def _read_from_xdmf_file(fun, directory, filename, suffix, components=None):
if components is not None:
filename = filename + "_component_" + "".join(components)
function_name = "function_" + "".join(components)
else:
function_name = "function"
fun_rank = fun.value_rank()
fun_dim = product(fun.value_shape())
assert fun_rank <= 2
if ((fun_rank is 1 and fun_dim not in (2, 3))
or (fun_rank is 2 and fun_dim not in (4, 9))):
fun_V = fun.function_space()
for i in range(fun_dim):
if components is not None:
filename_i = filename + "_subcomponent_" + str(i)
else:
filename_i = filename + "_component_" + str(i)
fun_i_V = get_function_subspace(fun_V, i)
fun_i = Function(fun_i_V)
if not _read_from_xdmf_file(fun_i, directory, filename_i, suffix,
None):
return False
else:
assign(fun.sub(i), fun_i)
return True
else:
full_filename_checkpoint = os.path.join(str(directory),
filename + "_checkpoint.xdmf")
file_exists = False
if is_io_process() and os.path.exists(full_filename_checkpoint):
file_exists = True
file_exists = is_io_process.mpi_comm.bcast(file_exists,
root=is_io_process.root)
if file_exists:
if suffix is not None:
assert SuffixIO.exists_file(directory, filename + "_suffix")
last_suffix = SuffixIO.load_file(directory,
filename + "_suffix")
if suffix <= last_suffix:
if full_filename_checkpoint in _all_xdmf_files:
assert _all_xdmf_latest_suffix[
full_filename_checkpoint] == suffix - 1
_all_xdmf_latest_suffix[
full_filename_checkpoint] = suffix
else:
assert suffix == 0
_all_xdmf_files[full_filename_checkpoint] = XDMFFile(
full_filename_checkpoint)
_all_xdmf_latest_suffix[full_filename_checkpoint] = 0
_all_xdmf_files[full_filename_checkpoint].read_checkpoint(
fun, function_name, suffix)
return True
else:
return False
else:
with XDMFFile(full_filename_checkpoint) as file_checkpoint:
file_checkpoint.read_checkpoint(fun, function_name, 0)
return True
else:
return False
def _read_from_file(fun, directory, filename, suffix, components=None):
if components is not None:
filename = filename + "_component_" + "".join(components)
function_name = "function_" + "".join(components)
else:
function_name = "function"
fun_rank = fun.value_rank()
fun_dim = product(fun.value_shape())
assert fun_rank <= 2
if ((fun_rank is 1 and fun_dim not in (2, 3))
or (fun_rank is 2 and fun_dim not in (4, 9))):
funs = fun.split(deepcopy=True)
for (i, fun_i) in enumerate(funs):
if components is not None:
filename_i = filename + "_subcomponent_" + str(i)
else:
filename_i = filename + "_component_" + str(i)
_read_from_file(fun_i, directory, filename_i, suffix, None)
assign(fun.sub(i), fun_i)
else:
if suffix is not None:
if suffix is 0:
# Remove from storage and re-create
try:
del _all_solution_files[(directory, filename)]
except KeyError:
pass
_all_solution_files[(directory, filename)] = SolutionFile(
directory, filename)
file_ = _all_solution_files[(directory, filename)]
file_.read(fun, function_name, suffix)
else:
file_ = SolutionFile(directory, filename)
file_.read(fun, function_name, 0)
def initialize(self, warp, istart):
self.istart = istart
for i in xrange(istart, istart + self.N):
rad = 0.0
ist = 0
for n, d in zip(self.Ns, self.Dias):
for j in xrange(n):
print j
fib = warp.fibrils[i * np.sum(self.Ns) + ist]
qhh = Geometry_Curves.qhh_stockinette2
temp_field = Function(fib.problem.spaces['V'])
p1 = rad * np.cos(2.0 * np.pi * float(j) / float(n))
p2 = rad * np.sin(2.0 * np.pi * float(j) / float(n))
for fix in xrange(3):
temp_field.interpolate(
Expression(qhh[fix],
sq=-(self.restL - self.setL) /
self.restL,
p=np.pi / self.restL * (4.0),
o=self.setL / 3.5,
A1=1.3 * self.width / self.N,
A2=self.width / self.N,
y1=p1,
y2=p2))
assign(fib.problem.fields['wx'].sub(fix), temp_field)
temp_field.interpolate(Constant((0.0, 0.0, 0.0)))
assign(fib.problem.fields['wv'].sub(fix), temp_field)
ist += 1
rad += d
def _write_to_pvd_file(fun, directory, filename, suffix, components=None):
if components is not None:
filename = filename + "_component_" + "".join(components)
fun_rank = fun.value_rank()
fun_dim = product(fun.value_shape())
assert fun_rank <= 2
if ((fun_rank is 1 and fun_dim not in (2, 3))
or (fun_rank is 2 and fun_dim not in (4, 9))):
funs = fun.split(deepcopy=True)
for (i, fun_i) in enumerate(funs):
if components is not None:
filename_i = filename + "_subcomponent_" + str(i)
else:
filename_i = filename + "_component_" + str(i)
_write_to_pvd_file(fun_i, directory, filename_i, suffix)
else:
full_filename = os.path.join(str(directory), filename + ".pvd")
if suffix is not None:
if full_filename in _all_pvd_files:
assert _all_pvd_latest_suffix[full_filename] == suffix - 1
_all_pvd_latest_suffix[full_filename] = suffix
else:
assert suffix == 0
_all_pvd_files[full_filename] = File(full_filename,
"compressed")
_all_pvd_latest_suffix[full_filename] = 0
_all_pvd_functions[full_filename] = fun.copy(deepcopy=True)
# Make sure to always use the same function, otherwise dolfin
# changes the numbering and visualization is difficult in ParaView
assign(_all_pvd_functions[full_filename], fun)
_all_pvd_files[full_filename] << _all_pvd_functions[full_filename]
else:
file_ = File(full_filename, "compressed")
file_ << fun
def hessianab(self, m1h, m2h):
""" m1h, m2h = Vector(V) """
setfct(self.m1, m1h)
setfct(self.m2, m2h)
assign(self.m.sub(0), self.m1)
assign(self.m.sub(1), self.m2)
return self.regTV.hessian(self.m.vector())
def hessianab(self, m1h, m2h):
""" m1h, m2h = Vector(V) """
setfct(self.m1h, m1h)
setfct(self.m2h, m2h)
assign(self.m12h.sub(0), self.m1h)
assign(self.m12h.sub(1), self.m2h)
return self.H * self.m12h.vector()
def hessianab(self, ahat, bhat):
""" ahat, bhat = Vector(V) """
setfct(self.ahat, ahat)
setfct(self.bhat, bhat)
assign(self.abhat.sub(0), self.ahat)
assign(self.abhat.sub(1), self.bhat)
return self.H * self.abhat.vector()
def solve(self, sol, rhs):
"""
Solve A.sol = rhs
Arguments:
sol = solution
rhs = rhs
"""
self.ab.vector().zero()
self.ab.vector().axpy(1.0, rhs)
a, b = self.ab.split(deepcopy=True)
xa, xb = self.X.split(deepcopy=True)
if self.param == 'a':
n_pcg = self.solver.solve(xa.vector(), a.vector())
xb.vector().zero()
xb.vector().axpy(1.0, b.vector())
elif self.param == 'b':
xa.vector().zero()
xa.vector().axpy(1.0, a.vector())
n_pcg = self.solver.solve(xb.vector(), b.vector())
dl.assign(self.X.sub(0), xa)
dl.assign(self.X.sub(1), xb)
sol.zero()
sol.axpy(1.0, self.X.vector())
return n_pcg
def diffusivity_field_simple(setup, r, ddata_bulk, boundary="poresolidb"):
"interpolates diffusivity field defined on the geometry given by setup"
# build 1D interpolations from data
fn, ft = preprocess_Dr(ddata_bulk, r)
setup.prerefine(visualize=True)
dist = distance_boundary_from_geo(setup.geo, boundary)
VV = dolfin.VectorFunctionSpace(setup.geo.mesh, "CG", 1)
normal = dolfin.project(dolfin.grad(dist), VV)
phys = setup.phys
D0 = phys.kT / (6. * np.pi * phys.eta * r * 1e-9)
def DBulk(x, i):
r = dist(x)
n = normal(x)
Dn = D0 * float(fn(r))
Dt = D0 * float(ft(r))
D = transformation(n, Dn, Dt)
return D[i][i]
D = lambda i: dict(fluid=lambda x: DBulk(x, i), )
dim = setup.geop.dim
DD = [harmonic_interpolation(setup, subdomains=D(i)) for i in range(dim)]
D = dolfin.Function(VV)
dolfin.assign(D, DD)
return dict(dist=dist, D=D)
def block_assign(object_to, object_from):
assert isinstance(object_to, BlockFunction) and isinstance(
object_from, BlockFunction)
as_backend_type(object_from.block_vector()).vec().copy(
as_backend_type(object_to.block_vector()).vec())
object_to.block_vector().apply("insert")
for (function_to, function_from) in zip(object_to, object_from):
assign(function_to, function_from)
def solve(self):
assert not hasattr(self, "_is_solving")
self._is_solving = True
f00 = project(self.f00, self.V00)
f01 = project(self.f01, self.V00)
assign(self._solution.sub(0).sub(0), f00)
assign(self._solution.sub(0).sub(1), f01)
delattr(self, "_is_solving")
return self._solution
def solve(self):
print("solving mock problem at mu =", self.mu)
assert not hasattr(self, "_is_solving")
self._is_solving = True
f00 = project(self.f00, self.V00)
f01 = project(self.f01, self.V00)
assign(self._solution.sub(0).sub(0), f00)
assign(self._solution.sub(0).sub(1), f01)
delattr(self, "_is_solving")
return self._solution
def function_load(fun, directory, filename, suffix=None):
fun_V = fun.function_space()
if hasattr(fun_V, "_index_to_components") and len(fun_V._index_to_components) > 1:
for (index, components) in fun_V._index_to_components.items():
sub_fun_V = get_function_subspace(fun_V, components)
sub_fun = Function(sub_fun_V)
_read_from_file(sub_fun, directory, filename, suffix, components)
assign(fun.sub(index), sub_fun)
else:
_read_from_file(fun, directory, filename, suffix)
def _split_func_to_vec(self, function):
"""
Given a split object (after a function.split(), returns a unified vector representation
:param function: tuple of functions after split
:return: dolfin.vector with elements assigned according to function values
"""
dolf_function = dolf.Function(self.forms.function_space)
for i in range(len(function)):
dolf.assign(dolf_function.sub(i), function[i])
return dolf_function.vector()
def update(self, f, field, step):
""" Set dolfin vector f with values from field. """
if field == "u":
u_data = self["u", step][:, :self.dim]
for i in range(self.dim):
self.set_val(self.dummy_function, u_data[:, i])
df.assign(f.sub(i), self.dummy_function)
else:
f_data = self[field, step][:]
self.set_val(f, f_data)
def reconstruct_solution(reduced_solution, N):
(mesh, _, _, restrictions) = read_mesh()
W = generate_block_function_space(mesh, restrictions)
reconstructed_solution = BlockFunction(W)
basis_functions = read_basis_functions(W, N)
for c in components:
assign(reconstructed_solution.sub(c),
(basis_functions[c] * reduced_solution[c]).sub(c))
reconstructed_solution.apply("from subfunctions")
return reconstructed_solution
def mult(self, ahat, y):
self.ahat.vector().zero()
self.ahat.vector().axpy(1.0, ahat)
self.abhat.vector().zero()
dl.assign(self.abhat.sub(0), self.ahat)
self.obj.mult(self.abhat.vector(), self.yab.vector())
ya, yb = self.yab.split(deepcopy=True)
y.zero()
y.axpy(1.0, ya.vector())
y.axpy(1.0, self.regul.hessian(ahat))
def compare_ab_global(self):
"""
Check that med param (a, b) are the same across all proc
"""
assign(self.ab.sub(0), self.PDE.a)
assign(self.ab.sub(1), self.PDE.b)
ab_recv = self.ab.vector().copy()
normabloc = np.linalg.norm(self.ab.vector().array())
MPIAllReduceVector(self.ab.vector(), ab_recv, self.mpicomm_global)
ab_recv /= MPI.size(self.mpicomm_global)
diff = ab_recv - self.ab.vector()
reldiff = np.linalg.norm(diff.array())/normabloc
assert reldiff < 2e-16, 'Diff in (a,b) across proc: {:.2e}'.format(reldiff)
def solve_time_step(self, t):
A = self.assembler.getMatrix()
P, P_diff = self.assembler.getPreconditioners()
b = self.assembler.getRHS(t, self.us_nm1, self.us_nm2, self.uf_nm1,
self.p_nm1)
for bc in self.bcs:
for obj in [A, P, b]:
bc.apply(obj)
if self.three_way:
bc.apply(P_diff)
if self.three_way:
for bc in self.bcs_diff:
bc.apply(P_diff)
if self.first_timestep:
self.create_solver(A, P, P_diff, b)
self.first_timestep = False
self.solver.set_up()
self.solver.solve(b.vec(), self.sol.vector().vec())
self.sol.vector().apply("") # Update ghost dofs
# Update solution
us, uf, p = self.sol.split(True)
df.assign(self.us_nm2, self.us_nm1)
df.assign(self.us_nm1, us)
df.assign(self.uf_nm1, uf)
df.assign(self.p_nm1, p)
return self.solver.getIterationNumber()
def initialize(self, warp, istart):
self.istart = istart
for i in xrange(istart, istart + self.NX):
for j in xrange(np.sum(self.pattern)):
fib = warp.fibrils[i * np.sum(self.pattern) + j]
qhh = Geometry_Curves.qhh_plain_0
temp_field = Function(fib.problem.spaces['V'])
for fix in xrange(3):
temp_field.interpolate(
Expression(qhh[fix],
sq=-(self.restX - self.setX) / self.restX,
p=np.pi / self.restX * (self.NY) / 2.0,
A1=(-1.0 if i % 2 == 0 else 1.0) *
self.height))
assign(fib.problem.fields['wx'].sub(fix), temp_field)
temp_field.interpolate(Constant((0.0, 0.0, 0.0)))
assign(fib.problem.fields['wv'].sub(fix), temp_field)
for i in xrange(istart + self.NX, istart + (self.NX + self.NY)):
for j in xrange(np.sum(self.pattern)):
fib = warp.fibrils[i * np.sum(self.pattern) + j]
qhh = Geometry_Curves.qhh_plain_1
temp_field = Function(fib.problem.spaces['V'])
for fix in xrange(3):
temp_field.interpolate(
Expression(qhh[fix],
sq=-(self.restY - self.setY) / self.restY,
p=np.pi / self.restY * (self.NX) / 2.0,
A1=(-1.0 if i % 2 == 1 else 1.0) *
self.height))
assign(fib.problem.fields['wx'].sub(fix), temp_field)
temp_field.interpolate(Constant((0.0, 0.0, 0.0)))
assign(fib.problem.fields['wv'].sub(fix), temp_field)
def testsplitassign():
USEi = True
mesh = dl.UnitSquareMesh(40, 40)
V1 = dl.FunctionSpace(mesh, "Lagrange", 2)
V2 = dl.FunctionSpace(mesh, "Lagrange", 2)
if USEi:
V1V2 = createMixedFSi([V1, V2])
splitassign = SplitAndAssigni([V1, V2], mesh.mpi_comm())
else:
V1V2 = createMixedFS(V1, V2)
splitassign = SplitAndAssign(V1, V2, mesh.mpi_comm())
mpirank = dl.MPI.rank(mesh.mpi_comm())
u = dl.interpolate(dl.Expression(("x[0]*x[1]", "11+x[0]+x[1]"), degree=10),
V1V2)
uu = dl.Function(V1V2)
u1, u2 = u.split(deepcopy=True)
u1v, u2v = splitassign.split(u.vector())
u11 = dl.interpolate(dl.Expression("x[0]*x[1]", degree=10), V1)
u22 = dl.interpolate(dl.Expression("11+x[0]+x[1]", degree=10), V2)
a,b,c,d= dl.norm(u1.vector()-u1v), dl.norm(u2.vector()-u2v),\
dl.norm(u1.vector()-u11.vector()), dl.norm(u2.vector()-u22.vector())
if mpirank == 0:
print '\nSplitting an interpolated function:', a, b, c, d
if USEi:
uv = splitassign.assign([u1v, u2v])
else:
uv = splitassign.assign(u1v, u2v)
dl.assign(uu.sub(0), u11)
dl.assign(uu.sub(1), u22)
a, b = dl.norm(uv - u.vector()), dl.norm(uv - uu.vector())
if mpirank == 0:
print 'Putting it back together:', a, b
for ii in xrange(10):
u.vector()[:] = np.random.randn(len(u.vector().array()))
u1, u2 = u.split(deepcopy=True)
u1v, u2v = splitassign.split(u.vector())
if USEi:
uv = splitassign.assign([u1v, u2v])
else:
uv = splitassign.assign(u1v, u2v)
a, b = dl.norm(u1.vector() - u1v), dl.norm(u2.vector() - u2v)
c = dl.norm(uv - u.vector())
if mpirank == 0:
print 'Splitting random numbers:', a, b
print 'Putting it back together:', c
def evaluate_expression(expression, function, replaced_expression=None):
if replaced_expression is None:
replaced_expression = expression
assert isinstance(expression, (BaseExpression, Function, Operator))
if isinstance(expression, BaseExpression):
LagrangeInterpolator.interpolate(function, replaced_expression)
elif isinstance(expression, Function):
assign(function, replaced_expression)
elif isinstance(expression, Operator):
project(replaced_expression,
function.function_space(),
function=function)
else:
raise ValueError("Invalid expression")
def solve(self, opt):
""" This procedure implements a first-order
semi-Lagrangian time-stepping scheme to solve a parabolic
second-order HJB equation in non-variational form
- du/dt - sup_gamma{a^gamma : D^2 u + b^gamma * D u + c^gamma * u - f^gamma}= 0
"""
if hasattr(self, 'dt'):
opt["timeSteps"] *= opt["timeStepFactor"]
nt = opt["timeSteps"]
nc = len(self.gamma)
Tspace = np.linspace(self.T[1], self.T[0], nt + 1)
self.dt = (self.T[1] - self.T[0]) / nt
self.u_np1 = Function(self.V)
print('Setting final time conditions')
assign(self.u, project(self.u_T, self.V))
if opt["saveSolution"]:
file_u = File('./pvd/u.pvd')
file_gamma = []
for i in range(nc):
file_gamma.append(File('./pvd/gamma_{}.pvd'.format(i)))
for i, s in enumerate(Tspace[1:]):
self.current_time = s
print('Iteration {}/{}:\t t = {}'.format(i + 1, nt, s))
self.iter = i
# Update time in coefficient functions
self.updateTime(s)
assign(self.u_np1, self.u)
# Solve problem for current time step
super().solve(opt)
# self.plotControl()
# self.plotSolution()
if opt["saveSolution"]:
file_u << self.u
for i in range(nc):
try:
file_gamma[i] << self.gamma[i]
except AttributeError:
file_gamma[i] << project(self.gamma[i],
self.controlSpace[i])
def update_w(self, mhat, alphaLS, compute_what=True):
""" update dual variable in direction what
and update re-scaled version """
# Update wx and wy
if compute_what: self.compute_what(mhat)
self.regTV.wx.vector().axpy(alphaLS, self.regTV.wxhat.vector())
self.regTV.wy.vector().axpy(alphaLS, self.regTV.wyhat.vector())
# Update rescaled variables
rescaledradiusdual = self.parameters['rescaledradiusdual']
# wx**2
as_backend_type(self.regTV.wxsq).vec().pointwiseMult(\
as_backend_type(self.regTV.wx.vector()).vec(),\
as_backend_type(self.regTV.wx.vector()).vec())
# wy**2
as_backend_type(self.regTV.wysq).vec().pointwiseMult(\
as_backend_type(self.regTV.wy.vector()).vec(),\
as_backend_type(self.regTV.wy.vector()).vec())
# |w|
self.w_loc.vector().zero()
self.w_loc.vector().axpy(1.0, self.regTV.wxsq + self.regTV.wysq)
normw1, normw2 = self.w_loc.split(deepcopy=True)
normw = normw1.vector() + normw2.vector()
as_backend_type(normw).vec().sqrtabs()
# |w|/r
as_backend_type(normw).vec().pointwiseDivide(\
as_backend_type(normw).vec(),\
as_backend_type(self.one*rescaledradiusdual).vec())
# max(1.0, |w|/r)
count = pointwiseMaxCount(self.factorw.vector(), normw, 1.0)
# rescale wx and wy
assign(self.factorww.sub(0), self.factorw)
assign(self.factorww.sub(1), self.factorw)
as_backend_type(self.regTV.wxrs.vector()).vec().pointwiseDivide(\
as_backend_type(self.regTV.wx.vector()).vec(),\
as_backend_type(self.factorww.vector()).vec())
as_backend_type(self.regTV.wyrs.vector()).vec().pointwiseDivide(\
as_backend_type(self.regTV.wy.vector()).vec(),\
as_backend_type(self.factorww.vector()).vec())
minf = self.factorw.vector().min()
maxf = self.factorw.vector().max()
if self.parameters['print']:
print ('[V_TVPD] perc. dual entries rescaled={:.2f} %, ' +\
'min(factorw)={}, max(factorw)={}').format(\
100.*float(count)/self.factorw.vector().size(), minf, maxf)
def assign_scalars_to_vectorfunctions(components, vector_func):
"""
Assign the values of scalar functions to the components of a vector field.
Parameters
----------
components : list, tuple
A list/tuple of scalar-valued dolfin.Function objects used to create a
vector-valued function.
vector_func : dolfin.Function
The vector-valued dolfin.Function object that the scalar components
are to be assigned to.
"""
for i, component in enumerate(components):
dlf.assign(vector_func.sub(i), component)
return None
def load_initial_conditions(DS, c):
V_phi = DS.subspace("phi", 0, deepcopy=True)
k = V_phi.ufl_element().degree()
phi_expr = df.Expression("0.5*(1.0 - tanh((2.0*x[1] - 1.0) / eps))",
degree=k,
eps=c[r"\eps"])
_phi = df.Function(V_phi)
_phi.interpolate(phi_expr)
pv0 = DS.primitive_vars_ptl(0)
phi = pv0["phi"].split()[0]
df.assign(phi, _phi) # with uncached dofmaps
# FIXME: consider creating FunctionAssigner instances within DS
# Copy interpolated initial condition also to CTL
for i, w in enumerate(DS.solution_ptl(0)):
DS.solution_ctl()[i].assign(w)
def mediummisfit(self, target_medium):
"""
Compute medium misfit at current position
"""
assign(self.ab.sub(0), self.PDE.a)
assign(self.ab.sub(1), self.PDE.b)
try:
diff = self.ab.vector() - target_medium.vector()
except:
diff = self.ab.vector() - target_medium
Md = self.Mass*diff
self.ab.vector().zero()
self.ab.vector().axpy(1.0, Md)
Mda, Mdb = self.ab.split(deepcopy=True)
self.ab.vector().zero()
self.ab.vector().axpy(1.0, diff)
da, db = self.ab.split(deepcopy=True)
medmisfita = np.sqrt(da.vector().inner(Mda.vector()))
medmisfitb = np.sqrt(db.vector().inner(Mdb.vector()))
return medmisfita, medmisfitb
def update_w(self, alpha):
""" update w and re-scale wH """
self.w.vector().axpy(alpha, self.dw.vector())
# project each w (coord-wise) onto unit sphere to get wH
(wx, wy) = self.w.split(deepcopy=True)
wxa, wya = wx.vector().array(), wy.vector().array()
normw = np.sqrt(wxa**2 + wya**2)
factorw = [max(1.0, ii) for ii in normw]
setfct(wx, wxa/factorw)
setfct(wy, wya/factorw)
assign(self.wH.sub(0), wx)
assign(self.wH.sub(1), wy)
# check
(wx,wy) = self.wH.split(deepcopy=True)
wxa, wya = wx.vector().array(), wy.vector().array()
assert np.amax(np.sqrt(wxa**2 + wya**2)) <= 1.0 + 1e-14
# Print results
dualresnorm = assemble(self.dualresnorm)
normgraddm = assemble(self.normgraddm)
print 'line search dual variable: max(|w|)={}, err(w,df)={}, |grad(dm)|={}'.\
format(np.amax(np.sqrt(normw)), np.sqrt(dualresnorm), np.sqrt(normgraddm))
def prepare_initial_condition(DS):
phi_cpp = """
class Expression_phi : public Expression
{
public:
double depth, eps, width_factor;
Expression_phi()
: Expression(), depth(0.5), eps(0.125), width_factor(1.0) {}
void eval(Array<double>& value, const Array<double>& x) const
{
double r = x[1] - depth;
if (r <= -0.5*width_factor*eps)
value[0] = 1.0;
else if (r >= 0.5*width_factor*eps)
value[0] = 0.0;
else
value[0] = 0.5*(1.0 - tanh(2.*r/eps));
}
};
"""
phi_prm = dict(eps=0.125, width_factor=3.0)
# Load ic for phi_0
_phi = dolfin.Function(DS.subspace("phi", 0, deepcopy=True))
expr = dolfin.Expression(phi_cpp, element=_phi.ufl_element())
for key, val in six.iteritems(phi_prm):
setattr(expr, key, val)
_phi.interpolate(expr)
pv0 = DS.primitive_vars_ptl(0)
phi = pv0["phi"].split()[0]
dolfin.assign(phi, _phi) # with uncached dofmaps
# Copy interpolated initial condition also to CTL
for i, w in enumerate(DS.solution_ptl(0)):
DS.solution_ctl()[i].assign(w)
return _phi
def data_to_S1(x, y, mesh, **values):
"2D data clouds of vector valued functions => dolfin S1 functions"
trid = dln.Triangulation(x, y)
#mesh = nanopores.RectangleMesh([0, -Ry], [Rx, Ry], Nx, Ny)
functions = []
for F in values.values():
Fi = [None] * 2
for i in (0, 1):
intp = trid.nn_interpolator(F[:, i])
intp2 = lambda x: intp([x[0]], [x[1]])
Fi[i] = lambda_to_S1(intp2, mesh)
V = dolfin.VectorFunctionSpace(mesh, "CG", 1)
FF = dolfin.Function(V)
dolfin.assign(FF, [Fi[0], Fi[1]])
functions.append(FF)
if len(functions) == 1:
return functions[0]
else:
return tuple(functions)
def _read_from_file(fun, directory, filename, suffix, components=None):
if components is not None:
filename = filename + "_component_" + "".join(components)
function_name = "function_" + "".join(components)
else:
function_name = "function"
fun_V_element = fun.function_space().ufl_element()
if isinstance(fun_V_element, MixedElement) and not isinstance(
fun_V_element, (TensorElement, VectorElement)):
funs = fun.split(deepcopy=True)
for (i, fun_i) in enumerate(funs):
if components is not None:
filename_i = filename + "_subcomponent_" + str(i)
else:
filename_i = filename + "_component_" + str(i)
_read_from_file(fun_i, directory, filename_i, suffix, None)
assign(fun.sub(i), fun_i)
else:
if fun_V_element.family() == "Real":
SolutionFile = SolutionFileXML
else:
if has_hdf5() and has_hdf5_parallel():
SolutionFile = SolutionFileXDMF
else:
SolutionFile = SolutionFileXML
if suffix is not None:
if suffix == 0:
# Remove from storage and re-create
try:
del _all_solution_files[(directory, filename)]
except KeyError:
pass
_all_solution_files[(directory, filename)] = SolutionFile(
directory, filename)
file_ = _all_solution_files[(directory, filename)]
file_.read(fun, function_name, suffix)
else:
file_ = SolutionFile(directory, filename)
file_.read(fun, function_name, 0)
from dolfin import (Constant, DirichletBC, Function, FunctionSpace, Point,
RectangleMesh, TestFunction, dx, grad, inner, interactive, near, plot,
solve, assign, interpolate, Expression, dot)
v = Constant((1.0, 0.0))
def left(x, on_boundary):
return on_boundary and near(x[0], 0.0)
mesh = RectangleMesh(Point(0.0, 0.0), Point(1.0, 1.0), 50, 50)
dt = 0.001
S = FunctionSpace(mesh, 'CG', 1)
T = Function(S)
T0 = interpolate(Expression("1.0 / (10.0 * x[0] + 1.0)"), S)
T_t = TestFunction(S)
r = (T_t * ((T - T0) + dt * dot(v, grad(T)))) * dx
bc1 = DirichletBC(S, 1.0, left)
t = 0.0
while t <= 1.0:
solve(r == 0, T, [bc1])
assign(T0, T)
plot(T, mesh)
t += dt
def run_with_params(Tb, mu_value, k_s, path):
run_time_init = clock()
mesh = BoxMesh(Point(0.0, 0.0, 0.0), Point(mesh_width, mesh_width, mesh_height), nx, ny, nz)
pbc = PeriodicBoundary()
WE = VectorElement('CG', mesh.ufl_cell(), 2)
SE = FiniteElement('CG', mesh.ufl_cell(), 1)
WSSS = FunctionSpace(mesh, MixedElement(WE, SE, SE, SE), constrained_domain=pbc)
# W = FunctionSpace(mesh, WE, constrained_domain=pbc)
# S = FunctionSpace(mesh, SE, constrained_domain=pbc)
W = WSSS.sub(0).collapse()
S = WSSS.sub(1).collapse()
temperature_vals = [27.0 + 273, Tb + 273, 1300.0 + 273, 1305.0 + 273]
temp_prof = TemperatureProfile(temperature_vals, element=S.ufl_element())
mu_a = mu_value # this was taken from the Blankenbach paper, can change
Ep = b / temp_prof.delta
mu_bot = exp(-Ep * (temp_prof.bottom * temp_prof.delta - 1573.0) + cc) * mu_a
# TODO: verify exponentiation
Ra = rho_0 * alpha * g * temp_prof.delta * h ** 3 / (kappa_0 * mu_a)
w0 = rho_0 * alpha * g * temp_prof.delta * h ** 2 / mu_a
tau = h / w0
p0 = mu_a * w0 / h
log(mu_a, mu_bot, Ra, w0, p0)
slip_vx = 1.6E-09 / w0 # Non-dimensional
slip_velocity = Constant((slip_vx, 0.0, 0.0))
zero_slip = Constant((0.0, 0.0, 0.0))
time_step = 3.0E11 / tau * 2
dt = Constant(time_step)
t_end = 3.0E15 / tau / 5.0 # Non-dimensional times
u = Function(WSSS)
# Instead of TrialFunctions, we use split(u) for our non-linear problem
v, p, T, Tf = split(u)
v_t, p_t, T_t, Tf_t = TestFunctions(WSSS)
T0 = interpolate(temp_prof, S)
mu_exp = Expression('exp(-Ep * (T_val * dTemp - 1573.0) + cc * x[2] / mesh_height)',
Ep=Ep, dTemp=temp_prof.delta, cc=cc, mesh_height=mesh_height, T_val=T0,
element=S.ufl_element())
Tf0 = interpolate(temp_prof, S)
mu = Function(S)
v0 = Function(W)
v_theta = (1.0 - theta) * v0 + theta * v
T_theta = (1.0 - theta) * T0 + theta * T
Tf_theta = (1.0 - theta) * Tf0 + theta * Tf
# TODO: Verify forms
r_v = (inner(sym(grad(v_t)), 2.0 * mu * sym(grad(v)))
- div(v_t) * p
- T * v_t[2]) * dx
r_p = p_t * div(v) * dx
heat_transfer = Constant(k_s) * (Tf_theta - T_theta) * dt
r_T = (T_t * ((T - T0) + dt * inner(v_theta, grad(T_theta))) # TODO: Inner vs dot
+ (dt / Ra) * inner(grad(T_t), grad(T_theta))
- T_t * heat_transfer) * dx
v_melt = Function(W)
z_hat = Constant((0.0, 0.0, 1.0))
# TODO: inner -> dot, take out Tf_t
r_Tf = (Tf_t * ((Tf - Tf0) + dt * inner(v_melt, grad(Tf_theta)))
+ Tf_t * heat_transfer) * dx
r = r_v + r_p + r_T + r_Tf
bcv0 = DirichletBC(WSSS.sub(0), zero_slip, top)
bcv1 = DirichletBC(WSSS.sub(0), slip_velocity, bottom)
bcv2 = DirichletBC(WSSS.sub(0).sub(1), Constant(0.0), back)
bcv3 = DirichletBC(WSSS.sub(0).sub(1), Constant(0.0), front)
bcp0 = DirichletBC(WSSS.sub(1), Constant(0.0), bottom)
bct0 = DirichletBC(WSSS.sub(2), Constant(temp_prof.surface), top)
bct1 = DirichletBC(WSSS.sub(2), Constant(temp_prof.bottom), bottom)
bctf1 = DirichletBC(WSSS.sub(3), Constant(temp_prof.bottom), bottom)
bcs = [bcv0, bcv1, bcv2, bcv3, bcp0, bct0, bct1, bctf1]
t = 0
count = 0
files = DefaultDictByKey(partial(create_xdmf, path))
while t < t_end:
mu.interpolate(mu_exp)
rhosolid = rho_0 * (1.0 - alpha * (T0 * temp_prof.delta - 1573.0))
deltarho = rhosolid - rho_melt
# TODO: project (accuracy) vs interpolate
assign(v_melt, project(v0 - darcy * (grad(p) * p0 / h - deltarho * z_hat * g) / w0, W))
# TODO: Written out one step later?
# v_melt.assign(v0 - darcy * (grad(p) * p0 / h - deltarho * yvec * g) / w0)
# TODO: use nP after to avoid projection?
solve(r == 0, u, bcs)
nV, nP, nT, nTf = u.split() # TODO: write with Tf, ... etc
if count % output_every == 0:
time_left(count, t_end / time_step, run_time_init) # TODO: timestep vs dt
# TODO: Make sure all writes are to the same function for each time step
files['T_fluid'].write(nTf, t)
files['p'].write(nP, t)
files['v_solid'].write(nV, t)
files['T_solid'].write(nT, t)
files['mu'].write(mu, t)
files['v_melt'].write(v_melt, t)
files['gradp'].write(project(grad(nP), W), t)
files['rho'].write(project(rhosolid, S), t)
files['Tf_grad'].write(project(grad(Tf), W), t)
files['advect'].write(project(dt * dot(v_melt, grad(nTf))), t)
files['ht'].write(project(heat_transfer, S), t)
assign(T0, nT)
assign(v0, nV)
assign(Tf0, nTf)
t += time_step
count += 1
log('Case mu={}, Tb={}, k={} complete. Run time = {:.2f} minutes'.format(mu_a, Tb, k_s, (clock() - run_time_init) / 60.0))
def RunJob(Tb, mu_value, path):
runtimeInit = clock()
tfile = File(path + '/t6t.pvd')
mufile = File(path + "/mu.pvd")
ufile = File(path + '/velocity.pvd')
gradpfile = File(path + '/gradp.pvd')
pfile = File(path + '/pstar.pvd')
parameters = open(path + '/parameters', 'w', 0)
vmeltfile = File(path + '/vmelt.pvd')
rhofile = File(path + '/rhosolid.pvd')
for name in dir():
ev = str(eval(name))
if name[0] != '_' and ev[0] != '<':
parameters.write(name + ' = ' + ev + '\n')
temp_values = [27. + 273, Tb + 273, 1300. + 273, 1305. + 273]
dTemp = temp_values[3] - temp_values[0]
temp_values = [x / dTemp for x in temp_values] # non dimensionalising temp
mu_a = mu_value # this was taken from the blankenbach paper, can change..
Ep = b / dTemp
mu_bot = exp(-Ep * (temp_values[3] * dTemp - 1573) + cc) * mu_a
Ra = rho_0 * alpha * g * dTemp * h**3 / (kappa_0 * mu_a)
w0 = rho_0 * alpha * g * dTemp * h**2 / mu_a
tau = h / w0
p0 = mu_a * w0 / h
print(mu_a, mu_bot, Ra, w0, p0)
vslipx = 1.6e-09 / w0
vslip = Constant((vslipx, 0.0)) # nondimensional
noslip = Constant((0.0, 0.0))
dt = 3.E11 / tau
tEnd = 3.E13 / tau # non-dimensionalising times
class PeriodicBoundary(SubDomain):
def inside(self, x, on_boundary):
return left(x, on_boundary)
def map(self, x, y):
y[0] = x[0] - MeshWidth
y[1] = x[1]
pbc = PeriodicBoundary()
class TempExp(Expression):
def eval(self, value, x):
if x[1] >= LAB(x):
value[0] = temp_values[0] + (temp_values[1] - temp_values[0]) * (MeshHeight - x[1]) / (MeshHeight - LAB(x))
else:
value[0] = temp_values[3] - (temp_values[3] - temp_values[2]) * (x[1]) / (LAB(x))
class FluidTemp(Expression):
def eval(self, value, x):
if value[0] < 1295:
value[0] = 1295
mesh = RectangleMesh(Point(0.0, 0.0), Point(MeshWidth, MeshHeight), nx, ny)
Svel = VectorFunctionSpace(mesh, 'CG', 2, constrained_domain=pbc)
Spre = FunctionSpace(mesh, 'CG', 1, constrained_domain=pbc)
Stemp = FunctionSpace(mesh, 'CG', 1, constrained_domain=pbc)
Smu = FunctionSpace(mesh, 'CG', 1, constrained_domain=pbc)
Sgradp = VectorFunctionSpace(mesh, 'CG', 2, constrained_domain=pbc)
Srho = FunctionSpace(mesh, 'CG', 1, constrained_domain=pbc)
S0 = MixedFunctionSpace([Svel, Spre, Stemp])
u = Function(S0)
v, p, T = split(u)
v_t, p_t, T_t = TestFunctions(S0)
T0 = interpolate(TempExp(), Stemp)
muExp = Expression('exp(-Ep * (T_val * dTemp - 1573) + cc * x[2] / meshHeight)', Smu.ufl_element(),
Ep=Ep, dTemp=dTemp, cc=cc, meshHeight=MeshHeight, T_val=T0)
mu = interpolate(muExp, Smu)
rhosolid = Function(Srho)
deltarho = Function(Srho)
v0 = Function(Svel)
vmelt = Function(Svel)
v_theta = (1. - theta)*v0 + theta*v
T_theta = (1. - theta)*T + theta*T0
r_v = (inner(sym(grad(v_t)), 2.*mu*sym(grad(v))) \
- div(v_t)*p \
- T*v_t[1] )*dx
r_p = p_t*div(v)*dx
r_T = (T_t*((T - T0) \
+ dt*inner(v_theta, grad(T_theta))) \
+ (dt/Ra)*inner(grad(T_t), grad(T_theta)) )*dx
# + k_s*(Tf-T_theta)*dt
Tf = T0.interpolate(FluidTemp())
# Tf = T0.interpolate(Expression('value[0] >= 1295.0 ? value[0] : 1295.0'))
# Tf.interpolate(Expression('value[0] >= 1295 ? value[0] : 1295'))
# project(Expression('value[0] >= 1295 ? value[0] : 1295'), Tf)
# Alex, a question for you:
# can you see if there is a way to set Tf = T in regions where T >=1295 celsius
#
# 1295 celsius is my arbitrary choice for the LAB isotherm. In regions
# where T < 1295 C, set Tf to be some constant for now, such as 1295 C.
# Once we do this, then we can add in a term like that last line above where
# it will only be non-zero when the solid temperature, T, is cooler than 1295
# can you do this? After this is done, we will then worry about a calculation
# where we solve for Tf as a function of time in the regions cooler than 1295 C
# Makes sense? If not, we can skype soon -- email me with questions
# 3/19/16
r = r_v + r_p + r_T
bcv0 = DirichletBC(S0.sub(0), noslip, top)
bcv1 = DirichletBC(S0.sub(0), vslip, bottom)
bcp0 = DirichletBC(S0.sub(1), Constant(0.0), bottom)
bct0 = DirichletBC(S0.sub(2), Constant(temp_values[0]), top)
bct1 = DirichletBC(S0.sub(2), Constant(temp_values[3]), bottom)
bcs = [bcv0, bcv1, bcp0, bct0, bct1]
t = 0
count = 0
while (t < tEnd):
solve(r == 0, u, bcs)
t += dt
nV, nP, nT = u.split()
gp = grad(nP)
rhosolid = rho_0 * (1 - alpha * (nT * dTemp - 1573))
deltarho = rhosolid - rhomelt
yvec = Constant((0.0, 1.0))
vmelt = nV * w0 - darcy * (gp * p0 / h - deltarho * yvec * g)
if (count % 100 == 0):
pfile << nP
ufile << nV
tfile << nT
mufile << mu
gradpfile << project(grad(nP), Sgradp)
mufile << project(mu * mu_a, Smu)
rhofile << project(rhosolid, Srho)
vmeltfile << project(vmelt, Svel)
count += 1
assign(T0, nT)
assign(v0, nV)
mu.interpolate(muExp)
print('Case mu=%g, Tb=%g complete.' % (mu_a, Tb), ' Run time =', clock() - runtimeInit, 's')
def solve(
mesh,
W_element, P_element, Q_element,
u0, p0, theta0,
kappa, rho, mu, cp,
g, extra_force,
heat_source,
u_bcs, p_bcs,
theta_dirichlet_bcs,
theta_neumann_bcs,
dx_submesh, ds_submesh
):
# First do a fixed_point iteration. This is usually quite robust and leads
# to a point from where Newton can converge reliably.
u0, p0, theta0 = solve_fixed_point(
mesh,
W_element, P_element, Q_element,
theta0,
kappa, rho, mu, cp,
g, extra_force,
heat_source,
u_bcs, p_bcs,
theta_dirichlet_bcs,
theta_neumann_bcs,
my_dx=dx_submesh,
my_ds=ds_submesh,
max_iter=100,
tol=1.0e-8
)
WPQ = FunctionSpace(
mesh, MixedElement([W_element, P_element, Q_element])
)
uptheta0 = Function(WPQ)
# Initial guess
assign(uptheta0.sub(0), u0)
assign(uptheta0.sub(1), p0)
assign(uptheta0.sub(2), theta0)
rho_const = rho(_average(theta0))
stokes_heat_problem = StokesHeat(
WPQ,
kappa, rho, rho_const, mu, cp,
g, extra_force,
heat_source,
u_bcs, p_bcs,
theta_dirichlet_bcs=theta_dirichlet_bcs,
theta_neumann_bcs=theta_neumann_bcs,
my_dx=dx_submesh,
my_ds=ds_submesh
)
# solver = FixedPointSolver()
from dolfin import PETScSNESSolver
solver = PETScSNESSolver()
# http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/SNES/SNESType.html
solver.parameters['method'] = 'newtonls'
# The Jacobian system for Stokes (+heat) are hard to solve.
# Use LU for now.
solver.parameters['linear_solver'] = 'lu'
solver.parameters['maximum_iterations'] = 100
# TODO tighten tolerance. might not always work though...
solver.parameters['absolute_tolerance'] = 1.0e-3
solver.parameters['relative_tolerance'] = 0.0
solver.parameters['report'] = True
solver.solve(stokes_heat_problem, uptheta0.vector())
# u0, p0, theta0 = split(uptheta0)
# Create a *deep* copy of u0, p0, theta0 to be able to deal with them
# as actually separate entities vectors.
u0, p0, theta0 = uptheta0.split(deepcopy=True)
return u0, p0, theta0