def run(self):
domain = self._create_domain()
mesh = generate_mesh(domain, MESH_PTS)
# fe.plot(mesh)
# plt.show()
self._create_boundary_expression()
Omega = fe.FiniteElement("Lagrange", mesh.ufl_cell(), 1)
R = fe.FiniteElement("Real", mesh.ufl_cell(), 0)
W = fe.FunctionSpace(mesh, Omega*R)
Theta, c = fe.TrialFunction(W)
v, d = fe.TestFunctions(W)
sigma = self.conductivity
LHS = (sigma * fe.inner(fe.grad(Theta), fe.grad(v)) + c*v + Theta*d) * fe.dx
RHS = self.boundary_exp * v * fe.ds
w = fe.Function(W)
fe.solve(LHS == RHS, w)
Theta, c = w.split()
print(c(0, 0))
# fe.plot(Theta, "solution", mode='color', vmin=-3, vmax=3)
# plt.show()
plot(fe.interpolate(Theta, fe.FunctionSpace(mesh, Omega)), mode='color')
plt.show()
def initWeakFormulation():
"""Define function spaces etc. to initialize weak formulation."""
P = fe.FiniteElement('P', mesh.ufl_cell(), 1)
V = fe.FunctionSpace(mesh, 'P', 1)
auxP = []
for k in range(nEvenMoments):
auxP.append(P)
VVec = fe.FunctionSpace(mesh, fe.MixedElement(auxP))
auxV = []
for k in range(nEvenMoments):
auxV.append(V)
assigner = fe.FunctionAssigner(auxV, VVec)
v = fe.TestFunctions(VVec)
u = fe.TrialFunctions(VVec)
uSol = fe.Function(VVec)
uSolComponents = []
for k in range(nEvenMoments):
uSolComponents.append(fe.Function(V))
# FEniCS work-around
if N_PN == 1:
solAssignMod = lambda uSolComponents, uSol: [
assigner.assign(uSolComponents[0], uSol)
]
else:
solAssignMod = lambda uSolComponents, uSol: assigner.assign(
uSolComponents, uSol)
return u, v, V, uSol, uSolComponents, solAssignMod
def __init__(self,
mesh: fe.Mesh,
density: fe.Expression,
constitutive_model: ConstitutiveModelBase,
bf: fe.Expression = fe.Expression('0', degree=0)):
self._mesh = mesh
self._density = density
self._constitutive_model = constitutive_model
self.bf = bf
element_v = fe.VectorElement("P", mesh.ufl_cell(), 1)
element_s = fe.FiniteElement("P", mesh.ufl_cell(), 1)
mixed_element = fe.MixedElement([element_v, element_v, element_s])
W = fe.FunctionSpace(mesh, mixed_element)
# Unknowns, values at previous step and test functions
w = fe.Function(W)
self.u, self.v, self.p = fe.split(w)
w0 = fe.Function(W)
self.u0, self.v0, self.p0 = fe.split(w0)
self.a0 = fe.Function(fe.FunctionSpace(mesh, element_v))
self.ut, self.vt, self.pt = fe.TestFunctions(W)
self.F = kin.def_grad(self.u)
self.F0 = kin.def_grad(self.u0)
def setup_governing_form(self):
""" Implement the variational form per @cite{zimmerman2018monolithic}. """
Pr = fenics.Constant(self.prandtl_number)
Ste = fenics.Constant(self.stefan_number)
f_B = self.make_buoyancy_function()
phi = self.make_semi_phasefield_function()
mu = self.make_phase_dependent_material_property_function(
P_L=fenics.Constant(self.liquid_viscosity),
P_S=fenics.Constant(self.solid_viscosity))
gamma = fenics.Constant(self.penalty_parameter)
p, u, T = fenics.split(self.state.solution)
u_t, T_t, phi_t = self.make_time_discrete_terms()
psi_p, psi_u, psi_T = fenics.TestFunctions(self.function_space)
dx = self.integration_metric
inner, dot, grad, div, sym = fenics.inner, fenics.dot, fenics.grad, fenics.div, fenics.sym
self.governing_form = (
-psi_p * (div(u) + gamma * p) +
dot(psi_u, u_t + f_B(T) + dot(grad(u), u)) - div(psi_u) * p +
2. * mu(phi(T)) * inner(sym(grad(psi_u)), sym(grad(u))) + psi_T *
(T_t - 1. / Ste * phi_t) +
dot(grad(psi_T), 1. / Pr * grad(T) - T * u)) * dx
def impl_dyn(w0, dt=1.e-5, t_end=1.e-4, show_plots=False):
(u0, p0, v0) = fe.split(w0)
bcs_u, bcs_p, bcs_v = load_2d_muscle_bc(V_upv.sub(0), V_upv.sub(1),
V_upv.sub(2), boundaries)
# Lagrange function (without constraint)
(u1, p1, v1) = fe.TrialFunctions(V_upv)
(eta, q, xi) = fe.TestFunctions(V_upv)
F = deformation_grad(u1)
I_1, I_2, J = invariants(F)
F_iso = isochronic_deformation_grad(F, J)
#I_1_iso, I_2_iso = invariants(F_iso)[0:2]
W = material_mooney_rivlin(I_1, I_2, c_10, c_01)
g = incompr_constr(J)
L = -W
P = first_piola_stress(L, F)
G = incompr_stress(g, F)
a_dyn_u = inner(u1 - u0, eta) * dx - dt * inner(v1, eta) * dx
a_dyn_p = inner(g, q) * dx
a_dyn_v = rho * inner(v1 - v0, xi) * dx + dt * (inner(
P, grad(xi)) * dx + inner(p1 * G, grad(xi)) * dx - inner(B, xi) * dx)
a = a_dyn_u + a_dyn_p + a_dyn_v
w1 = fe.Function(V_upv)
sol = []
t = 0
while t < t_end:
print("progress: %f" % (100. * t / t_end))
fe.solve(a == 0, w1, bcs_u + bcs_p + bcs_v)
if fe.norm(w1.vector()) > 1e7:
print('ERROR: norm explosion')
break
# update initial values for next step
w0.assign(w1)
t += dt
if show_plots:
# plot result
fe.plot(w0.sub(0), mode='displacement')
plt.show()
# save solutions
sol.append(Solution(t=t))
sol[-1].upv.assign(w0)
return sol, W, kappa
def solve_steady_state_heiser_weissinger(kappa):
w = fe.Function(V_up)
(u, p) = fe.split(w)
p = fe.variable(p)
(eta, q) = fe.TestFunctions(V_up)
dw = fe.TrialFunction(V_up)
kappa = fe.Constant(kappa)
bcs_u, bcs_p, bcs_v = load_2d_muscle_bc(V_up.sub(0), V_up.sub(1), None,
boundaries)
F = deformation_grad(u)
I_1, I_2, J = invariants(F)
F_iso = isochronic_deformation_grad(F, J)
I_1_iso, I_2_iso = invariants(F)[0:2]
W = material_mooney_rivlin(I_1_iso, I_2_iso, c_10,
c_01) #+ incompr_relaxation(p, kappa)
g = incompr_constr(J)
# Lagrange function (without constraint)
L = -W
# Modified Lagrange function (with constraints)
L_mod = L - p * g
P = first_piola_stress(L, F)
G = incompr_stress(g, F) # = J*fe.inv(F.T)
Lp = const_eq(L_mod, p)
a_static = weak_div_term(P + p * G,
eta) + inner(B, eta) * dx + inner(Lp, q) * dx
J_static = fe.derivative(a_static, w, dw)
ffc_options = {"optimize": True}
problem = fe.NonlinearVariationalProblem(
a_static,
w,
bcs_u + bcs_p,
J=J_static,
form_compiler_parameters=ffc_options)
solver = fe.NonlinearVariationalSolver(problem)
solver.solve()
return w
def __init__(self,
mesh: fe.Mesh,
constitutive_model: ConstitutiveModelBase,
u_order=1,
p_order=0):
# TODO a lot here...
element_v = fe.VectorElement("P", mesh.ufl_cell(), u_order)
element_s = fe.FiniteElement("DG", mesh.ufl_cell(), p_order)
# mixed_element = fe.MixedElement([element_v, element_v, element_s])
mixed_element = fe.MixedElement([element_v, element_s])
self.W = fe.FunctionSpace(mesh, mixed_element)
self.V, self.Q = self.W.split()
self.w = fe.Function(self.W)
self.u, self.p = fe.split(self.w)
w0 = fe.Function(self.W)
self.u0, self.p0 = fe.split(w0)
self.ut, self.pt = fe.TestFunctions(self.W)
self.F = kin.def_grad(self.u)
self.F0 = kin.def_grad(self.u0)
S_iso = constitutive_model.iso_stress(self.u)
mod_p = constitutive_model.p(self.u)
J = fe.det(self.F)
F_inv = fe.inv(self.F)
if mod_p is None:
mod_p = J**2 - 1.
else:
mod_p -= self.p
S = S_iso + J * self.p * F_inv * F_inv.T
self.d_LHS = fe.inner(fe.grad(self.ut), self.F * S) * fe.dx \
+ fe.inner(mod_p, self.pt) * fe.dx
# + fe.inner(mod_p, fe.tr(fe.nabla_grad(self.ut)*fe.inv(self.F))) * fe.dx
self.d_RHS = (fe.inner(fe.Constant((0., 0., 0.)), self.ut) * fe.dx)
def forward(rho):
"""Solve the forward problem for a given fluid distribution rho(x)."""
w = fenics_adjoint.Function(W)
(u, p) = fenics.split(w)
(v, q) = fenics.TestFunctions(W)
inner, grad, dx, div = ufl.inner, ufl.grad, ufl.dx, ufl.div
F = (
alpha(rho) * inner(u, v) * dx
+ inner(grad(u), grad(v)) * dx
+ inner(grad(p), v) * dx
+ inner(div(u), q) * dx
)
bcs = [
fenics_adjoint.DirichletBC(W.sub(0).sub(1), 0, "on_boundary"),
fenics_adjoint.DirichletBC(W.sub(0).sub(0), inflow_outflow_bc, "on_boundary"),
]
fenics_adjoint.solve(F == 0, w, bcs=bcs)
return w
def run(self):
e_domain = self._create_e_domain()
mesh = generate_mesh(e_domain, MESH_PTS)
self._create_boundary_expression()
Omega_e = fe.FiniteElement("Lagrange", mesh.ufl_cell(), 1)
Omega_i = fe.FiniteElement("Lagrange",
self.passive_seg.mesh.ufl_cell(), 1)
Omega = fe.FunctionSpace(mesh, Omega_e * Omega_i)
Theta_e, Theta_i = fe.TrialFunction(Omega)
v_e, v_i = fe.TestFunctions(Omega)
sigma_e, sigma_i = 0.3, 0.4
LHS = sigma_e * fe.inner(fe.grad(Theta_e),
fe.grad(v_e)) * fe.dx # poisson
LHS += sigma_i * fe.inner(fe.grad(Theta_i),
fe.grad(v_i)) * fe.dx # poisson
LHS -= sigma_e * fe.grad(Theta_e) * v_e * fe.ds # current
LHS += sigma_i * fe.grad(Theta_i) * v_i * fe.ds # current
RHS = self.boundary_exp * v_e * fe.ds # source term
# TODO: solve Poisson in extracellular space
w = fe.Function(Omega)
fe.solve(LHS == RHS, w)
Theta_e, Theta_i = w.split()
plot(fe.interpolate(Theta, fe.FunctionSpace(mesh, Omega)),
mode='color')
plt.show()
# Set the potential just inside the membrane to Ve (just computed)
# minus V_m (from prev timestep)
self.passive_seg.set_v(Theta, self.passive_seg_vm)
# Solve for the potential and current inside the passive cell
self.passive_seg.run()
# Use Im to compute a new Vm for the next timestep, eq (8)
self.passive_seg_vm = self.passive_seg_vm + self.dt / self.cm * (
self.passive_seg_im - self.passive_seg_vm / self.rm)
def _create_variational_problem(m0, u0, W, dt):
"""We set up the variational problem."""
p, q = fc.TestFunctions(W)
w = fc.Function(W) # Function to solve for
m, u = fc.split(w)
# Relabel i.e. initialise m_prev, u_prev as m0, u0.
m_prev, u_prev = m0, u0
m_mid = 0.5 * (m + m_prev)
u_mid = 0.5 * (u + u_prev)
F = (
(q * u + q.dx(0) * u.dx(0) - q * m) * fc.dx + # q part
(p * (m - m_prev) + dt * (p * m_mid * u_mid.dx(0) - p.dx(0) * m_mid * u_mid)) * fc.dx # p part
)
J = fc.derivative(F, w)
problem = fc.NonlinearVariationalProblem(F, w, J=J)
solver = fc.NonlinearVariationalSolver(problem)
solver.parameters["newton_solver"]["maximum_iterations"] = 100 # Default is 50
solver.parameters["newton_solver"]["error_on_nonconvergence"] = False
return solver, w, m_prev, u_prev
dt = 0.1
# Re = 10 / 1e-4 = 1e5
V = fe.VectorElement("Lagrange", mesh.ufl_cell(), 2)
P = fe.FiniteElement("Lagrange", mesh.ufl_cell(), 1)
NU = fe.FiniteElement("Lagrange", mesh.ufl_cell(), 1)
if MODEL: M = fe.MixedElement([V, P, NU])
else: M = fe.MixedElement([V, P])
W = fe.FunctionSpace(mesh, M)
W0 = fe.Function(W)
We = fe.Function(W)
u0, p0 = fe.split(We)
#u0 = fe.Function((W0[0], W0[1]), 'Velocity000023.vtu')
#p0 = fe.Function(W0[2])
v, q = fe.TestFunctions(W)
#u, p = fe.split(W0)
u, p = (fe.as_vector((W0[0], W0[1])), W0[2])
#-------------------------------------------------------
# Defining essential/Dirichlet boundary conditions
# Step 1: Identify all boundary segments forming Gamma_d
#-------------------------------------------------------
# (-3., 2.5)
# |
# |
# |_______(0, 1.)
# bc1 |
# bc2|__________(3., ,0.)
# (0,0) bc3
mesh = fn.RectangleMesh(fn.Point(-width / 2, 0.0), fn.Point(width / 2, height),
52, 39) # 52 * 0.75 = 39, elements are square
nn = fn.FacetNormal(mesh)
# Defintion of function spaces
Vh = fn.VectorElement("CG", mesh.ufl_cell(), 2)
Zh = fn.FiniteElement("CG", mesh.ufl_cell(), 1)
Qh = fn.FiniteElement("CG", mesh.ufl_cell(), 2)
# spaces for displacement and total pressure should be compatible
# whereas the space for fluid pressure can be "anything". In particular the one for total pressure
Hh = fn.FunctionSpace(mesh, fn.MixedElement([Vh, Zh, Qh]))
(u, phi, p) = fn.TrialFunctions(Hh)
(v, psi, q) = fn.TestFunctions(Hh)
fileU = fn.File(mesh.mpi_comm(), "Output/2_5_1_Footing_wall_removed/u.pvd")
filePHI = fn.File(mesh.mpi_comm(), "Output/2_5_1_Footing_wall_removed/phi.pvd")
fileP = fn.File(mesh.mpi_comm(), "Output/2_5_1_Footing_wall_removed/p.pvd")
# ******** Model constants ********** #
E = 3.0e4
nu = 0.4995
lmbda = E * nu / ((1. + nu) * (1. - 2. * nu))
mu = E / (2. * (1. + nu))
c0 = 1.0e-3
kappa = 1.0e-6
alpha = 0.1
sigma0 = 1.5e4
def explicit_relax_dyn(w0, kappa=1e5, dt=1.e-5, t_end=1.e-4, show_plots=False):
(u0, p0, v0) = fe.split(w0)
bcs_u, bcs_p, bcs_v = load_2d_muscle_bc(V_upv.sub(0), V_upv.sub(1),
V_upv.sub(2), boundaries)
kappa = fe.Constant(kappa)
F = deformation_grad(u0)
I_1, I_2, J = invariants(F)
F_iso = isochronic_deformation_grad(F, J)
#I_1_iso, I_2_iso = invariants(F_iso)[0:2]
W = material_mooney_rivlin(I_1, I_2, c_10, c_01) + incompr_relaxation(
p0, kappa)
g = incompr_constr(J)
# Lagrange function (without constraint)
L = -W
P = first_piola_stress(L, F)
G = incompr_stress(g, F)
(u1, p1, v1) = fe.TrialFunctions(V_upv)
(eta, q, xi) = fe.TestFunctions(V_upv)
a_dyn_u = inner(u1 - u0, eta) * dx - dt * inner(v1, eta) * dx
a_dyn_p = (p1 - p0) * q * dx - dt * kappa * div(v1) * J * q * dx
#a_dyn_v = rho*inner(v1-v0, xi)*dx + dt*(inner(P + p0*G, grad(xi))*dx - inner(B, xi)*dx)
a_dyn_v = rho * inner(v1 - v0, xi) * dx + dt * (inner(
P, grad(xi)) * dx + inner(p0 * G, grad(xi)) * dx - inner(B, xi) * dx)
a = fe.lhs(a_dyn_u + a_dyn_p + a_dyn_v)
l = fe.rhs(a_dyn_u + a_dyn_p + a_dyn_v)
w1 = fe.Function(V_upv)
w2 = fe.Function(V_upv)
sol = []
vol = fe.assemble(1. * dx)
t = 0
while t < t_end:
print("progress: %f" % (100. * t / t_end))
A = fe.assemble(a)
L = fe.assemble(l)
for bc in bcs_u + bcs_p + bcs_v:
bc.apply(A, L)
fe.solve(A, w1.vector(), L)
if fe.norm(w1.vector()) > 1e7:
print('ERROR: norm explosion')
break
# update initial values for next step
w0.assign(w1)
t += dt
if show_plots:
# plot result
fe.plot(w0.sub(0), mode='displacement')
plt.show()
# save solutions
sol.append(Solution(t=t))
sol[-1].upv.assign(w0)
return sol, W, kappa
def half_exp_dyn(w0, dt=1.e-5, t_end=1.e-4, show_plots=False):
u0 = w0.u
p0 = w0.p
v0 = w0.v
bcs_u, bcs_p, bcs_v = load_2d_muscle_bc(V_u, V_pv.sub(0), V_pv.sub(1),
boundaries)
F = deformation_grad(u0)
I_1, I_2, J = invariants(F)
F_iso = isochronic_deformation_grad(F, J)
#I_1_iso, I_2_iso = invariants(F_iso)[0:2]
W = material_mooney_rivlin(I_1, I_2, c_10, c_01)
g = incompr_constr(J)
# Lagrange function (without constraint)
L = -W
P = first_piola_stress(L, F)
G = incompr_stress(g, F)
# a_dyn_u = inner(u1 - u0, eta) * dx - dt * inner(v1, eta) * dx
u1 = fe.TrialFunction(V_u)
eta = fe.TestFunction(V_u)
#u11 = fe.Function(V_u)
#F1 = deformation_grad(u11)
#g1 = incompr_constr(fe.det(F1))
#G1 = incompr_stress(g1, F1)
(p1, v1) = fe.TrialFunctions(V_pv)
(q, xi) = fe.TestFunctions(V_pv)
a_dyn_u = inner(u1 - u0, eta) * dx - dt * inner(v0, eta) * dx
a_dyn_p = fe.tr(G * grad(v1)) * q * dx
#a_dyn_v = rho*inner(v1-v0, xi)*dx + dt*(inner(P + p0*G, grad(xi))*dx - inner(B, xi)*dx)
a_dyn_v = rho * inner(v1 - v0, xi) * dx + dt * (inner(
P, grad(xi)) * dx + inner(p1 * G, grad(xi)) * dx - inner(B, xi) * dx)
a_u = fe.lhs(a_dyn_u)
l_u = fe.rhs(a_dyn_u)
a_pv = fe.lhs(a_dyn_p + a_dyn_v)
l_pv = fe.rhs(a_dyn_p + a_dyn_v)
u1 = fe.Function(V_u)
pv1 = fe.Function(V_pv)
sol = []
vol = fe.assemble(1. * dx)
A_u = fe.assemble(a_u)
A_pv = fe.assemble(a_pv)
for bc in bcs_u:
bc.apply(A_u)
t = 0
while t < t_end:
print("progress: %f" % (100. * t / t_end))
# update displacement u
L_u = fe.assemble(l_u)
fe.solve(A_u, u1.vector(), L_u)
u0.assign(u1)
L_pv = fe.assemble(l_pv)
for bc in bcs_p + bcs_v:
bc.apply(A_pv, L_pv)
fe.solve(A_pv, pv1.vector(), L_pv)
if fe.norm(pv1.vector()) > 1e8:
print('ERROR: norm explosion')
break
# update initial values for next step
w0.u = u1
w0.pv = pv1
p0.assign(w0.p)
v0.assign(w0.v)
t += dt
if show_plots:
# plot result
fe.plot(w0.sub(0), mode='displacement')
plt.show()
# save solutions
sol.append(Solution(t=t))
sol[-1].upv.assign(w0)
return sol, W
rho = fe.Constant(1)
RE = 50
lmx = 1 # mixing length :)
# Re = 10 / 1e-4 = 1e5
V = fe.VectorElement("Lagrange", mesh.ufl_cell(), 2)
P = fe.FiniteElement("Lagrange", mesh.ufl_cell(), 1)
NU = fe.FiniteElement("Lagrange", mesh.ufl_cell(), 1)
if MODEL: M = fe.MixedElement([V, P, NU])
else: M = fe.MixedElement([V, P])
W = fe.FunctionSpace(mesh, M)
W0 = fe.Function(W)
if MODEL:
(v, q, nu_test) = fe.TestFunctions(W)
(u, p, nu_trial) = fe.split(W0)
else:
(
v,
q,
) = fe.TestFunctions(W)
(
u,
p,
) = fe.split(W0)
nu_trial = fe.Constant(5) # artificial viscosity!!!
fv1 = fe.Constant(1)
#-------------------------------------------------------
# Defining essential/Dirichlet boundary conditions
# define potentials and concentrations
u_GND = fn.Expression('0', degree=2) #Ground
u_DD = fn.Expression('0.5', degree=2) #pontential
c_avg = fn.Expression('0.0001', degree=2) #average concentration
# set boundary conditions
bcs = []
bcs += [fn.DirichletBC(V.sub(0), u_DD, mf, 3)]
bcs += [fn.DirichletBC(V.sub(0), u_GND, mf, 1)]
# define problem
UC = fn.Function(V)
uc = fn.split(UC) # trial function potential concentration lagrange multi
u, c, lam = uc[0], uc[1:M + 1], uc[M + 1:]
VW = fn.TestFunctions(
V) # test function potential concentration lagrange multi
v, w, mu = VW[0], VW[1:M + 1], VW[M + 1:]
#lets try rot
r = fn.Expression('x[0]', degree=0)
# changing concentrations charges
Rho = 0
for i in range(M):
if i % 2:
Rho += -c[i]
else:
Rho += c[i]
PoissonLeft = (fn.dot(fn.grad(u),
fn.grad(v))) * fn.dx # weak solution Poisson left
def monolithic_solve(self):
self.U = fe.VectorElement('CG', self.mesh.ufl_cell(), 1)
self.W = fe.FiniteElement("CG", self.mesh.ufl_cell(), 1)
self.M = fe.FunctionSpace(self.mesh, self.U * self.W)
self.WW = fe.FunctionSpace(self.mesh, 'DG', 0)
m_test = fe.TestFunctions(self.M)
m_delta = fe.TrialFunctions(self.M)
m_new = fe.Function(self.M)
self.eta, self.zeta = m_test
self.x_new, self.d_new = fe.split(m_new)
self.H_old = fe.Function(self.WW)
vtkfile_u = fe.File('data/pvd/{}/u.pvd'.format(self.case_name))
vtkfile_d = fe.File('data/pvd/{}/d.pvd'.format(self.case_name))
self.build_weak_form_monolithic()
dG = fe.derivative(self.G, m_new)
self.set_bcs_monolithic()
p = fe.NonlinearVariationalProblem(self.G, m_new, self.BC, dG)
solver = fe.NonlinearVariationalSolver(p)
for i, (disp, rp) in enumerate(
zip(self.displacements, self.relaxation_parameters)):
print('\n')
print(
'================================================================================='
)
print('>> Step {}, disp boundary condition = {} [mm]'.format(
i, disp))
print(
'================================================================================='
)
self.H_old.assign(
fe.project(
history(self.H_old, self.psi(strain(fe.grad(self.x_new))),
self.psi_cr), self.WW))
self.presLoad.t = disp
newton_prm = solver.parameters['newton_solver']
newton_prm['maximum_iterations'] = 100
newton_prm['absolute_tolerance'] = 1e-4
newton_prm['relaxation_parameter'] = rp
solver.solve()
self.x_plot, self.d_plot = m_new.split()
self.x_plot.rename("u", "u")
self.d_plot.rename("d", "d")
vtkfile_u << self.x_plot
vtkfile_d << self.d_plot
force_upper = float(fe.assemble(self.sigma[1, 1] * self.ds(1)))
print("Force upper {}".format(force_upper))
self.delta_u_recorded.append(disp)
self.sigma_recorded.append(force_upper)
print(
'================================================================================='
)
Mh = fn.FiniteElement("CG", mesh.ufl_cell(), 1)
Wh = fn.TensorElement("CG", mesh.ufl_cell(), 1)
# function spaces
Vhf = fn.FunctionSpace(mesh, Vh)
Zhf = fn.FunctionSpace(mesh, Zh)
Qhf = fn.FunctionSpace(mesh, Qh)
Mhf = fn.FunctionSpace(mesh, Mh)
Whf = fn.FunctionSpace(mesh, Wh)
Hh = fn.FunctionSpace(mesh, fn.MixedElement([Vh,Zh,Qh]))
Nh = fn.FunctionSpace(mesh, fn.MixedElement([Mh, Mh]))
# functions and test functions
u, phi, p = fn.TrialFunctions(Hh)
v, psi, q = fn.TestFunctions(Hh)
E, n = fn.TrialFunctions(Nh)
F, m = fn.TestFunctions(Nh)
# pvd files
pvdU = fn.File(mesh.mpi_comm(), "Output/3_Combined_models/u.pvd")
pvdPHI = fn.File(mesh.mpi_comm(), "Output/3_Combined_models/phi.pvd")
pvdP = fn.File(mesh.mpi_comm(), "Output/3_Combined_models/p.pvd")
pvdE = fn.File(mesh.mpi_comm(), "Output/3_Combined_models/E.pvd")
pvdN = fn.File(mesh.mpi_comm(), "Output/3_Combined_models/n.pvd")
# constants for poroelasticity model (taken from footing-scaled-BCs.py)
EE = fn.Constant(3.0e4)
nu = fn.Constant(0.4995)
lmbda = EE*nu/((1.+nu)*(1.-2.*nu))
Ain = (Pin*A0/beta+np.sqrt(A0))**2;
# -- Spatial domain
ne = 2**7
L = 15
mesh = fe.IntervalMesh(int(ne),0,L)
degQ = 1
degA = 1
QE = fe.FiniteElement("Lagrange", cell=mesh.ufl_cell(), degree=degQ)
AE = fe.FiniteElement("Lagrange", cell=mesh.ufl_cell(), degree=degA)
ME = fe.MixedElement([AE,QE])
V = fe.FunctionSpace(mesh,ME)
V_A = V.sub(0)
V_Q = V.sub(1)
(v1,v2) = fe.TestFunctions(V)
dv1 = fe.grad(v1)[0]
dv2 = fe.grad(v2)[0]
(u1,u2) = fe.TrialFunctions(V)
U0 = fe.Function(V)
U0.assign( fe.Expression( ( 'A0', 'Q0' ) , A0=A0, Q0=Q0, degree=1 ) )
Un = fe.Function(V)
Un.assign( fe.Expression( ( 'A0', 'Q0' ) , A0=A0, Q0=Q0, degree=1 ) )
(u01,u02) = fe.split(U0)
(un1,un2) = fe.split(Un)
du01 = fe.grad(u01)[0] ; du02 = fe.grad(u02)[0]
dun1 = fe.grad(un1)[0] ; dun2 = fe.grad(un2)[0]
B0 = getB(u01,u02)
H0 = getH(u01,u02)
def xest_implement_1d_myosin(self):
#Parameters
total_time = 10.0
number_of_time_steps = 1000
# delta_t = fenics.Constant(total_time/number_of_time_steps)
delta_t = total_time / number_of_time_steps
nx = 1000
domain_size = 1.0
b = fenics.Constant(6.0)
k = fenics.Constant(0.5)
z_1 = fenics.Constant(-10.5) #always negative
# z_1 = fenics.Constant(0.0) #always negative
z_2 = 0.1 # always positive
xi_0 = fenics.Constant(1.0) #always positive
xi_1 = fenics.Constant(1.0) #always positive
xi_2 = 0.001 #always positive
xi_3 = 0.0001 #always negative
d = fenics.Constant(0.15)
alpha = fenics.Constant(1.0)
c = fenics.Constant(0.1)
# Sub domain for Periodic boundary condition
class PeriodicBoundary(fenics.SubDomain):
# Left boundary is "target domain" G
def inside(self, x, on_boundary):
return bool(-fenics.DOLFIN_EPS < x[0] < fenics.DOLFIN_EPS
and on_boundary)
def map(self, x, y):
y[0] = x[0] - 1
periodic_boundary_condition = PeriodicBoundary()
#Set up finite elements
mesh = fenics.IntervalMesh(nx, 0.0, 1.0)
vector_element = fenics.FiniteElement('P', fenics.interval, 1)
single_element = fenics.FiniteElement('P', fenics.interval, 1)
mixed_element = fenics.MixedElement(vector_element, single_element)
V = fenics.FunctionSpace(
mesh,
mixed_element,
constrained_domain=periodic_boundary_condition)
# V = fenics.FunctionSpace(mesh, mixed_element)
v, r = fenics.TestFunctions(V)
full_trial_function = fenics.Function(V)
u, rho = fenics.split(full_trial_function)
full_trial_function_n = fenics.Function(V)
u_n, rho_n = fenics.split(full_trial_function_n)
u_initial = fenics.Constant(0.0)
# rho_initial = fenics.Expression('1.0*sin(pi*x[0])*sin(pi*x[0])+1.0/k0', degree=2,k0 = k)
rho_initial = fenics.Expression('1/k0', degree=2, k0=k)
u_n = fenics.interpolate(u_initial, V.sub(0).collapse())
rho_n = fenics.interpolate(rho_initial, V.sub(1).collapse())
# perturbation = np.zeros(rho_n.vector().size())
# perturbation[:int(perturbation.shape[0]/2)] = 1.0
rho_n.vector().set_local(
np.array(rho_n.vector()) + 1.0 *
(0.5 - np.random.random(rho_n.vector().size())))
# u_n.vector().set_local(np.array(u_n.vector())+4.0*(0.5-np.random.random(u_n.vector().size())))
fenics.assign(full_trial_function_n, [u_n, rho_n])
u_n, rho_n = fenics.split(full_trial_function_n)
F = (u * v * fenics.dx - u_n * v * fenics.dx + delta_t *
(b + (z_1 * rho) /
(1 + z_2 * rho) * c * xi_1) * u.dx(0) * v.dx(0) * fenics.dx -
delta_t * (z_1 * rho) / (1 + z_2 * rho) * c * c * xi_2 / 2.0 *
u.dx(0) * u.dx(0) * v.dx(0) * fenics.dx + delta_t * (z_1 * rho) /
(1 + z_2 * rho) * c * c * c * xi_3 / 6.0 * u.dx(0) * u.dx(0) *
u.dx(0) * v.dx(0) * fenics.dx - delta_t * z_1 * rho /
(1 + z_2 * rho) * xi_0 * v.dx(0) * fenics.dx +
u.dx(0) * v.dx(0) * fenics.dx - u_n.dx(0) * v.dx(0) * fenics.dx +
rho * r * fenics.dx - rho_n * r * fenics.dx -
rho * u * r.dx(0) * fenics.dx + rho * u_n * r.dx(0) * fenics.dx +
delta_t * d * rho.dx(0) * r.dx(0) * fenics.dx +
delta_t * k * fenics.exp(alpha * u.dx(0)) * rho * r * fenics.dx -
delta_t * r * fenics.dx + delta_t * c * u.dx(0) * r * fenics.dx)
vtkfile_rho = fenics.File(
os.path.join(os.path.dirname(__file__), 'output', 'myosin_2d',
'solution_rho.pvd'))
vtkfile_u = fenics.File(
os.path.join(os.path.dirname(__file__), 'output', 'myosin_2d',
'solution_u.pvd'))
# rho_0 = fenics.Expression(((('0.0'),('0.0'),('0.0')),('sin(x[0])')), degree=1 )
# full_trial_function_n = fenics.project(rho_0, V)
# print('initial u and rho')
# print(u_n.vector())
# print(rho_n.vector())
time = 0.0
not_initialised = True
plt.figure()
for time_index in range(number_of_time_steps):
# Update current time
time += delta_t
# Compute solution
fenics.solve(F == 0, full_trial_function)
# Save to file and plot solution
vis_u, vis_rho = full_trial_function.split()
plt.subplot(311)
fenics.plot(vis_u, color='blue')
plt.ylim(-0.5, 0.5)
plt.subplot(312)
fenics.plot(-vis_u.dx(0), color='blue')
plt.ylim(-2, 2)
plt.title('actin density change')
plt.subplot(313)
fenics.plot(vis_rho, color='blue')
plt.title('myosin density')
plt.ylim(0, 7)
plt.tight_layout()
if not_initialised:
animation_camera = celluloid.Camera(plt.gcf())
not_initialised = False
animation_camera.snap()
print('time is')
print(time)
# plt.savefig(os.path.join(os.path.dirname(__file__),'output','this_output_at_time_' + '{:04d}'.format(time_index) + '.png'))
# print('this u and rho')
# print(np.array(vis_u.vector()))
# print(np.array(vis_rho.vector()))
# vtkfile_rho << (vis_rho, time)
# vtkfile_u << (vis_u, time)
full_trial_function_n.assign(full_trial_function)
animation = animation_camera.animate()
animation.save(
os.path.join(os.path.dirname(__file__), 'output', 'myosin_1D.mp4'))
filen = fn.File("Output/1_4_Karma/n.pvd")
t = 0.0; dt = 0.3; Tfinal = 600.0; frequency = 100;
# mesh
L = 6.72; nps = 64;
mesh = fn.RectangleMesh(fn.Point(0, 0), fn.Point(L, L),
nps, nps, "crossed")
# element and function spaces
Mhe = fn.FiniteElement("CG", mesh.ufl_cell(), 1)
Mh = fn.FunctionSpace(mesh, Mhe)
Nh = fn.FunctionSpace(mesh, fn.MixedElement([Mhe,Mhe]))
# trial and test functions
v, n = fn.TrialFunctions(Nh)
w, m = fn.TestFunctions(Nh)
# solution
Ksol = fn.Function(Nh)
# model constants
diffScale = fn.Constant(1e-3)
D0 = 1.1 * diffScale
tauv = fn.Constant(2.5)
taun = fn.Constant(250.0)
Re = fn.Constant(1.0)
M = fn.Constant(5.0)
beta = fn.Constant(0.008)
vstar = fn.Constant(1.5415)
vh = fn.Constant(3.0)
vn = fn.Constant(1.0)
import fenics
import matplotlib
N = 4
mesh = fenics.UnitSquareMesh(N, N)
P2 = fenics.VectorElement('P', mesh.ufl_cell(), 2)
P1 = fenics.FiniteElement('P', mesh.ufl_cell(), 1)
P2P1 = fenics.MixedElement([P2, P1])
W = fenics.FunctionSpace(mesh, P2P1)
psi_u, psi_p = fenics.TestFunctions(W)
w = fenics.Function(W)
u, p = fenics.split(w)
dynamic_viscosity = 0.01
mu = fenics.Constant(dynamic_viscosity)
inner, dot, grad, div, sym = fenics.inner, fenics.dot, fenics.grad, fenics.div, fenics.sym
momentum = dot(psi_u, dot(grad(u), u)) - div(psi_u) * p + 2. * mu * inner(
sym(grad(psi_u)), sym(grad(u)))
mass = -psi_p * div(u)
def discretize(self):
"""Builds function space, call again after introducing constraints"""
# FEniCS interface
self.mesh = fn.IntervalMesh(self.N, self.x0_scaled, self.x1_scaled)
# http://www.femtable.org/
# Argyris* ARG
# Arnold-Winther* AW
# Brezzi-Douglas-Fortin-Marini* BDFM
# Brezzi-Douglas-Marini BDM
# Bubble B
# Crouzeix-Raviart CR
# Discontinuous Lagrange DG
# Discontinuous Raviart-Thomas DRT
# Hermite* HER
# Lagrange CG
# Mardal-Tai-Winther* MTW
# Morley* MOR
# Nedelec 1st kind H(curl) N1curl
# Nedelec 2nd kind H(curl) N2curl
# Quadrature Q
# Raviart-Thomas RT
# Real R
# construct test and trial function space from elements
# spanned by Lagrange polynomials for the pyhsical variables of
# potential and concentration and global elements with a single degree
# of freedom ('Real') for constraints.
# For an example of this approach, refer to
# https://fenicsproject.org/docs/dolfin/latest/python/demos/neumann-poisson/demo_neumann-poisson.py.html
# For another example on how to construct and split function spaces
# for solving coupled equations, refer to
# https://fenicsproject.org/docs/dolfin/latest/python/demos/mixed-poisson/demo_mixed-poisson.py.html
P = fn.FiniteElement('Lagrange', fn.interval, 3)
R = fn.FiniteElement('Real', fn.interval, 0)
elements = [P] * (1 + self.M) + [R] * self.K
H = fn.MixedElement(elements)
self.W = fn.FunctionSpace(self.mesh, H)
# solution functions
self.w = fn.Function(self.W)
# set initial values if available
P = fn.FunctionSpace(self.mesh, 'P', 1)
dof2vtx = fn.vertex_to_dof_map(P)
if self.ui0 is not None:
x = np.linspace(self.x0_scaled, self.x1_scaled, self.ui0.shape[0])
ui0 = scipy.interpolate.interp1d(x, self.ui0)
# use linear interpolation on mesh
self.u0_func = fn.Function(P)
self.u0_func.vector()[:] = ui0(self.X)[dof2vtx]
fn.assign(self.w.sub(0),
fn.interpolate(self.u0_func,
self.W.sub(0).collapse()))
if self.ni0 is not None:
x = np.linspace(self.x0_scaled, self.x1_scaled, self.ni0.shape[1])
ni0 = scipy.interpolate.interp1d(x, self.ni0)
self.p0_func = [fn.Function(P)] * self.ni0.shape[0]
for k in range(self.ni0.shape[0]):
self.p0_func[k].vector()[:] = ni0(self.X)[k, :][dof2vtx]
fn.assign(
self.w.sub(1 + k),
fn.interpolate(self.p0_func[k],
self.W.sub(k + 1).collapse()))
# u represents voltage , p concentrations
uplam = fn.split(self.w)
self.u, self.p, self.lam = (uplam[0], [*uplam[1:(self.M + 1)]],
[*uplam[(self.M + 1):]])
# v, q and mu represent respective test functions
vqmu = fn.TestFunctions(self.W)
self.v, self.q, self.mu = (vqmu[0], [*vqmu[1:(self.M + 1)]],
[*vqmu[(self.M + 1):]])
def __init__(self, L, ne, r0, Q0, E, h0, theta, dt, degA=1, degQ=1):
# -- Setup domain
self.L = L
self.ne = ne
self.dt = dt
self.mesh = fe.IntervalMesh(ne, 0, L)
QE = fe.FiniteElement("Lagrange",
cell=self.mesh.ufl_cell(),
degree=degQ)
AE = fe.FiniteElement("Lagrange",
cell=self.mesh.ufl_cell(),
degree=degA)
ME = fe.MixedElement([AE, QE])
# -- Setup functionspaces
self.V = fe.FunctionSpace(self.mesh, ME)
self.V_A = self.V.sub(0)
self.V_Q = self.V.sub(1)
(self.v1, self.v2) = fe.TestFunctions(self.V)
self.dv1 = fe.grad(self.v1)[0]
self.dv2 = fe.grad(self.v2)[0]
self.E = E
self.h0 = h0
self.beta = E * h0 * np.sqrt(np.pi)
self.A0 = np.pi * r0**2
self.Q0 = Q0
self.U0 = fe.Function(self.V)
self.Un = fe.Function(self.V)
# -- Setup initial conditions
self.U0.assign(fe.Expression(('A0', 'Q0'), A0=self.A0, Q0=Q0,
degree=1))
self.Un.assign(fe.Expression(('A0', 'Q0'), A0=self.A0, Q0=Q0,
degree=1))
(self.u01, self.u02) = fe.split(self.U0)
(self.un1, self.un2) = fe.split(self.Un)
self.du01 = fe.grad(self.u01)[0]
self.du02 = fe.grad(self.u02)[0]
self.dun1 = fe.grad(self.un1)[0]
self.dun2 = fe.grad(self.un2)[0]
(self.W1_initial,
self.W2_initial) = self.getCharacteristics(self.A0, self.Q0)
# -- Setup weakform terms
B0 = self.getB(self.u01, self.u02)
Bn = self.getB(self.un1, self.un2)
H0 = self.getH(self.u01, self.u02)
Hn = self.getH(self.un1, self.un2)
HdUdz0 = matMult(H0, [self.du01, self.du02])
HdUdzn = matMult(Hn, [self.dun1, self.dun2])
# -- Setup weakform
wf = -self.un1 * self.v1 - self.un2 * self.v2
wf += self.u01 * self.v1 + self.u02 * self.v2
wf += -dt * theta * (HdUdzn[0] + Bn[0]) * self.v1 - dt * theta * (
HdUdzn[1] + Bn[1]) * self.v2
wf += -dt * (1 - theta) * (HdUdz0[0] + B0[0]) * self.v1 - dt * (
1 - theta) * (HdUdz0[1] + B0[1]) * self.v2
wf = wf * fe.dx
self.wf = wf
self.J = fe.derivative(wf, self.Un, fe.TrialFunction(self.V))
def demo16(self, permeability, obs_case=1):
"""This demo program solves the mixed formulation of Poisson's
equation:
sigma + grad(u) = 0 in Omega
div(sigma) = f in Omega
du/dn = g on Gamma_N
u = u_D on Gamma_D
The corresponding weak (variational problem)
<sigma, tau> + <grad(u), tau> = 0
for all tau
- <sigma, grad(v)> = <f, v> + <g, v>
for all v
is solved using DRT (Discontinuous Raviart-Thomas) elements
of degree k for (sigma, tau) and CG (Lagrange) elements
of degree k + 1 for (u, v) for k >= 1.
"""
mesh = UnitSquareMesh(15, 15)
ak_values = permeability
flux_order = 3
s = scenarios.darcy_problem_1()
DRT = fenics.FiniteElement("DRT", mesh.ufl_cell(), flux_order)
# Lagrange
CG = fenics.FiniteElement("CG", mesh.ufl_cell(), flux_order + 1)
if s.integral_constraint:
# From https://fenicsproject.org/qa/14184/how-to-solve-linear-system-with-constaint
R = fenics.FiniteElement("R", mesh.ufl_cell(), 0)
W = fenics.FunctionSpace(mesh, fenics.MixedElement([DRT, CG, R]))
# Define trial and test functions
(sigma, u, r) = fenics.TrialFunctions(W)
(tau, v, r_) = fenics.TestFunctions(W)
else:
W = fenics.FunctionSpace(mesh, DRT * CG)
# Define trial and test functions
(sigma, u) = fenics.TrialFunctions(W)
(tau, v) = fenics.TestFunctions(W)
f = s.source_function
g = s.g
# Define property field function
W_CG = fenics.FunctionSpace(mesh, "Lagrange", 1)
if s.ak is None:
ak = property_field.get_conductivity(W_CG, ak_values)
else:
ak = s.ak
# Define variational form
a = (fenics.dot(sigma, tau) + fenics.dot(ak * fenics.grad(u), tau) +
fenics.dot(sigma, fenics.grad(v))) * fenics.dx
L = -f * v * fenics.dx + g * v * fenics.ds
# L = 0
if s.integral_constraint:
# Lagrange multiplier? See above link.
a += r_ * u * fenics.dx + v * r * fenics.dx
# Define Dirichlet BC
bc = fenics.DirichletBC(W.sub(1), s.dirichlet_bc, s.gamma_dirichlet)
# Compute solution
w = fenics.Function(W)
fenics.solve(a == L, w, bc)
# fenics.solve(a == L, w)
if s.integral_constraint:
(sigma, u, r) = w.split()
else:
(sigma, u) = w.split()
x = u.compute_vertex_values(mesh)
x2 = sigma.compute_vertex_values(mesh)
p = x
pre = p.reshape((16, 16))
vx = x2[:256].reshape((16, 16))
vy = x2[256:].reshape((16, 16))
if obs_case == 1:
dd = np.zeros([8, 8])
pos = np.full((8 * 8, 2), 0)
col = [1, 3, 5, 7, 9, 11, 13, 15]
position = [1, 3, 5, 7, 9, 11, 13, 15]
for i in range(8):
for j in range(8):
row = position
pos[8 * i + j, :] = [col[i], row[j]]
dd[i, j] = pre[col[i], row[j]]
like = dd.reshape(8 * 8, )
return like, pre, vx, vy, ak_values, pos
def navierStokes(projectId, mesh, faceSets, boundarySets, config):
log("Navier Stokes Analysis has started")
# this is the default directory, when user request for download all files in this directory is being compressed and sent to the user
resultDir = "./Results/"
if len(config["steps"]) > 1:
return "more than 1 step is not supported yet"
# config is a dictionary containing all the user inputs for solver configurations
t_init = 0.0
t_final = float(config['steps'][0]["finalTime"])
t_num = int(config['steps'][0]["iterationNo"])
dt = ((t_final - t_init) / t_num)
t = t_init
#
# Viscosity coefficient.
#
nu = float(config['materials'][0]["viscosity"])
rho = float(config['materials'][0]["density"])
#
# Declare Finite Element Spaces
# do not use triangle directly
P2 = fn.VectorElement("P", mesh.ufl_cell(), 2)
P1 = fn.FiniteElement("P", mesh.ufl_cell(), 1)
TH = fn.MixedElement([P2, P1])
V = fn.VectorFunctionSpace(mesh, "P", 2)
Q = fn.FunctionSpace(mesh, "P", 1)
W = fn.FunctionSpace(mesh, TH)
#
# Declare Finite Element Functions
#
(u, p) = fn.TrialFunctions(W)
(v, q) = fn.TestFunctions(W)
w = fn.Function(W)
u0 = fn.Function(V)
p0 = fn.Function(Q)
#
# Macros needed for weak formulation.
#
def contract(u, v):
return fn.inner(fn.nabla_grad(u), fn.nabla_grad(v))
def b(u, v, w):
return 0.5 * (fn.inner(fn.dot(u, fn.nabla_grad(v)), w) -
fn.inner(fn.dot(u, fn.nabla_grad(w)), v))
# Define boundaries
bcs = []
for BC in config['BCs']:
if BC["boundaryType"] == "wall":
for edge in json.loads(BC["edges"]):
bcs.append(
fn.DirichletBC(W.sub(0),
fn.Constant((0.0, 0.0, 0.0)),
boundarySets,
int(edge),
method='topological'))
if BC["boundaryType"] == "inlet":
vel = json.loads(BC['value'])
for edge in json.loads(BC["edges"]):
bcs.append(
fn.DirichletBC(W.sub(0),
fn.Expression(
(str(vel[0]), str(vel[1]), str(vel[2])),
degree=2),
boundarySets,
int(edge),
method='topological'))
if BC["boundaryType"] == "outlet":
for edge in json.loads(BC["edges"]):
bcs.append(
fn.DirichletBC(W.sub(1),
fn.Constant(float(BC['value'])),
boundarySets,
int(edge),
method='topological'))
f = fn.Constant((0.0, 0.0, 0.0))
# weak form NSE
NSE = (1.0/dt)*fn.inner(u, v)*fn.dx + b(u0, u, v)*fn.dx + nu * \
contract(u, v)*fn.dx - fn.div(v)*p*fn.dx + q*fn.div(u)*fn.dx
LNSE = fn.inner(f, v) * fn.dx + (1. / dt) * fn.inner(u0, v) * fn.dx
velocity_file = fn.XDMFFile(resultDir + "/vel.xdmf")
pressure_file = fn.XDMFFile(resultDir + "/pressure.xdmf")
velocity_file.parameters["flush_output"] = True
velocity_file.parameters["functions_share_mesh"] = True
pressure_file.parameters["flush_output"] = True
pressure_file.parameters["functions_share_mesh"] = True
#
# code for projecting a boundary condition into a file for visualization
#
# for bc in bcs:
# bc.apply(w.vector())
# fn.File("para_plotting/bc.pvd") << w.sub(0)
for jj in range(0, t_num):
t = t + dt
# print('t = ' + str(t))
A, b = fn.assemble_system(NSE, LNSE, bcs)
fn.solve(A, w.vector(), b)
# fn.solve(NSE==LNSE,w,bcs)
fn.assign(u0, w.sub(0))
fn.assign(p0, w.sub(1))
# Save Solutions to Paraview File
if (jj % 20 == 0):
velocity_file.write(u0, t)
pressure_file.write(p0, t)
sendFile(projectId, resultDir + "vel.xdmf")
sendFile(projectId, resultDir + "vel.h5")
sendFile(projectId, resultDir + "pressure.xdmf")
sendFile(projectId, resultDir + "pressure.h5")
statusUpdate(projectId, "STARTED", {"progress": jj / t_num * 100})
def demo64(self, permeability, obs_case=1):
mesh = UnitSquareMesh(63, 63)
ak_values = permeability
flux_order = 3
s = scenarios.darcy_problem_1()
DRT = fenics.FiniteElement("DRT", mesh.ufl_cell(), flux_order)
# Lagrange
CG = fenics.FiniteElement("CG", mesh.ufl_cell(), flux_order + 1)
if s.integral_constraint:
# From https://fenicsproject.org/qa/14184/how-to-solve-linear-system-with-constaint
R = fenics.FiniteElement("R", mesh.ufl_cell(), 0)
W = fenics.FunctionSpace(mesh, fenics.MixedElement([DRT, CG, R]))
# Define trial and test functions
(sigma, u, r) = fenics.TrialFunctions(W)
(tau, v, r_) = fenics.TestFunctions(W)
else:
W = fenics.FunctionSpace(mesh, DRT * CG)
# Define trial and test functions
(sigma, u) = fenics.TrialFunctions(W)
(tau, v) = fenics.TestFunctions(W)
f = s.source_function
g = s.g
# Define property field function
W_CG = fenics.FunctionSpace(mesh, "Lagrange", 1)
if s.ak is None:
ak = property_field.get_conductivity(W_CG, ak_values)
else:
ak = s.ak
# Define variational form
a = (fenics.dot(sigma, tau) + fenics.dot(ak * fenics.grad(u), tau) +
fenics.dot(sigma, fenics.grad(v))) * fenics.dx
L = -f * v * fenics.dx + g * v * fenics.ds
# L = 0
if s.integral_constraint:
# Lagrange multiplier? See above link.
a += r_ * u * fenics.dx + v * r * fenics.dx
# Define Dirichlet BC
bc = fenics.DirichletBC(W.sub(1), s.dirichlet_bc, s.gamma_dirichlet)
# Compute solution
w = fenics.Function(W)
fenics.solve(a == L, w, bc)
# fenics.solve(a == L, w)
if s.integral_constraint:
(sigma, u, r) = w.split()
else:
(sigma, u) = w.split()
x = u.compute_vertex_values(mesh)
x2 = sigma.compute_vertex_values(mesh)
p = x
pre = p.reshape((64, 64))
vx = x2[:4096].reshape((64, 64))
vy = x2[4096:].reshape((64, 64))
if obs_case == 1:
dd = np.zeros([8, 8])
pos = np.full((8 * 8, 2), 0)
col = [4, 12, 20, 28, 36, 44, 52, 60]
position = [4, 12, 20, 28, 36, 44, 52, 60]
for i in range(8):
for j in range(8):
row = position
pos[8 * i + j, :] = [col[i], row[j]]
dd[i, j] = pre[col[i], row[j]]
like = dd.reshape(8 * 8, )
return like, pre, vx, vy, ak_values, pos
# set boundary conditions
GammaGND = fn.DirichletBC(V.sub(0), u_GND, boundaryGND) # ground potential at straight electrode
GammaHigh = fn.DirichletBC(V.sub(0), u_DD, boundaryHigh) # high potential at shaped electrode
#GammaC_GND0 = fn.DirichletBC(V.sub(0) , c_INIT, boundaryGND)
#GammaC_GND1 = fn.DirichletBC(V.sub(1) , c_INIT, boundaryGND)
#GammaC_GND2 = fn.DirichletBC(V.sub(2) , c_INIT, boundaryGND)
bcs=[GammaGND,GammaHigh]
#bcs=[GammaGND,GammaHigh,GammaC_GND0,GammaC_GND1,GammaC_GND2]
# %%
# define problem
UC = fn.Function(V)
uc = fn.split(UC)
u, c1, c2, lam1, lam2 = uc[0], uc[1], uc[2], uc[3], uc[4]
VW = fn.TestFunctions(V)
v, w1, w2, mu1, mu2 = VW[0], VW[1], VW[2], VW[3], VW[4]
#create rotation
#r = fn.Expression('x[0]', degree=1)
# changing concentrations charges
PoissonLeft = (fn.dot(fn.grad(u), fn.grad(v)))*fn.dx
PoissonRight = c1*v*fn.dx - c2*v*fn.dx
NernstPlanck1 = fn.dot((-fn.grad(c1) - (c1)*fn.grad(u)),fn.grad(w1))*fn.dx
NernstPlanck2 = fn.dot((-fn.grad(c2) + (c2)*fn.grad(u)),fn.grad(w2))*fn.dx
Constraint1 = lam1 * w1 * fn.dx + ((c1) - c_AVG) * mu1 * fn.dx
Constraint2 = lam2 * w2 * fn.dx + ((c2) - c_AVG) * mu2 * fn.dx
PNP_xy = PoissonLeft - PoissonRight + NernstPlanck1 + NernstPlanck2 + Constraint1 + Constraint2
left = fe.CompiledSubDomain("near(x[0], side) && on_boundary", side=0.0)
right = fe.CompiledSubDomain("near(x[0], side) && on_boundary", side=1.0)
# Define Dirichlet boundary (x = 0 or x = 1)
u_left = fe.Expression(("0.0", "0.0", "0.0"), element=element_3)
u_right = fe.Expression(("0.0", "0.0", "0.0"), element=element_3)
p_left = fe.Constant(0.)
# Define acting force
b = fe.Constant((0.0, 0.0, 0.0)) # Body force per unit volume
t_bar = fe.Constant((0.0, 0.0, 0.0)) # Traction force on the boundary
# Define test and trial functions
w = fe.Function(V) # most recently computed solution
(u, p) = fe.split(w)
(v, q) = fe.TestFunctions(V)
dw = fe.TrialFunction(V)
# Kinematics
d = u.geometric_dimension()
I = fe.Identity(d) # Identity tensor
F = fe.variable(I + grad(u)) # Deformation gradient
C = fe.variable(F.T * F) # Right Cauchy-Green tensor
J = fe.det(C)
DE = lambda v: 0.5 * (F.T * grad(v) + grad(v).T * F)
a_0 = fe.as_vector([[1.0], [0.], [0.]])
# Invariants
# mesh setup
nps = 64 # number of points
mesh = fn.UnitSquareMesh(nps, nps)
fileu = fn.File(mesh.mpi_comm(), "Output/1_3_Schnackenberg/u.pvd")
filev = fn.File(mesh.mpi_comm(), "Output/1_3_Schnackenberg/v.pvd")
# function spaces
P1 = fn.FiniteElement("Lagrange", mesh.ufl_cell(), 1)
Mh = fn.FunctionSpace(mesh, "Lagrange", 1)
Nh = fn.FunctionSpace(mesh, fn.MixedElement([P1, P1]))
Sol = fn.Function(Nh)
# trial and test functions
u, v = fn.TrialFunctions(Nh)
uT, vT = fn.TestFunctions(Nh)
# model constants
a = fn.Constant(0.1305)
b = fn.Constant(0.7695)
c1 = fn.Constant(0.05)
c2 = fn.Constant(1.0)
d = fn.Constant(170.0)
# initial value
uinit = fn.Expression('a + b + 0.001 * exp(-100.0 * (pow(x[0] - 1.0/3, 2)' +
' + pow(x[1] - 0.5, 2)))',
a=a,
b=b,
degree=3)