def set_boundary_conditions(self):
if self._space_dim == 2:
# boundary conditions
gamma01 = PointSubDomain((0.0, 0.0), tol=1e-10)
gamma02 = dlfn.CompiledSubDomain("near(x[1], 0.0)")
self._bcs = [
(DisplacementBCType.fixed_pointwise, gamma01, None),
(DisplacementBCType.fixed_component_pointwise, gamma02, 1,
None),
(DisplacementBCType.constant_component,
CylinderBoundaryMarkers.top.value, 1, self._top_displacement)
]
if self._space_dim == 3:
# boundary conditions
gamma01 = PointSubDomain((0.0, 0.0, 0.0), tol=1e-10)
gamma02 = dlfn.CompiledSubDomain("near(x[2], 0.0)")
gamma03 = PointSubDomain((0.0, 0.1, 0.0), tol=1e-10)
self._bcs = [
(DisplacementBCType.fixed_pointwise, gamma01, None),
(DisplacementBCType.fixed_component_pointwise, gamma02, 2,
None),
(DisplacementBCType.fixed_component_pointwise, gamma03, 0,
None),
(DisplacementBCType.constant_component,
CylinderBoundaryMarkers.top.value, 2, self._top_displacement)
]
def __init__(self, pointa, pointb, *, eps = csg_eps):
eps *= numpy.linalg.norm(numpy.array(pointb)-numpy.array(pointa))
super().__init__(mshr.Rectangle(dolfin.Point(*pointa), dolfin.Point(*pointb)), csg_boundaries = [
dolfin.CompiledSubDomain('on_boundary && near(x[0], xx, eps)', xx = pointa[0], eps = eps),
dolfin.CompiledSubDomain('on_boundary && near(x[0], xx, eps)', xx = pointb[0], eps = eps),
dolfin.CompiledSubDomain('on_boundary && near(x[1], xx, eps)', xx = pointa[1], eps = eps),
dolfin.CompiledSubDomain('on_boundary && near(x[1], xx, eps)', xx = pointb[1], eps = eps)
])
def get_2d_rectangular_mesh_boundaries(xl, xr, yb, yt):
left_bndry = dl.CompiledSubDomain(
"near(x[0],%e)&&on_boundary" % xl)
right_bndry = dl.CompiledSubDomain(
"near(x[0],%e)&&on_boundary" % xr)
bottom_bndry = dl.CompiledSubDomain(
"near(x[1],%e)&&on_boundary" % yb)
top_bndry = dl.CompiledSubDomain(
"near(x[1],%e)&&on_boundary" % yt)
return left_bndry, right_bndry, bottom_bndry, top_bndry
def test_centers(self):
mesh = df.UnitCubeMesh(4, 4, 4)
facet_f = df.MeshFunction('size_t', mesh, 2, 0)
df.CompiledSubDomain('near(x[0], 0)').mark(facet_f, 1)
df.CompiledSubDomain('near(x[0], 1)').mark(facet_f, 2)
x = np.array(get_geom_centers(facet_f, (1, 2)))
y = np.array([[0, 0.5, 0.5], [1, 0.5, 0.5]])
self.assertTrue(np.linalg.norm(x - y) < 1E-13)
def test_from_DG0(self):
def main(n, chi, measure, restrict):
mesh = df.UnitCubeMesh(2, n, n)
facet_f = df.MeshFunction('size_t', mesh, 2, 0)
chi.mark(facet_f, 1)
submesh = EmbeddedMesh(facet_f, 1)
transfer = SubMeshTransfer(mesh, submesh)
V = df.FunctionSpace(mesh, 'Discontinuous Lagrange Trace', 0)
Vsub = df.FunctionSpace(submesh, 'DG', 0)
to_V = transfer.compute_map(V, Vsub, strict=False)
# Set degree 0 to get the quad order right
f = df.Expression('x[0] + 2*x[1] - x[2]', degree=0)
fsub = df.interpolate(f, Vsub)
fV = df.Function(V)
to_V(fV, fsub)
y = V.tabulate_dof_coordinates().reshape((V.dim(), -1))
x = Vsub.tabulate_dof_coordinates().reshape((Vsub.dim(), -1))
# Correspondence of coordinates
self.assertTrue(np.linalg.norm(y[transfer.cache] - x) < 1E-13)
# These are all the coordinates
idx = list(set(range(V.dim())) - set(transfer.cache))
self.assertTrue(not any(chi.inside(xi, True) for xi in y[idx]))
dS_ = df.Measure(measure, domain=mesh, subdomain_data=facet_f)
# Stange that this is not exact
error = df.inner(restrict(fV - f), restrict(fV - f))*dS_(1)
error = df.sqrt(abs(df.assemble(error, form_compiler_parameters={'quadrature_degree': 0})))
return error
# Trick domains boundary beacuse we want to use inside properly?
bdry = df.CompiledSubDomain(' || '.join(['near(x[0]*(1-x[0]), 0)',
'near(x[1]*(1-x[1]), 0)',
'near(x[2]*(1-x[2]), 0)']))
inputs = ((df.CompiledSubDomain('near(x[0], 0.5)'), 'dS', df.avg),
(bdry, 'ds', lambda x: x))
for chi, measure, restrict in inputs:
errors = []
for n in (2, 4, 8, 16):
e = main(n, chi, measure, restrict)
self.assertTrue(not errors or e < errors[-1])
errors.append(e)
def boundaries_of_rectangle_mesh(mesh):
x0, y0 = mesh.coordinates().min(0)
x1, y1 = mesh.coordinates().max(0)
atol_x = (x1 - x0) * EPS
atol_y = (y1 - y0) * EPS
bot = dolfin.CompiledSubDomain('x[1] < y0 && on_boundary', y0=y0+atol_y)
rhs = dolfin.CompiledSubDomain('x[0] > x1 && on_boundary', x1=x1-atol_x)
top = dolfin.CompiledSubDomain('x[1] > y1 && on_boundary', y1=y1-atol_y)
lhs = dolfin.CompiledSubDomain('x[0] < x0 && on_boundary', x0=x0+atol_x)
return bot, rhs, top, lhs
def get_brain(case_id, conductivity) -> CoupledBrainModel:
time_constant = df.Constant(0)
mesh, cell_function, interface_function = get_mesh("rose_meshes", "rose")
cell_tags = CellTags(CSF=3, GM=2, WM=1, Kinf=4)
interface_tags = InterfaceTags(skull=None, CSF_GM=None, GM_WM=None, CSF=None, GM=None, WM=None)
test_cell_function = df.MeshFunction("size_t", mesh, mesh.geometric_dimension())
test_cell_function.set_all(0)
df.CompiledSubDomain("x[1] >= -pi/16*x[0]").mark(test_cell_function, 4)
if case_id == 1:
df.CompiledSubDomain("x[1] >= 25*pi/16*x[0]").mark(test_cell_function, 2)
elif case_id == 2:
df.CompiledSubDomain("x[1] >= 7*pi/32*x[0]").mark(test_cell_function, 2)
cell_function.array()[(cell_function.array() == 2) & (test_cell_function.array() == 4)] = 4
Chi = 1.26e3 # 1/cm -- Dougherty 2015
Cm = 1.0 # muF/cm^2 -- Dougherty 2015
Mi_dict = {
3: df.Constant(1e-12), # Set to zero? 1e-12
1: df.Constant(conductivity), # Dlougherty isotropic WM intracellular conductivity 1.0 [mS/cm]
2: df.Constant(conductivity), # Dlougherty isotropic GM intracellular conductivity 1.0 [mS/cm]
4: df.Constant(conductivity), # Dlougherty isotropic GM intracellular conductivity 1.0 [mS/cm]
}
Me_dict = {
3: df.Constant(16.54), # Dougherty isotropic CSF conductivity 16.54 [mS/cm] 16.54
1: df.Constant(1.26), # 1.26 # Dougherty isotropic WM extracellular conductivity 1.26 [mS/cm]
2: df.Constant(2.76), # 2.76 # Dougherty isotropic GM extracellular conductivity 2.76 [mS/cm]
4: df.Constant(2.76), # 2.76 # Dougherty isotropic GM extracellular conductivity 2.76 [mS/cm]
}
brain = CoupledBrainModel(
time=time_constant,
mesh=mesh,
cell_model=Cressman(),
cell_function=cell_function,
cell_tags=cell_tags,
interface_function=interface_function,
interface_tags=interface_tags,
intracellular_conductivity=Mi_dict,
other_conductivity=Me_dict, # Either lmbda or extracellular
surface_to_volume_factor=Chi,
membrane_capacitance=Cm
)
return brain
def test3D(self):
nx = 10
ny = 15
nz = 20
mesh = dl.UnitCubeMesh(nx, ny, nz)
true_sub = dl.CompiledSubDomain("x[0] <= .5")
true_marker = dl.MeshFunction('size_t', mesh, 3, value=0)
true_sub.mark(true_marker, 1)
np_sub_x = np.ones(nx, dtype=np.uint)
np_sub_x[nx // 2:] = 0
np_sub_y = np.ones(ny, dtype=np.uint)
np_sub_z = np.ones(nz, dtype=np.uint)
np_sub_xx, np_sub_yy, np_sub_zz = np.meshgrid(np_sub_x,
np_sub_y,
np_sub_z,
indexing='ij')
np_sub = np_sub_xx * np_sub_yy * np_sub_zz
h = np.array([1. / nx, 1. / ny, 1. / nz])
marker = dl.MeshFunction('size_t', mesh, 3)
numpy2MeshFunction(mesh, h, np_sub, marker)
assert_allclose(marker.array(),
true_marker.array(),
rtol=1e-7,
atol=1e-9)
def set_boundary_conditions(self):
# boundary conditions
self._bcs = []
BCType = DisplacementBCType
if self._bc_type == "floating":
self._bcs.append((BCType.fixed_component,
HyperCubeBoundaryMarkers.left.value, 0, None))
self._bcs.append((BCType.fixed_component,
HyperCubeBoundaryMarkers.bottom.value, 1, None))
self._bcs.append((BCType.constant_component,
HyperCubeBoundaryMarkers.right.value, 0, 0.1))
elif self._bc_type == "clamped":
self._bcs.append(
(BCType.fixed, HyperCubeBoundaryMarkers.left.value, None))
self._bcs.append(
(BCType.constant, HyperCubeBoundaryMarkers.right.value, (0.1,
0.0)))
elif self._bc_type == "clamped_free":
self._bcs.append(
(BCType.fixed, HyperCubeBoundaryMarkers.left.value, None))
self._bcs.append((BCType.constant_component,
HyperCubeBoundaryMarkers.right.value, 0, 0.1))
elif self._bc_type == "pointwise":
gamma01 = PointSubDomain((0.0, ) * self._space_dim, tol=1e-10)
gamma02 = dlfn.CompiledSubDomain("near(x[0], 0.0)")
self._bcs.append((BCType.fixed_pointwise, gamma01, None))
self._bcs.append(
(BCType.fixed_component_pointwise, gamma02, 0, None))
self._bcs.append((BCType.constant_component,
HyperCubeBoundaryMarkers.right.value, 0, 0.1))
def mark_rectangular_subdomain(p0, p1, mesh):
'''Get markers for a rectangular subdomain.
Parameters
----------
p0 : point-like
Bottom-left vertex coordinates.
p1 : point-like
Top-right vertex coordinates.
mesh : dolfin.Mesh
Domain mesh.
Returns
-------
domain_markers : dolfin.MeshFunction
Domain markers where displacement measurements are known. The subdomain
is identified with mesh function values equal to 1.
'''
SUBDOMAIN_MARKER_ID = 1
subdomain = dolfin.CompiledSubDomain(
"x[0] > x0 && x[0] < x1 && x[1] > y0 && x[1] < y1",
x0=p0[0], y0=p0[1], x1=p1[0], y1=p1[1])
subdomain_markers = dolfin.MeshFunction('size_t',
mesh, dim=mesh.topology().dim(), value=0)
subdomain.mark(subdomain_markers, SUBDOMAIN_MARKER_ID)
return subdomain_markers, SUBDOMAIN_MARKER_ID
def test_to_DG0_subdomain(self):
mesh = df.UnitSquareMesh(4, 4)
cell_f = df.MeshFunction('size_t', mesh, 2, 0)
df.CompiledSubDomain('x[0] < 0.5 + DOLFIN_EPS').mark(cell_f, 1)
submesh = EmbeddedMesh(cell_f, 1)
transfer = SubMeshTransfer(mesh, submesh)
V = df.FunctionSpace(mesh, 'DG', 0)
Vsub = df.FunctionSpace(submesh, 'DG', 0)
to_Vsub = transfer.compute_map(Vsub, V, strict=True)
# Set degree 0 to get the quad order right
f = df.Expression('x[0] + 2*x[1]', degree=0)
fV = df.interpolate(f, V)
fsub = df.Function(Vsub)
to_Vsub(fsub, fV)
error = df.inner(fsub - f, fsub - f)*df.dx(domain=submesh)
error = df.sqrt(abs(df.assemble(error)))
self.assertTrue(error < 1E-13)
def test_to_DG0(self):
subdomains = (df.CompiledSubDomain('near(x[0], 0.5)'), df.DomainBoundary())
for subd in subdomains:
mesh = df.UnitCubeMesh(4, 4, 4)
facet_f = df.MeshFunction('size_t', mesh, 2, 0)
subd.mark(facet_f, 1)
submesh = EmbeddedMesh(facet_f, 1)
transfer = SubMeshTransfer(mesh, submesh)
V = df.FunctionSpace(mesh, 'Discontinuous Lagrange Trace', 0)
Vsub = df.FunctionSpace(submesh, 'DG', 0)
to_Vsub = transfer.compute_map(Vsub, V, strict=False)
# Set degree 0 to get the quad order right
f = df.Expression('x[0] + 2*x[1] - x[2]', degree=0)
fV = df.interpolate(f, V)
fsub = df.Function(Vsub)
to_Vsub(fsub, fV)
error = df.inner(fsub - f, fsub - f)*df.dx(domain=submesh)
error = df.sqrt(abs(df.assemble(error)))
self.assertTrue(error < 1E-13)
def __init__(self, center, radius, *, maxh = 1., eps = csg_eps): segments = max(int(4*radius/maxh), 32) eps *= radius super().__init__(mshr.Circle(dolfin.Point(*center), radius, segments), csg_boundaries = [ dolfin.CompiledSubDomain( 'on_boundary && near((x[0]-c0)*(x[0]-c0) + (x[1]-c1)*(x[1]-c1), rr, eps)', c0 = center[0], c1 = center[1], rr = radius * radius, eps = eps ) ])
def union(domains, A=inner_size, tol=1E-10):
def body(domains):
if isinstance(domains, str):
if domains:
return '( %s )' % domains
else:
return ''
else:
return ' || '.join(map(body, domains))
return df.CompiledSubDomain(body(domains), A=A, tol=tol)