def _priority(self, priority_order, facet_domains):
if len(priority_order) == 0:
ds = [Measure("ds")]
bcs = [None]
return ds, bcs
ds = Measure("ds")[facet_domains]
unprioritized = list(
set(np.unique(facet_domains.array())) - set(priority_order))
unprioritized = gather(unprioritized, 0)
unprioritized = np.unique(np.array(unprioritized))
unprioritized = broadcast(unprioritized, 0)
unprioritized = unprioritized.astype(np.int)
_ds = []
if len(unprioritized) > 0:
nds = ds(unprioritized[0])
for i in unprioritized[1:]:
nds += ds(i)
_ds.append(nds)
_ds += [ds(i) for i in priority_order]
bcs = [
DirichletBC(V, Constant((0, ) * V.num_sub_spaces()), facet_domains,
i) for i in priority_order
]
if len(unprioritized) > 0:
bcs = [None] + bcs
return _ds, bcs
def compute(self, get):
# Get field to probe
u = get(self.valuename)
# Evaluate in all points
self.probes(u)
# Fetch array with probe values at this timestep
#results = self.probes.array(self._probetimestep)
results = self.probes.array()
if MPI.rank(mpi_comm_world()) != 0:
results = np.array([], dtype=np.float_)
if results.shape == ():
results = results.reshape(1,)
# Broadcast array to all processes
if self.params.broadcast_results:
results = broadcast(results, 0)
self.probes.clear()
# Return as list to store without 'array(...)' text.
if u.value_rank() > 0:
if len(results.shape) == 1:
return list(results)
return list(tuple(res) for res in results)
elif results.size == 1:
return float(results)
else:
return list(results)
def create_submesh(mesh, markers, marker):
"This function allows for a SubMesh-equivalent to be created in parallel"
# Build mesh
submesh = Mesh()
mesh_editor = MeshEditor()
mesh_editor.open(submesh,
mesh.ufl_cell().cellname(),
mesh.ufl_cell().topological_dimension(),
mesh.ufl_cell().geometric_dimension())
# Return empty mesh if no matching markers
if MPI.sum(mpi_comm_world(), int(marker in markers.array())) == 0:
cbc_warning(
"Unable to find matching markers in meshfunction. Submesh is empty."
)
mesh_editor.close()
return submesh
base_cell_indices = np.where(markers.array() == marker)[0]
base_cells = mesh.cells()[base_cell_indices]
base_vertex_indices = np.unique(base_cells.flatten())
base_global_vertex_indices = sorted(
[mesh.topology().global_indices(0)[vi] for vi in base_vertex_indices])
gi = mesh.topology().global_indices(0)
shared_local_indices = set(base_vertex_indices).intersection(
set(mesh.topology().shared_entities(0).keys()))
shared_global_indices = [gi[vi] for vi in shared_local_indices]
unshared_global_indices = list(
set(base_global_vertex_indices) - set(shared_global_indices))
unshared_vertices_dist = distribution(len(unshared_global_indices))
# Number unshared vertices on separate process
idx = sum(unshared_vertices_dist[:MPI.rank(mpi_comm_world())])
base_to_sub_global_indices = {}
for gi in unshared_global_indices:
base_to_sub_global_indices[gi] = idx
idx += 1
# Gather all shared process on process 0 and assign global index
all_shared_global_indices = gather(shared_global_indices,
on_process=0,
flatten=True)
all_shared_global_indices = np.unique(all_shared_global_indices)
shared_base_to_sub_global_indices = {}
idx = int(
MPI.max(mpi_comm_world(),
float(max(base_to_sub_global_indices.values() + [-1e16]))) + 1)
if MPI.rank(mpi_comm_world()) == 0:
for gi in all_shared_global_indices:
shared_base_to_sub_global_indices[int(gi)] = idx
idx += 1
# Broadcast global numbering of all shared vertices
shared_base_to_sub_global_indices = dict(
zip(broadcast(shared_base_to_sub_global_indices.keys(), 0),
broadcast(shared_base_to_sub_global_indices.values(), 0)))
# Join shared and unshared numbering in one dict
base_to_sub_global_indices = dict(
base_to_sub_global_indices.items() +
shared_base_to_sub_global_indices.items())
# Create mapping of local indices
base_to_sub_local_indices = dict(
zip(base_vertex_indices, range(len(base_vertex_indices))))
# Define sub-cells
sub_cells = [None] * len(base_cells)
for i, c in enumerate(base_cells):
sub_cells[i] = [base_to_sub_local_indices[j] for j in c]
# Store vertices as sub_vertices[local_index] = (global_index, coordinates)
sub_vertices = {}
for base_local, sub_local in base_to_sub_local_indices.items():
sub_vertices[sub_local] = (base_to_sub_global_indices[
mesh.topology().global_indices(0)[base_local]],
mesh.coordinates()[base_local])
## Done with base mesh
# Distribute meshdata on (if any) empty processes
sub_cells, sub_vertices = distribute_meshdata(sub_cells, sub_vertices)
global_cell_distribution = distribution(len(sub_cells))
#global_vertex_distribution = distribution(len(sub_vertices))
global_num_cells = MPI.sum(mpi_comm_world(), len(sub_cells))
global_num_vertices = sum(unshared_vertices_dist) + MPI.sum(
mpi_comm_world(), len(all_shared_global_indices))
mesh_editor.init_vertices(len(sub_vertices))
#mesh_editor.init_cells(len(sub_cells))
mesh_editor.init_cells_global(len(sub_cells), global_num_cells)
global_index_start = sum(
global_cell_distribution[:MPI.rank(mesh.mpi_comm())])
for index, cell in enumerate(sub_cells):
if LooseVersion(dolfin_version()) >= LooseVersion("1.6.0"):
mesh_editor.add_cell(index, *cell)
else:
mesh_editor.add_cell(int(index), global_index_start + index,
np.array(cell, dtype=np.uintp))
for local_index, (global_index, coordinates) in sub_vertices.items():
#print coordinates
mesh_editor.add_vertex_global(int(local_index), int(global_index),
coordinates)
mesh_editor.close()
submesh.topology().init(0, len(sub_vertices), global_num_vertices)
submesh.topology().init(mesh.ufl_cell().topological_dimension(),
len(sub_cells), global_num_cells)
# FIXME: Set up shared entities
# What damage does this do?
submesh.topology().shared_entities(0)[0] = []
# The code below sets up shared vertices, but lacks shared facets.
# It is considered incomplete, and therefore commented out
'''
#submesh.topology().shared_entities(0)[0] = []
from dolfin import compile_extension_module
cpp_code = """
void set_shared_entities(Mesh& mesh, std::size_t idx, const Array<std::size_t>& other_processes)
{
std::set<unsigned int> set_other_processes;
for (std::size_t i=0; i<other_processes.size(); i++)
{
set_other_processes.insert(other_processes[i]);
//std::cout << idx << " --> " << other_processes[i] << std::endl;
}
//std::cout << idx << " --> " << set_other_processes[0] << std::endl;
mesh.topology().shared_entities(0)[idx] = set_other_processes;
}
"""
set_shared_entities = compile_extension_module(cpp_code).set_shared_entities
base_se = mesh.topology().shared_entities(0)
se = submesh.topology().shared_entities(0)
for li in shared_local_indices:
arr = np.array(base_se[li], dtype=np.uintp)
sub_li = base_to_sub_local_indices[li]
set_shared_entities(submesh, base_to_sub_local_indices[li], arr)
'''
return submesh
def duplicate_meshfunction(mf, new_mesh):
"Duplicate meshfunction defined on a different mesh"
# Rebuild meshfunction
mesh = mf.mesh()
dim = mf.dim()
if isinstance(mf, MeshFunctionSizet):
f = MeshFunction("size_t", new_mesh, dim)
dtype = np.uintp
elif isinstance(mf, MeshFunctionDouble):
f = MeshFunction("double", new_mesh, dim)
dtype = np.float_
elif isinstance(mf, MeshFunctionBool):
f = MeshFunction("bool", new_mesh, dim)
dtype = np.bool
elif isinstance(mf, MeshFunctionInt):
f = MeshFunction("int", new_mesh, dim)
dtype = np.int
# Midpoint of old mesh
connectivity = mesh.topology()(dim, 0)().reshape(mesh.num_entities(dim),
-1)
midpoints = np.mean(mesh.coordinates()[connectivity], axis=1)
indices = np.lexsort(midpoints.T[::-1])
sorted_midpoints = midpoints[indices]
values = mf.array()[indices]
gdim = midpoints.shape[1]
sorted_midpoints = sorted_midpoints.flatten()
sorted_midpoints = gather(sorted_midpoints, 0)
sorted_midpoints = np.hstack(sorted_midpoints).flatten()
sorted_midpoints = broadcast(sorted_midpoints, 0)
_sorted_midpoints = []
i = 0
for arr in sorted_midpoints:
_sorted_midpoints.append(arr)
sorted_midpoints = np.reshape(sorted_midpoints, newshape=(-1, gdim))
values = gather(values, 0)
values = np.hstack(values).flatten()
values = broadcast(values, 0)
# Workaround for bug in np.uint64
if dtype == np.uintp:
M = max(values)
if M == dtype(-1):
values[values == M] = -1
values = values.astype(dtype)
_values = []
for arr in values:
_values.append(arr)
values = np.array(_values, dtype=dtype)
indices = np.lexsort(sorted_midpoints.T[::-1])
values = values[indices]
sorted_midpoints = sorted_midpoints[indices]
# Now has full list of midpoint+values on all processes
# Sort midpoints on new mesh on current process
connectivity = new_mesh.topology()(dim,
0)().reshape(new_mesh.num_entities(dim),
-1)
midpoints = np.mean(new_mesh.coordinates()[connectivity], axis=1)
indices = np.lexsort(midpoints.T[::-1])
midpoints = midpoints[indices]
idx = 0
omp = sorted_midpoints[idx]
tol = 1e-8
for i, mp in enumerate(midpoints):
for j in xrange(gdim):
while omp[j] < mp[j] - tol:
idx += 1
omp[:] = sorted_midpoints[idx]
f[int(indices[i])] = values[idx]
return f
def compute_connectivity(mesh, cell_connectivity=True):
"""Compute connected regions of mesh.
Regions are considered connected if they share a vertex through an edge.
"""
# Compute first vertex connectivity (defined by sharing edges)
mesh.init(0,1)
regions = VertexFunction("size_t", mesh)
regions.set_all(0)
i = 0
while True:
i += 1
unset = np.where(regions.array()==0)[0]
if len(unset) == 0:
break
start = unset[0]
tic()
connectivity = _compute_connected_vertices(mesh, start)
regions.array()[connectivity.array()] = i
dist = distribution(np.max(regions.array()))
# Make all regions separate (regions on different processes are currently considered disjoint)
regions.array()[:] += np.sum(dist[:MPI.rank(mesh.mpi_comm())])
# Find global indices of all vertices shared by more than one process
global_indices = mesh.topology().global_indices(0)
se = mesh.topology().shared_entities(0)
gi_local = np.array([global_indices[i] for i in se.keys()])
#mapping = dict(zip(gi_local,se.keys()))
gi = gather(gi_local, 0)
gi = np.hstack(gi).flatten()
gi = broadcast(gi, 0)
# gi is now common on all processes
# Connect disjointed regions through shared vertices
while True:
v = regions.array()[se.keys()]
d = dict(zip(gi_local,v))
shift = dict()
for gidx in gi:
#lidx = mapping.get(gidx, -1)
this_v = d.get(gidx, np.inf)
v = int(MPI.min(mesh.mpi_comm(), float(this_v)))
if this_v == v or this_v == np.inf:
continue
shift[this_v] = v
# Check if no shift is needed, and if so, break
no_shift = bool(int(MPI.min(mesh.mpi_comm(), float(int(shift==dict())))))
if no_shift:
break
for k,v in shift.items():
regions.array()[regions.array()==k] = v
# Condense regions, so that M == number of regions
M = int(MPI.max(mesh.mpi_comm(), float(np.max(regions.array()))))
values = np.unique(regions.array())
for i in range(1,M+1):
has_value = MPI.max(mesh.mpi_comm(), float(i in values))
if has_value == 0:
regions.array()[regions.array()>i] -= 1
values = np.unique(regions.array())
if cell_connectivity:
cf = CellFunction("size_t", mesh)
cf.set_all(0)
cells = mesh.cells()[:,0]
cf.array()[:] = regions.array()[cells]
regions = cf
return regions
def restriction_map(V, Vb, _all_coords=None, _all_coordsb=None):
"Return a map between dofs in Vb to dofs in V. Vb's mesh should be a submesh of V's Mesh."
if V.ufl_element().family(
) == "Discontinuous Lagrange" and V.ufl_element().degree() > 0:
raise RuntimeError(
"This function does not work for DG-spaces of degree >0 \
(several dofs associated with same point in same subspace)."
)
if V.ufl_element().family() != "Lagrange":
cbc_warning("This function is only tested for CG-spaces.")
assert V.ufl_element().family() == Vb.ufl_element().family(
), "ufl elements differ in the two spaces"
assert V.ufl_element().degree() == Vb.ufl_element().degree(
), "ufl elements differ in the two spaces"
assert V.ufl_element().cell() == Vb.ufl_element().cell(
), "ufl elements differ in the two spaces"
D = V.mesh().geometry().dim()
# Recursively call this function if V has sub-spaces
if V.num_sub_spaces() > 0:
mapping = {}
if MPI.size(mpi_comm_world()) == 1:
if _all_coords is None:
try:
# For 1.6.0+ and newer
all_coords = V.tabulate_dof_coordinates().reshape(
V.dim(), D)
all_coordsb = Vb.tabulate_dof_coordinates().reshape(
Vb.dim(), D)
except:
# For 1.6.0 and older
all_coords = V.dofmap().tabulate_all_coordinates(
V.mesh()).reshape(V.dim(), D)
all_coordsb = Vb.dofmap().tabulate_all_coordinates(
Vb.mesh()).reshape(Vb.dim(), D)
else:
all_coords = _all_coords
all_coordsb = _all_coordsb
else:
all_coords = None
all_coordsb = None
for i in range(V.num_sub_spaces()):
mapping.update(
restriction_map(V.sub(i), Vb.sub(i), all_coords, all_coordsb))
return mapping
dm = V.dofmap()
dmb = Vb.dofmap()
N = len(dm.dofs())
Nb = len(dmb.dofs())
dofs = dm.dofs()
# Extract coordinates of dofs
if dm.is_view():
if _all_coords is not None:
coords = _all_coords[V.dofmap().dofs()]
else:
try:
# For 1.6.0+ and newer
coords = V.collapse().tabulate_dof_coordinates().reshape(N, D)
except:
# For 1.6.0 and older
coords = V.collapse().dofmap().tabulate_all_coordinates(
V.mesh()).reshape(N, D)
if _all_coordsb is not None:
coordsb = _all_coordsb[Vb.dofmap().dofs()]
else:
try:
# For 1.6.0+ and newer
coordsb = Vb.collapse().tabulate_dof_coordinates().reshape(
Nb, D)
except:
# For 1.6.0 and older
coordsb = Vb.collapse().dofmap().tabulate_all_coordinates(
Vb.mesh()).reshape(Nb, D)
else:
if LooseVersion(dolfin_version()) > LooseVersion("1.6.0"):
# For 1.6.0+ and newer
coords = V.tabulate_dof_coordinates().reshape(N, D)
coordsb = Vb.tabulate_dof_coordinates().reshape(Nb, D)
else:
# For 1.6.0 and older
coords = V.dofmap().tabulate_all_coordinates(V.mesh()).reshape(
N, D)
coordsb = Vb.dofmap().tabulate_all_coordinates(Vb.mesh()).reshape(
Nb, D)
# Build KDTree to compute distances from coordinates in base
kdtree = KDTree(coords)
eps = 1e-12
mapping = {}
request_dofs = np.array([])
distances, indices = kdtree.query(coordsb)
for i, subdof in enumerate(dmb.dofs()):
# Find closest dof in base
#d, idx = kdtree.query(coordsb[i])
d, idx = distances[i], indices[i]
if d < eps:
# Dof found on this process, add to map
dof = dofs[idx]
assert subdof not in mapping
mapping[subdof] = dof
else:
# Search for this dof on other processes
add_dofs = np.hstack(([subdof], coordsb[i]))
request_dofs = np.append(request_dofs, add_dofs)
del distances
del indices
# Scatter all dofs not found on current process to all processes
all_request_dofs = [None] * MPI.size(mpi_comm_world())
for j in xrange(MPI.size(mpi_comm_world())):
all_request_dofs[j] = broadcast(request_dofs, j)
# Re-order all requested dofs
# Remove items coming from this process
all_request_dofs[MPI.rank(mpi_comm_world())] = []
all_request_dofs = np.hstack(all_request_dofs)
all_request_dofs = all_request_dofs.reshape(
len(all_request_dofs) / (D + 1), D + 1)
all_request_dofs = dict(
zip(all_request_dofs[:, 0], all_request_dofs[:, 1:]))
# Search this process for all dofs not found on same process as subdof
for subdof, coordsbi in all_request_dofs.items():
subdof = int(subdof)
# Find closest dof in base
d, idx = kdtree.query(coordsbi)
if d < eps:
# Dof found on this process, add to map
dof = dofs[idx]
assert subdof not in mapping
mapping[subdof] = dof
return mapping
def solve(self, problem, timer):
assert isinstance(problem, FSIProblem)
mesh = problem.mesh
bmesh = BoundaryMesh(mesh, "exterior")
dim = mesh.geometry().dim()
dx = problem.dx
ds = problem.ds
n = FacetNormal(mesh)
dt, timesteps, start_timestep = compute_regular_timesteps(problem)
dt = Constant(dt)
t = Constant(timesteps[start_timestep], name="TIME")
# Function spaces
spaces = NSSpacePoolSplit(mesh, self.params.u_degree,
self.params.p_degree)
V = spaces.V
Q = spaces.Q
D = spaces.spacepool.get_custom_space("CG", 1, (dim, ))
Db = spaces.spacepool.get_custom_space("CG", 1, (dim, ), boundary=True)
Dgb = spaces.spacepool.get_custom_space("CG",
1, (dim, ),
boundary=True)
# Trial- and testfunctions
u, v = TrialFunction(V), TestFunction(V) # Velocity
p, q = TrialFunction(Q), TestFunction(Q) # Pressure
eta, x = TrialFunction(Dgb), TestFunction(Dgb) # Boundary displacement
d, e = TrialFunction(D), TestFunction(D) # Mesh displacement
# Solution functions
U = Function(V) # Velocity
P = Function(Q) # Pressure
DF = Function(D) # Fluid (full mesh) displacement
# Helper functions
U1 = Function(V)
U2 = Function(V)
DF1 = Function(D)
DF2 = Function(D)
ETA1 = Function(Dgb) # eta time derivatives
Uext = Extrapolation(V, self.params.r) # Velocity extrapolation
Pext = Extrapolation(Q, self.params.s) # Pressure extrapolation
phi = p - Pext
phiext = Extrapolation(Q, self.params.r)
DFext = Extrapolation(D, self.params.s)
DFext1, DFext2 = Function(D), Function(D)
w = Function(D)
db = Function(Db)
dgb = Function(Dgb)
dgb1, dgb2 = Function(Dgb), Function(Dgb)
traction = Function(Dgb)
# Get functions for data assimilation
observations = problem.observations(spaces, t)
controls = problem.controls(spaces)
# Make scheme-specific representation of bcs
bcs = problem.boundary_conditions(spaces, U, P, t, None)
bcu = make_velocity_bcs(problem, spaces, bcs)
bcp = make_pressure_bcs(problem, spaces, bcs)
bcs_eta = [DirichletBC(D, DF, DomainBoundary())
] # Are these for eta or full (fluid) mesh displacement?
bcs_eta += [
DirichletBC(D, expr, problem.facet_domains, i)
for expr, i in bcs[2]
]
# Dgb defined in bdry_mesh, facet domains on mesh
# Create a facet
dgb_mesh = Dgb.mesh()
dgb_dim = dgb_mesh.topology().dim()
eta_boundaries = MeshFunction('size_t', dgb_mesh, dgb_dim - 1)
eta_boundaries.set_all(0)
Left().mark(eta_boundaries, 1)
Right().mark(eta_boundaries, 2)
#plot(eta_boundaries, interactive=True)
#embed()
#sys.exit()
#bcs_shell = [DirichletBC(Dgb, expr, DomainBoundary(), method="pointwise") for expr, i in bcs[2]] # really for eta
#shellbc1 = DirichletBC(Dgb, Constant((0, 0)), eta_boundaries, 1, method="pointwise")
#shellbc2 = DirichletBC(Dgb, Constant((0, 0)), eta_boundaries, 2, method="pointwise")
shellbc1 = DirichletBC(Dgb, Constant((0, 0)), eta_boundaries, 1)
shellbc2 = DirichletBC(Dgb, Constant((0, 0)), eta_boundaries, 2)
bcs_shell = [shellbc1, shellbc2]
#embed()
#sys.exit()
# Create boundary integrals over structure and non-structure part of mesh
# nds = non-fixed part of boundary
# fds = fixed part of boundary (has bcs for displacement)
fixed_boundaries = [i for _, i in bcs[2]] # bc2 is bceta
nonfixed_boundaries = list(
set(np.unique(problem.facet_domains.array())) -
set(fixed_boundaries))
nonfixed_boundaries = gather(nonfixed_boundaries, 0)
nonfixed_boundaries = np.unique(np.array(nonfixed_boundaries))
nonfixed_boundaries = broadcast(nonfixed_boundaries, 0)
nonfixed_boundaries = nonfixed_boundaries.astype(np.int)
assert len(nonfixed_boundaries) > 0
nds = ds(nonfixed_boundaries[0]) # Is nds Sigma?
for i in nonfixed_boundaries[1:]:
nds += ds(i)
if len(fixed_boundaries) > 0:
fds = ds(fixed_boundaries[0]) # Is fds Gamma?
for i in fixed_boundaries[1:]:
fds += ds(i)
def par(f, n):
"Return parallel/tangential component of f"
return f - dot(f, n) * n
mu = Constant(problem.params.mu) # Fluid viscosity
rho_f = Constant(problem.params.rho) # Fluid density
rho_s = Constant(problem.params.rho_s) # Structure density
h_s = Constant(problem.params.h) # Thickness
if isinstance(problem.params.R, float):
R = Constant(problem.params.R)
else:
R = problem.params.R
beta = Constant(problem.params.E * float(h_s) /
(1 - problem.params.nu**2) * 1.0 / R**2)
beta1 = Constant(0.5 * problem.params.E * float(h_s) /
(1 + problem.params.nu))
alpha = Constant(1)
alpha1 = Constant(1e-3)
# Set up Field (see cbcpost documentation) to compute boundary traction
T_bdry = BoundaryTraction()
T_bdry.before_first_compute(lambda x: U)
r = self.params.r
s = self.params.s
I = SpatialCoordinate(mesh)
A = I + DF # ALE map
F = grad(A)
J = det(F)
# Tentative velocity, Eq. 30, mapped to reference mesh
# Eq. 30.1
a1 = inner(rho_f *
(u - U1) / dt, v) * J * dx() # Is this mapping correct?
#a1 = inner(rho_f*(u-U1)/dt, v)*dx() # Is this mapping correct?
a1 += rho_f * inner((grad(u) * inv(F)) * (U1 - w), v) * J * dx()
#a1 += rho_f*inner(grad(u)*U1, v)*dx()
a1 += inner(J * Sigma(mu, u, Pext, F) * inv(F).T, grad(v)) * dx()
#a1 += inner(sigma(mu, u, Pext), grad(v))*dx()
a1 -= inner(J * Sigma(mu, u, Pext, F) * inv(F).T * n, v) * ds()
#a1 -= inner(sigma(mu, u, Pext)*n, v)*ds()
a1 += rho_f * inner(
(grad(u) * inv(F)) * (U1 - w), v) * J * dx() # dot or *
a1 += inner(J * Sigma(mu, u, Pext, F) * inv(F).T, grad(v)) * dx()
# Eq. 30.2
#a1 += inner(sigma(mu, u, Pext)*n, v)*fds # Inflow/outflow. Should be Sigma?
a1 += inner(Sigma(mu, u, Pext, F) * n,
v) * fds # Matters only if Gamma is non-fixed?
#a1 += inner(sigma(mu, u, Pext)*n, v)*fds # Matters only if Gamma is non-fixed?
# Eq. 30.3
#a1 += inner(J*sigma(mu, u, Pext)*inv(F).T*n, v)*nds # Should be Sigma?
a1 += inner(J * Sigma(mu, u, Pext, F) * inv(F).T * n,
v) * nds # Sigma because boundary moves?
a1 += inner(sigma(mu, u, Pext) * n,
v) * nds # Sigma because boundary moves?
a1 += rho_s * h_s / dt * inner(u, v) * nds # Should contain J?
a1 -= rho_s * h_s / dt * inner(
(DF1 - DF2) / dt +
par(dt * (DFext - 2 * DFext1 + DFext2) / dt**2, n), v) * nds
# Extrapolation cases of RHS of Eq. 30.3
if r == 1:
_F = grad(I + DF1)
_J = det(_F)
#a1 -= 2*mu*inner(par(_J*Epsilon(U1, _F)*inv(_F).T*n, n), v)*nds
a1 -= 2 * mu * inner(par(epsilon(U1) * n, n), v) * nds
elif r == 2:
_F = grad(I + DF1)
_J = det(_F)
a1 -= 2 * 2 * mu * inner(
par(_J * Epsilon(U1, _F) * inv(_F).T * n, n), v) * nds
_F = grad(I + DF2)
_J = det(_F)
a1 += 2 * mu * inner(par(_J * Epsilon(U2, _F) * inv(_F).T * n, n),
v) * nds
L1 = rhs(a1)
a1 = lhs(a1)
A1 = assemble(a1)
b1 = assemble(L1)
solver_u_tent = create_solver("gmres", "additive_schwarz")
# Pressure, Eq 31, mapped to reference mesh (note phi=p - Pext)
# Eq. 31.1
#a2 = inner(J*inv(F)*inv(F).T*grad(phi), grad(q))*dx()
a2 = inner(dt / rho_f * J * inv(F) * inv(F).T * grad(phi),
grad(q)) * dx()
#a2 = inner(dt/rho_f*grad(phi), grad(q))*dx()
#a2 -= inner(J*inv(F)*inv(F).T*grad(phi), q*n)*ds()
a2 -= inner(dt / rho_f * J * inv(F) * inv(F).T * grad(phi),
q * n) * ds()
#a2 -= inner(dt/rho_f*grad(phi), q*n)*ds()
a2 += div(J * inv(F) * U) * dx()
#a2 += div(U)*dx()
# Eq. 31.2
a2 += phi * q * fds
a2 -= (P - Pext) * q * fds
# Eq. 31.3
# Why no J?
#a2 += dt/rho_f*dot(dot(grad(phi), n), q)*nds
#a2 += dt/(rho_s*h_s)*phi*q*nds
#a2 -= dt/(rho_s*h_s)*phiext*q*nds
#a2 -= inner(Uext - (DFext - DFext1)/dt, n)*q*nds
a2 += dt / rho_f * J * dot(dot(inv(F).T * grad(phi),
inv(F).T * n), q) * nds
a2 += dt / (rho_s * h_s) * J * phi * q * nds
a2 -= dt / (rho_s * h_s) * J * phiext * q * nds
a2 -= J * inner(Uext - (DFext - DFext1) / dt, inv(F).T * n) * q * nds
# J*grad(phi)*inf(F), grad(q)*inf(F)
a2 = inner(J * inv(F) * inv(F).T * grad(phi),
grad(q)) * dx() # symmetry and *
a2 -= inner(J * inv(F) * inv(F).T * grad(phi), q * n) * ds() # remove?
a2 += div(J * inv(F) * U) * dx()
#a2 += div(J*U*inv(F).T)*dx()
# Eq. 31.2
a2 += phi * q * fds # jacobian missing?
a2 -= (P - Pext) * q * fds # p_{gamma}(t_n) - Pext
# Eq. 31.3
a2 += dt / rho_f * dot(dot(grad(phi), n),
q) * nds # Are Fs and stuff missing?
a2 += dt / (rho_s * h_s) * phi * q * nds
a2 -= dt / (rho_s * h_s) * phiext * q * nds
a2 -= inner(Uext - (DFext - DFext1) / dt, n) * q * nds
L2 = rhs(a2)
a2 = lhs(a2)
A2 = assemble(a2, keep_diagonal=True)
b2 = assemble(L2)
solver_p_corr = create_solver("bicgstab", "amg")
#solver_p_corr = LinearSolver()
# Velocity correction (u^n = tilde(u)^n+tau/rho*grad phi^n)
a3 = inner(v, u) * dx()
a3 -= inner(v, U) * dx()
a3 += dt / rho_f * inner(v, grad(P - Pext)) * dx()
a3 += dt / rho_f * inner(v, grad(P - Pext)) * dx() # missing F?
L3 = rhs(a3)
a3 = lhs(a3)
A3 = assemble(a3)
b3 = assemble(L3)
solver_u_corr = create_solver("gmres", "additive_schwarz")
# Solid on boundary mesh (currently very simple model)
# Is this solid sub-step eq. 1 p. 18?
_dx = Measure("dx")
a4 = rho_s * h_s / dt**2 * inner(
eta - 2 * dgb1 + dgb2,
x) * _dx # Second time-derivative of boundary displacement
# Elastic operator
a4 += inner(beta * eta, x) * _dx
a4 += inner(beta1 * grad(eta), grad(x)) * _dx # -lambda1*dxx(eta)
# Viscous operator
a4 += inner(alpha * rho_s * h_s * (eta - ETA1) / dt, x) * _dx
a4 += inner(alpha1 * beta1 * grad((eta - ETA1) / dt), grad(x)) * _dx
a4 = rho_s * h_s / dt**2 * inner(
eta - 2 * dgb1 + dgb2,
x) * _dx # Second time-derivative of boundary displacement
a4 += inner(beta * eta, x) * _dx
#a4 += inner(PI(eta),x)*_dx
a4 += inner(traction, x) * _dx # Force term
L4 = rhs(a4)
a4 = lhs(a4)
A4 = assemble(a4)
b4 = assemble(L4)
solver_solid = create_solver("gmres", "hypre_euclid")
# Mesh displacement (solve poisson equation with boundary displacement as bcs)
a5 = inner(grad(d), grad(e)) * dx()
L5 = inner(Constant((0, ) * dim), e) * dx()
A5 = assemble(a5)
b5 = assemble(L5)
solver_displacement = create_solver(
"gmres", "hypre_euclid") # same as solid solver. Seems to work
#solver_displacement = create_solver("cg", "ml_amg") # fails to return a valid solver.
# Helper functionality for getting boundary displacement as boundary condition
local_dofmapping = boundarymesh_to_mesh_dofmap(bmesh, Db, D)
_keys, _values = zip(*local_dofmapping.iteritems())
_keys = np.array(_keys, dtype=np.intc)
_values = np.array(_values, dtype=np.intc)
ofile = open("jconst.txt", "w")
for timestep in xrange(start_timestep + 1, len(timesteps)):
t.assign(timesteps[timestep])
# Update various functions
problem.update(spaces, U, P, t, timestep, bcs, None, None)
timer.completed("problem update")
# Solve tentative velocity
assemble(a1, tensor=A1)
assemble(L1, tensor=b1)
for bc in bcu:
bc.apply(A1, b1)
#solve(A1, U.vector(), b1)
solver_u_tent.solve(A1, U.vector(), b1)
# Solve pressure correction
#assemble(a2, tensor=A2, keep_diagonal=True)
b2.apply('insert')
assemble(a2, tensor=A2)
assemble(L2, tensor=b2)
for bc in bcp:
bc.apply(A2, b2)
#solve(A2, P.vector(), b2)
b2.apply("insert")
solver_p_corr.solve(A2, P.vector(), b2)
#P-vector().zero()
#P.vector().axpy(1.0, phi.vector())
#P.vector().axpy(1.0, Pext.vector())
# Solve updated velocity
assemble(a3, tensor=A3)
assemble(L3, tensor=b3)
for bc in bcu:
bc.apply(A3, b3)
#solve(A3, U.vector(), b3)
solver_u_corr.solve(A3, U.vector(), b3)
# Solve solid
traction.assign(
T_bdry.compute(
lambda x: {
"Velocity": U,
"Pressure": P,
"DynamicViscosity": mu,
"Displacement": DF
}[x]))
assemble(a4, tensor=A4)
assemble(L4, tensor=b4)
# missing BC for eta?, i.e. a4 or is it don ethrough b4?
#for bc in bcs_shell:
# bc.apply(A4, b4)
#embed()
#sys.exit()
#b4.array()[np.array([0, -1])] = 0
#solve(A4, dgb.vector(), b4)
solver_solid.solve(A4, dgb.vector(), b4)
# Solve mesh displacement
db.interpolate(dgb) # Interpolate to vertices on boundary
get_set_vector(DF.vector(), _keys, db.vector(),
_values) # Set boundary values to function
for bc in bcs_eta:
bc.apply(A5, b5)
solver_displacement.solve(A5, DF.vector(), b5)
# Rotate functions
U1.assign(U)
DF2.assign(DF1)
DF1.assign(DF)
dgb2.assign(dgb1)
dgb1.assign(dgb)
w.assign(DF - DF1)
w.vector()[:] *= 1. / float(dt) # Mesh velocity
ETA1.assign(dgb) # FIXME: Not sure about this
# Update extrapolations
Uext.update(U)
phiext.update(P - Pext)
Pext.update(P)
DFext2.assign(DFext1)
DFext1.assign(DFext)
DFext.update(DF)
ofile.write("%s\n" % assemble(J * dx))
yield ParamDict(spaces=spaces,
observations=None,
controls=None,
t=float(t),
timestep=timestep,
u=U,
p=P,
d=DF,
state=(U, P, DF))