def get_2d_slice_of_3d_function_on_Oz(mesh, u, T, dim, v_degree):
# create a boundary mesh
bmesh = BoundaryMesh(mesh, "exterior")
cell_func = CellFunction('size_t', bmesh, 0)
coordinates = bmesh.coordinates()
z_indeces = postprocess.allocate_array(dim)
for cell in cells(bmesh):
indx = 0
for vertex in vertices(cell):
z_indeces[indx] = coordinates[vertex.index()][dim - 1]
indx += 1
#print "Vertex index with coordinates", vertex.index(), coordinates[vertex.index()][dim-1]
if (dim == 3 and near(z_indeces[0], T) and near(z_indeces[1], T)
and near(z_indeces[2], T)) or (dim == 2 and near(
z_indeces[0], T) and near(z_indeces[1], T)):
#print "right cell", cell.index()
cell_func[cell] = 1
submesh = SubMesh(bmesh, cell_func, 1)
# create a FunctionSpace on the submesh-
Vs = FunctionSpace(submesh, "Lagrange", v_degree)
us = interpolate(u, Vs)
return us, submesh
def construct_boundary_faces(self, mesh):
# Get boundary facets function
facet_funcs = FacetFunction('size_t', mesh)
# Dirichlet part of the boudary is marked by 0
dirichlet_marker = 0
facet_funcs.set_all(dirichlet_marker)
neumann_marker = dirichlet_marker + 1
# Mark different parts of the domain for non-homogeneous Dirichlet BC
if test_num == 45:
# Creat parts of the boundary as subdomains
bottom = AutoSubDomain(lambda x: near(x[1], 0))
# Mark part of the domain with non-zero Dirichlet condition
bottom.mark(facet_funcs, dirichlet_marker + 1)
elif test_num == 48:
# Creat parts of the boundary as subdomains
right = AutoSubDomain(lambda x: near(x[0], 1))
# Mark part of the domain with non-zero Dirichlet condition
right.mark(facet_funcs, neumann_marker)
ds = Measure('ds')[facet_funcs]
dS = Measure('dS')[facet_funcs]
return facet_funcs, ds, dS
def map(self, x, y):
if near(x[0], 1.0) and near(x[1], 1.0):
y[0] = x[0] - 1.0
y[1] = x[1] - 1.0
elif near(x[0], 1.0):
y[0] = x[0] - 1.0
y[1] = x[1]
elif near(x[1], 1.0):
y[0] = x[0]
y[1] = x[1] - 1.0
def geometry_3d():
"""Prepares 3D geometry. Returns facet function with 1, 2 on parts of
the boundary."""
mesh = Mesh('lego_beam.xml')
gdim = mesh.geometry().dim()
x0 = mesh.coordinates()[:, 0].min()
x1 = mesh.coordinates()[:, 0].max()
boundary_parts = FacetFunction('size_t', mesh)
left = AutoSubDomain(lambda x: near(x[0], x0))
right = AutoSubDomain(lambda x: near(x[0], x1))
left.mark(boundary_parts, 1)
right.mark(boundary_parts, 2)
boundary_parts._mesh = mesh # Workaround issue #467
return boundary_parts
def geometry_2d(length):
"""Prepares 2D geometry. Returns facet function with 1, 2 on parts of
the boundary."""
n = 4
x0 = 0.0
x1 = x0 + length
y0 = 0.0
y1 = 1.0
mesh = RectangleMesh(x0, y0, x1, y1, int((x1 - x0) * n), int(
(y1 - y0) * n), 'crossed')
boundary_parts = FacetFunction('size_t', mesh)
left = AutoSubDomain(lambda x: near(x[0], x0))
right = AutoSubDomain(lambda x: near(x[0], x1))
left.mark(boundary_parts, 1)
right.mark(boundary_parts, 2)
boundary_parts._mesh = mesh # Workaround issue #467
return boundary_parts
def eval(self, value, x):
x_dist2 = float((x[0] - self.center[0]) * (x[0] - self.center[0]))
y_dist2 = float((x[1] - self.center[1]) * (x[1] - self.center[1]))
z_dist2 = float((x[2] - self.center[2]) * (x[2] - self.center[2]))
rad = float(sqrt(x_dist2 + y_dist2 + z_dist2))
# do not evaluate on boundaries or outside of circle:
velocity = 0 if near(rad, self.radius) or rad > self.radius else \
2.*self.onset_factor*self.factor*self.itp(self.t)*(1.0 - rad*rad/(self.radius*self.radius))
value[0] = velocity * self.normal[0]
value[1] = velocity * self.normal[1]
value[2] = velocity * self.normal[2]
def eval(self, value, x):
x_dist2 = float((x[0]-self.center[0])*(x[0]-self.center[0]))
y_dist2 = float((x[1]-self.center[1])*(x[1]-self.center[1]))
z_dist2 = float((x[2]-self.center[2])*(x[2]-self.center[2]))
rad = float(sqrt(x_dist2+y_dist2+z_dist2))
# do not evaluate on boundaries or outside of circle:
velocity = 0 if near(rad, self.radius) or rad > self.radius else \
2.*self.onset_factor*self.factor*self.itp(self.t)*(1.0 - rad*rad/(self.radius*self.radius))
value[0] = velocity * self.normal[0]
value[1] = velocity * self.normal[1]
value[2] = velocity * self.normal[2]
def solve_elasticity(mesh: Mesh) -> Function:
V = VectorFunctionSpace(mesh, 'P', 1)
bc = DirichletBC(V, Constant((0, 0, 0)), lambda x, on_boundary: on_boundary and near(x[2], 0))
u = TrialFunction(V)
v = TestFunction(V)
f = Expression(('0', '0', '-rho*g'), rho=_c.rho, g=_c.g, degree=3)
T = Constant((0, 0, 0))
a = inner(sigma(u), sym(nabla_grad(v))) * dx
L = dot(f, v) * dx + dot(T, v) * ds
u = Function(V)
solve(a == L, u, bc)
return u
time = 0.2
nu_factor = 10.
length = 20.0
v_in = 10.0
nu = Constant(3.7 * nu_factor)
dt = Constant(timestep)
f = Constant(0.0)
mesh_size = 10
# Create meshes and facet function
mesh = IntervalMesh(mesh_size, 0.0, length)
mesh_plot = IntervalMesh(8*mesh_size, 0.0, length)
boundary_parts = FacetFunction('size_t', mesh)
right = AutoSubDomain(lambda x: near(x[0], length))
left = AutoSubDomain(lambda x: near(x[0], 0.0))
right.mark(boundary_parts, 2)
left.mark(boundary_parts, 1)
# Create function spaces
V = FunctionSpace(mesh, 'Lagrange', 2)
# Vplot = FunctionSpace(mesh_plot, 'Lagrange', 1)
Vplot = V
Q = FunctionSpace(mesh, 'Lagrange', 1)
# BC conditions, nullspace
v_in_expr = Constant(v_in)
plt = plot(interpolate(v_in_expr, V), range_min=0., range_max=2*v_in, window_width= width, window_height= height)
plt.write_png('%s/correct' % dir)
# v_in_expr = Expression('(t<1.0)?t*v:v', v=Constant(v_in), t=0.0)
def inside(self, x, on_boundary):
return bool((near(x[0], 0.0) and near(x[1], 0.0))
and (not ((near(x[0], 0.0) and near(x[1], 1.0)) or
(near(x[0], 1.0) and near(x[1], 0.0))))
and on_boundary)
def construct_boundary_faces(self, mesh):
# Get boundary facets function
facet_funcs = FacetFunction('size_t', mesh)
facet_funcs.set_all(0)
# Dirichlet part of the boudary is marked by 0
# dirichlet_bc_marker = 1
# By default left and right is Dirichlet BC
left = AutoSubDomain(lambda x: near(x[0], 0.0)) # x_min
right = AutoSubDomain(lambda x: near(x[0], 1.0)) # x_max
left.mark(facet_funcs, dirichlet_bc_marker)
right.mark(facet_funcs, dirichlet_bc_marker)
if dim == 3:
# By default left and right is Dirichlet BC
top = AutoSubDomain(lambda x: near(x[1], 0.0)) # x_min
bottom = AutoSubDomain(lambda x: near(x[1], 1.0)) # x_max
top.mark(facet_funcs, dirichlet_bc_marker)
bottom.mark(facet_funcs, dirichlet_bc_marker)
#neumann_bc_marker = dirichlet_bc_marker + 1
if self.test_num == 24:
left = AutoSubDomain(lambda x: near(x[0], 0.0)) # x_min
right = AutoSubDomain(lambda x: near(x[0], 10.0)) # x_max
left.mark(facet_funcs, neumann_bc_marker)
right.mark(facet_funcs, neumann_bc_marker)
if self.test_num == 37:
right = AutoSubDomain(lambda x: near(x[0], 1.0)) # x_max
right.mark(facet_funcs, neumann_bc_marker)
if self.test_num == 38 or test_num == 39 or test_num == 40 or test_num == 41 or test_num == 42:
left = AutoSubDomain(lambda x: near(x[0], 0.0)) # x_min
right = AutoSubDomain(lambda x: near(x[0], 1.0)) # x_max
left.mark(facet_funcs, neumann_bc_marker)
right.mark(facet_funcs, neumann_bc_marker)
# The boundary with IC
#init_bc_marker = neumann_bc_marker + 1 # = 3
sigma_0 = AutoSubDomain(lambda x: near(x[1], 0.0))
sigma_0.mark(facet_funcs, init_bc_marker)
# The top of the space-time cylinder
#do_nothing_bc_marker = init_bc_marker + 1 # = 4
sigma_T = AutoSubDomain(lambda x: near(x[1], self.T))
sigma_T.mark(facet_funcs, do_nothing_bc_marker)
ds = Measure('ds')[facet_funcs]
dS = Measure('dS')[facet_funcs]
return facet_funcs, ds, dS
def inside(self, x, on_boundary):
return on_boundary and near(x[1], 0)
def inside(self, x, on_boundary):
return near( geoNormals[i].dot(Point(x)-geo._points[geoBndPoints[i]]), 0.0 ) and on_boundary
def on_upper_surface(self, x, on_boundary):
return on_boundary and near(x[2], self.H)
def on_bottom_surface(self, x, on_boundary):
return on_boundary and near(x[2], 0)
time = 0.2
nu_factor = 10.
length = 20.0
v_in = 10.0
nu = Constant(3.7 * nu_factor)
dt = Constant(timestep)
f = Constant(0.0)
mesh_size = 10
# Create meshes and facet function
mesh = IntervalMesh(mesh_size, 0.0, length)
mesh_plot = IntervalMesh(8 * mesh_size, 0.0, length)
boundary_parts = FacetFunction('size_t', mesh)
right = AutoSubDomain(lambda x: near(x[0], length))
left = AutoSubDomain(lambda x: near(x[0], 0.0))
right.mark(boundary_parts, 2)
left.mark(boundary_parts, 1)
# Create function spaces
V = FunctionSpace(mesh, 'Lagrange', 2)
# Vplot = FunctionSpace(mesh_plot, 'Lagrange', 1)
Vplot = V
Q = FunctionSpace(mesh, 'Lagrange', 1)
# BC conditions, nullspace
v_in_expr = Constant(v_in)
plt = plot(interpolate(v_in_expr, V),
range_min=0.,
range_max=2 * v_in,
