def unitcube_geometry():
N = 3
mesh = UnitCubeMesh(mpi_comm_world(), N, N, N)
ffun = dolfin.MeshFunction("size_t", mesh, 2)
ffun.set_all(0)
fixed.mark(ffun, fixed_marker)
free.mark(ffun, free_marker)
marker_functions = MarkerFunctions(ffun=ffun)
# Fibers
V_f = dolfin.VectorFunctionSpace(mesh, "CG", 1)
f0 = interpolate(Expression(("1.0", "0.0", "0.0"), degree=1), V_f)
s0 = interpolate(Expression(("0.0", "1.0", "0.0"), degree=1), V_f)
n0 = interpolate(Expression(("0.0", "0.0", "1.0"), degree=1), V_f)
microstructure = Microstructure(f0=f0, s0=s0, n0=n0)
geometry = Geometry(
mesh=mesh,
marker_functions=marker_functions,
microstructure=microstructure,
)
return geometry
def _build_geo(self, gamma_sp, length, x1, x2, dim):
if dim == 2:
self.Gsub2 = None
# Construct the actual fenics map
self.gamma = Expression((ccode(gamma_sp[0]).replace(
'M_PI', 'pi'), ccode(gamma_sp[1]).replace('M_PI', 'pi')),
pi=pi,
length=length,
degree=DEGREE,
name="gamma")
# Get the induced base from the mapping to the referrential geometry
# G_2 = ∂X/xi^2
self.Gsub1 = Expression(
(ccode(gamma_sp[0].diff(x1)).replace('M_PI', 'pi'),
ccode(gamma_sp[1].diff(x1)).replace('M_PI', 'pi')),
pi=pi,
length=length,
degree=DEGREE,
name="Gsub1")
if dim == 3:
# Construct the actual fenics map
self.gamma = Expression((ccode(
gamma_sp[0]).replace('M_PI', 'pi'), ccode(gamma_sp[1]).replace(
'M_PI', 'pi'), ccode(gamma_sp[2]).replace('M_PI', 'pi')),
pi=pi,
length=length,
degree=DEGREE,
name="gamma")
# Get the induced base from the mapping to the referrential geometry
# G_2 = ∂X/xi^2
self.Gsub1 = Expression(
(ccode(gamma_sp[0].diff(x1)).replace('M_PI', 'pi'),
ccode(gamma_sp[1].diff(x1)).replace('M_PI', 'pi'),
ccode(gamma_sp[2].diff(x1)).replace('M_PI', 'pi')),
pi=pi,
length=length,
degree=DEGREE,
name="Gsub1")
self.Gsub2 = Expression(
(ccode(gamma_sp[0].diff(x2)).replace('M_PI', 'pi'),
ccode(gamma_sp[1].diff(x2)).replace('M_PI', 'pi'),
ccode(gamma_sp[2].diff(x2)).replace('M_PI', 'pi')),
pi=pi,
length=length,
degree=DEGREE,
name="Gsub2")
def build_derivative(self, diff_args=None, name=None):
return Expression(tuple(
[ccode(i.diff(*diff_args)) for i in self.gamma_sp]),
eta=self.eta,
w=self.w,
degree=DEGREE,
name=name)
def __init__(self, w=None, eta=None, dim=None):
self.w = Constant(w, name="width")
self.eta = Constant(eta, name="eta")
W, eta, x1, x2 = sp.symbols('w, eta, x[0], x[1]')
self.dependencies = [W, eta]
X, Z = ligaro(W, eta)
# R = L/eta
if dim == 2:
self.gamma_sp = gamma_sp = [X, Z]
self.Gsub2 = None
if dim == 3:
self.gamma_sp = gamma_sp = [X, x2, Z]
# for dim==2 or dim ==3:
self.gamma = Expression(tuple([ccode(i) for i in gamma_sp]),
eta=self.eta,
w=self.w,
degree=DEGREE,
name="gamma")
self.Gsub1 = self.build_derivative([x1], name='Gsub1')
if ADJOINT:
# adjoint gamma
self.gamma.dependencies = [self.w, self.eta]
self.gamma.user_defined_derivatives = {}
self.gamma.user_defined_derivatives[
self.w] = self.build_derivative([W], name='d_gamma_dw')
self.gamma.user_defined_derivatives[
self.eta] = self.build_derivative([eta], name='d_gamma_deta')
# adjoint Gsub1
self.Gsub1.dependencies = [self.w, self.eta]
self.Gsub1.user_defined_derivatives = {}
self.Gsub1.user_defined_derivatives[
self.w] = self.build_derivative([x1, W], name='d_Gsub1_dw')
self.Gsub1.user_defined_derivatives[
self.eta] = self.build_derivative([x1, eta],
name='d_Gsub1_deta')
if dim == 3:
self.Gsub2 = self.build_derivative([x2], name='Gsub2')
if ADJOINT:
self.Gsub2.dependencies = [self.w, self.eta]
self.Gsub2.user_defined_derivatives = {}
self.Gsub2.user_defined_derivatives[
self.w] = self.build_derivative([x2, W], name='d_Gsub2_dw')
self.Gsub2.user_defined_derivatives[
self.eta] = self.build_derivative([x2, eta],
name='d_Gsub2_deta')
free_marker = 2
free.mark(ffun, free_marker)
# Create a cell function (but we are not using it)
cfun = dolfin.MeshFunction("size_t", mesh, 3)
cfun.set_all(0)
# Collect the functions containing the markers
marker_functions = pulse.MarkerFunctions(ffun=ffun, cfun=cfun)
# Create mictrotructure
V_f = dolfin.VectorFunctionSpace(mesh, "CG", 1)
# Fibers
f0 = interpolate(Expression(("1.0", "0.0", "0.0"), degree=1), V_f)
# Sheets
s0 = interpolate(Expression(("0.0", "1.0", "0.0"), degree=1), V_f)
# Fiber-sheet normal
n0 = interpolate(Expression(("0.0", "0.0", "1.0"), degree=1), V_f)
# Collect the mictrotructure
microstructure = pulse.Microstructure(f0=f0, s0=s0, n0=n0)
# Create the geometry
geometry = pulse.Geometry(
mesh=mesh,
marker_functions=marker_functions,
microstructure=microstructure,
)
def __init__(self, w=None, eta=None, dim=None, length=1):
self.w = Constant(w, name="width")
self.eta = Constant(eta, name="eta")
self.t = Constant(length, name="length")
W, eta, x1, x2, t = sp.symbols('w, eta, x[0], x[1], t')
X, Z = ligaro(W, eta)
if dim == 2:
self.Gsub2 = None
self.gamma_sp = gamma_sp = [X, Z]
self.gamma = Expression(tuple([ccode(i) for i in gamma_sp]),
eta=self.eta,
w=self.w,
degree=DEGREE,
name="gamma")
if dim == 3:
self.gamma_sp = gamma_sp = [X, t * x2, Z]
# fixed-end open surface volume correction
# ONLY VALID FOR FIXED EDGES
R = self.w / sqrt(2 * (1 - cos(self.eta)))
Area = -0.5 * R**2 * (self.eta - sin(self.eta)
) # negative because upsidedown #TODO fix
self.vol_correct = (Area * self.t / 3)
self.gamma = Expression(tuple([ccode(i) for i in gamma_sp]),
eta=self.eta,
w=self.w,
t=self.t,
degree=DEGREE,
name="gamma")
self.Gsub1 = self.build_derivative([x1], name='Gsub1')
if dim == 3:
self.Gsub2 = self.build_derivative([x2], name='Gsub2')
if ADJOINT:
# adjoint gamma
self.gamma.dependencies = [self.w, self.eta, self.t]
self.gamma.user_defined_derivatives = {}
self.gamma.user_defined_derivatives[
self.w] = self.build_derivative([W], name='d_gamma_dw')
self.gamma.user_defined_derivatives[
self.eta] = self.build_derivative([eta], name='d_gamma_deta')
self.gamma.user_defined_derivatives[
self.t] = self.build_derivative([t], name='d_gamma_dt')
# adjoint Gsub1
self.Gsub1.dependencies = [self.w, self.eta, self.t]
self.Gsub1.user_defined_derivatives = {}
self.Gsub1.user_defined_derivatives[
self.w] = self.build_derivative([x1, W], name='d_Gsub1_dw')
self.Gsub1.user_defined_derivatives[
self.eta] = self.build_derivative([x1, eta],
name='d_Gsub1_deta')
self.Gsub1.user_defined_derivatives[
self.t] = self.build_derivative([x1, t], name='d_Gsub1_dt')
if dim == 3:
# adjoint Gsub2
self.Gsub2.dependencies = [self.w, self.eta, self.t]
self.Gsub2.user_defined_derivatives = {}
self.Gsub2.user_defined_derivatives[
self.w] = self.build_derivative([x2, W], name='d_Gsub2_dw')
self.Gsub2.user_defined_derivatives[
self.eta] = self.build_derivative([x2, eta],
name='d_Gsub2_deta')
self.Gsub2.user_defined_derivatives[
self.t] = self.build_derivative([x2, t], name='d_Gsub2_dt')
left = dolfin.CompiledSubDomain("near(x[0], side) && on_boundary", side=0)
bottom = dolfin.CompiledSubDomain("near(x[2], side) && on_boundary", side=0)
boundary_markers = dolfin.MeshFunction("size_t", mesh,
mesh.topology().dim() - 1)
boundary_markers.set_all(0)
left_marker = 1
left.mark(boundary_markers, 1)
bottom_marker = 2
bottom.mark(boundary_markers, 2)
marker_functions = pulse.MarkerFunctions(ffun=boundary_markers)
# Create mictrotructure
f0 = Expression(("1.0", "0.0", "0.0"), degree=1, cell=mesh.ufl_cell())
s0 = Expression(("0.0", "1.0", "0.0"), degree=1, cell=mesh.ufl_cell())
n0 = Expression(("0.0", "0.0", "1.0"), degree=1, cell=mesh.ufl_cell())
# Collect the mictrotructure
microstructure = pulse.Microstructure(f0=f0, s0=s0, n0=n0)
# Create the geometry
geometry = pulse.Geometry(
mesh=mesh,
marker_functions=marker_functions,
microstructure=microstructure,
)
# Create the material
material_parameters = pulse.Guccione.default_parameters()
def __init__(self, w=None, L=None, dim=3):
w_val = w
self.length = L
W, eta, L = sp.symbols('w, eta, length')
x1, x2 = sp.symbols('x[0], x[1]')
CC = W / L
a, b, c, d, e, f = sp.symbols('a, b,c,d,e,f')
eta = a + b * CC + c * CC**2 + d * CC**3 + e * sp.cos(f * CC)
eta_fit = np.linspace(-6.28, 0.001, 100)
x_data = np.sqrt(2 * (1 - np.cos(eta_fit)) / eta_fit**2)
def test_func(x, a, b, c, d, e, f):
return a + b * x + c * x**2 + d * x**3 + e * np.cos(f * x)
from scipy import optimize
params, params_covariance = optimize.curve_fit(test_func,
x_data,
eta_fit,
maxfev=10000)
X, Z = ligaro(W, eta)
R = L / eta
if dim == 2:
self.Gsub2 = None
gamma_sp = [None, None]
gamma_sp[0] = X
gamma_sp[1] = Z
self.gamma = Expression((ccode(gamma_sp[0]).replace(
'M_PI', 'pi'), ccode(gamma_sp[1]).replace('M_PI', 'pi')),
pi=pi,
length=self.length,
w=w_val,
a=params[0],
b=params[1],
c=params[2],
d=params[3],
e=params[4],
f=params[5],
degree=DEGREE,
name="gamma")
# spatial derivative of above gamma (needed for PDE), similarly for \partial\gamma / \partial x2
self.Gsub1 = Expression(
(ccode(gamma_sp[0].diff(x1)).replace('M_PI', 'pi'),
ccode(gamma_sp[1].diff(x1)).replace('M_PI', 'pi')),
pi=pi,
length=self.length,
w=w_val,
a=params[0],
b=params[1],
c=params[2],
d=params[3],
e=params[4],
f=params[5],
degree=DEGREE,
name="Gsub1")
# Now need the derivatives of the above wrt length for dolfin-adjoint
self.d_gamma = Expression(
(ccode(gamma_sp[0].diff(L)).replace('M_PI', 'pi'),
ccode(gamma_sp[1].diff(L)).replace('M_PI', 'pi')),
pi=pi,
length=self.length,
w=w_val,
a=params[0],
b=params[1],
c=params[2],
d=params[3],
e=params[4],
f=params[5],
degree=DEGREE,
name="d_gamma")
self.d_Gsub1 = Expression(
(ccode(gamma_sp[0].diff(x1, L)).replace('M_PI', 'pi'),
ccode(gamma_sp[1].diff(x1, L)).replace('M_PI', 'pi')),
pi=pi,
length=self.length,
w=w_val,
a=params[0],
b=params[1],
c=params[2],
d=params[3],
e=params[4],
f=params[5],
degree=DEGREE,
name="d_Gsub1")
# per the example, store the derivatives as dictionaries
self.gamma.dependencies = [self.length]
self.gamma.user_defined_derivatives = {self.length: self.d_gamma}
self.Gsub1.dependencies = [self.length]
self.Gsub1.user_defined_derivatives = {self.length: self.d_Gsub1}
if dim == 3:
gamma_sp = [None, None, None]
gamma_sp[0] = X
gamma_sp[1] = x2
gamma_sp[2] = Z
self.gamma = Expression((ccode(
gamma_sp[0]).replace('M_PI', 'pi'), ccode(gamma_sp[1]).replace(
'M_PI', 'pi'), ccode(gamma_sp[2]).replace('M_PI', 'pi')),
pi=pi,
length=self.length,
w=w_val,
a=params[0],
b=params[1],
c=params[2],
d=params[3],
e=params[4],
f=params[5],
degree=DEGREE,
name="gamma")
# spatial derivative of above gamma (needed for PDE), similarly for \partial\gamma / \partial x2
self.Gsub1 = Expression(
(ccode(gamma_sp[0].diff(x1)).replace('M_PI', 'pi'),
ccode(gamma_sp[1].diff(x1)).replace('M_PI', 'pi'),
ccode(gamma_sp[2].diff(x1)).replace('M_PI', 'pi')),
pi=pi,
length=self.length,
w=w_val,
a=params[0],
b=params[1],
c=params[2],
d=params[3],
e=params[4],
f=params[5],
degree=DEGREE,
name="Gsub1")
self.Gsub2 = Expression(
(ccode(gamma_sp[0].diff(x2)).replace('M_PI', 'pi'),
ccode(gamma_sp[1].diff(x2)).replace('M_PI', 'pi'),
ccode(gamma_sp[2].diff(x2)).replace('M_PI', 'pi')),
pi=pi,
length=self.length,
w=w_val,
a=params[0],
b=params[1],
c=params[2],
d=params[3],
e=params[4],
f=params[5],
degree=DEGREE,
name="Gsub2")
# Now need the derivatives of the above wrt length for dolfin-adjoint
self.d_gamma = Expression(
(ccode(gamma_sp[0].diff(L)).replace('M_PI', 'pi'),
ccode(gamma_sp[1].diff(L)).replace('M_PI', 'pi'),
ccode(gamma_sp[2].diff(L)).replace('M_PI', 'pi')),
pi=pi,
length=self.length,
w=w_val,
a=params[0],
b=params[1],
c=params[2],
d=params[3],
e=params[4],
f=params[5],
degree=DEGREE,
name="d_gamma")
self.d_Gsub1 = Expression(
(ccode(gamma_sp[0].diff(x1, L)).replace('M_PI', 'pi'),
ccode(gamma_sp[1].diff(x1, L)).replace('M_PI', 'pi'),
ccode(gamma_sp[2].diff(x1, L)).replace('M_PI', 'pi')),
pi=pi,
length=self.length,
w=w_val,
a=params[0],
b=params[1],
c=params[2],
d=params[3],
e=params[4],
f=params[5],
degree=DEGREE,
name="d_Gsub1")
self.d_Gsub2 = Expression(
(ccode(gamma_sp[0].diff(x2, L)).replace('M_PI', 'pi'),
ccode(gamma_sp[1].diff(x2, L)).replace('M_PI', 'pi'),
ccode(gamma_sp[2].diff(x2, L)).replace('M_PI', 'pi')),
pi=pi,
length=self.length,
w=w_val,
a=params[0],
b=params[1],
c=params[2],
d=params[3],
e=params[4],
f=params[5],
degree=DEGREE,
name="d_Gsub2")
# per the example, store the derivatives as dictionaries
self.gamma.dependencies = [self.length]
self.gamma.user_defined_derivatives = {self.length: self.d_gamma}
self.Gsub1.dependencies = [self.length]
self.Gsub1.user_defined_derivatives = {self.length: self.d_Gsub1}
self.Gsub2.dependencies = [self.length]
self.Gsub2.user_defined_derivatives = {self.length: self.d_Gsub2}