface_tags - _interface_function_values}."
raise ValueError(msg)
# Crete integration measures -- Interfaces
self._dGamma = df.Measure("ds",
domain=self._mesh,
subdomain_data=self._interface_function)
# Crete integration measures -- Cells
self._dOmega = df.Measure("dx",
domain=self._mesh,
subdomain_data=self._cell_function)
# Create variational forms
self._timestep = df.Constant(self._parameters.timestep)
self._lhs, self._rhs = self._variational_forms()
# Preassemble left-hand side (will be updated if time-step changes)
self._lhs_matrix = df.assemble(self._lhs)
self._rhs_vector = df.Vector(mesh.mpi_comm(), self._lhs_matrix.size(0))
self._lhs_matrix.init_vector(self._rhs_vector, 0)
self._linear_solver = create_linear_solver(self._lhs_matrix,
self._parameters)
# Timestepping
Tend = 2.
dt = Constant(0.02)
num_steps = np.rint(Tend / float(dt))
# Output directory
store_step = 1
outdir = './../../results/SlottedDisk_Rotation_AddDelete/'
# Mesh
mesh = Mesh('./../../meshes/circle_0.xml')
mesh = refine(mesh)
mesh = refine(mesh)
mesh = refine(mesh)
outfile = XDMFFile(mesh.mpi_comm(), outdir + "psi_h.xdmf")
# Set slotted disk
psi0_expr = SlottedDisk(radius=rdisk,
center=[xc, yc],
width=rwidth,
depth=0.,
degree=3,
lb=lb,
ub=ub)
# Function space and velocity field
W = FunctionSpace(mesh, 'DG', k)
psi_h = Function(W)
V = VectorFunctionSpace(mesh, 'DG', 3)
def scalar_laplacians(
mesh: df.Mesh,
markers: Optional[Dict[str, int]] = None,
ffun: Optional[MeshFunction] = None,
use_krylov_solver: bool = False,
krylov_solver_atol: Optional[float] = None,
krylov_solver_rtol: Optional[float] = None,
krylov_solver_max_its: Optional[int] = None,
verbose: bool = False,
strict: bool = False,
) -> Dict[str, df.Function]:
"""
Calculate the laplacians
Arguments
---------
mesh : dolfin.Mesh
A dolfin mesh
markers : dict (optional)
A dictionary with the markers for the
different bondaries defined in the facet function
or within the mesh itself.
The follwing markers must be provided:
'base', 'lv', 'epi, 'rv' (optional).
If the markers are not provided the following default
vales will be used: base = 10, rv = 20, lv = 30, epi = 40.
fiber_space : str
A string on the form {familiy}_{degree} which
determines for what space the fibers should be calculated for.
use_krylov_solver: bool
If True use Krylov solver, by default False
krylov_solver_atol: float (optional)
If a Krylov solver is used, this option specifies a
convergence criterion in terms of the absolute
residual. Default: 1e-15.
krylov_solver_rtol: float (optional)
If a Krylov solver is used, this option specifies a
convergence criterion in terms of the relative
residual. Default: 1e-10.
krylov_solver_max_its: int (optional)
If a Krylov solver is used, this option specifies the
maximum number of iterations to perform. Default: 10000.
verbose: bool
If true, print more info, by default False
strict: bool
If true raise RuntimeError if solutions does not sum to 1.0
"""
if not isinstance(mesh, df.Mesh):
raise TypeError("Expected a dolfin.Mesh as the mesh argument.")
# Init connectivities
mesh.init(2)
if ffun is None:
ffun = df.MeshFunction("size_t", mesh, 2, mesh.domains())
# Boundary markers, solutions and cases
cases, boundaries, markers = find_cases_and_boundaries(ffun, markers)
markers_str = "\n".join(
["{}: {}".format(k, v) for k, v in markers.items()])
df.info(("Compute scalar laplacian solutions with the markers: \n"
"{}").format(markers_str, ), )
check_boundaries_are_marked(
mesh=mesh,
ffun=ffun,
markers=markers,
boundaries=boundaries,
)
# Compte the apex to base solutons
num_vertices = mesh.num_vertices()
num_cells = mesh.num_cells()
if mesh.mpi_comm().size > 1:
num_vertices = mesh.mpi_comm().allreduce(num_vertices)
num_cells = mesh.mpi_comm().allreduce(num_cells)
df.info(" Num vertices: {0}".format(num_vertices))
df.info(" Num cells: {0}".format(num_cells))
if "mv" in cases and "av" in cases:
# Use Doste approach
pass
# Else use the Bayer approach
return bayer(
cases=cases,
mesh=mesh,
markers=markers,
ffun=ffun,
verbose=verbose,
use_krylov_solver=use_krylov_solver,
strict=strict,
krylov_solver_atol=krylov_solver_atol,
krylov_solver_rtol=krylov_solver_rtol,
krylov_solver_max_its=krylov_solver_max_its,
)
