def cylinder(dim, radii, height, n_refinements=0):
"""
Creates the mesh of a cylinder using the mshr module.
"""
assert isinstance(dim, int)
assert dim == 2 or dim == 3
assert isinstance(radii, (list, tuple)) and len(radii) == 2
rt, rb = radii
assert isinstance(rb, float) and rb > 0.
assert isinstance(rt, float) and rt > 0.
assert isinstance(height, float) and height > 0.
assert isinstance(n_refinements, int) and n_refinements >= 0
# mesh generation
if dim == 2:
bottom = dlfn.Point(0., 0.)
top = dlfn.Point(0., height)
elif dim == 3:
bottom = dlfn.Point(0., 0., 0.)
top = dlfn.Point(0., 0., height)
if dim == 2:
domain = Polygon([
dlfn.Point(-rb / 2., 0.), bottom,
dlfn.Point(rb / 2., 0.),
dlfn.Point(rt / 2., height), top,
dlfn.Point(-rt / 2., height)
])
mesh = generate_mesh(domain, 10)
elif dim == 3:
domain = Cylinder(top, bottom, rt, rb, segments=100)
mesh = generate_mesh(domain, 32)
# mesh refinement
for i in range(n_refinements):
mesh = dlfn.refine(mesh)
# MeshFunction for boundaries ids
facet_marker = dlfn.MeshFunction("size_t", mesh, mesh.topology().dim() - 1)
facet_marker.set_all(0)
# calculate radius depending on the x[3] coordinate
def radius(z):
return rb + z * (rt - rb) / height
# mark boundaries
BoundaryMarkers = CylinderBoundaryMarkers
gamma_side = CylinderBoundary(mesh=mesh, radius=radius)
gamma_side.mark(facet_marker, BoundaryMarkers.side.value)
if dim == 2:
gamma_top = dlfn.CompiledSubDomain("near(x[1], height) && on_boundary",
height=height)
gamma_top.mark(facet_marker, BoundaryMarkers.top.value)
gamma_bottom = dlfn.CompiledSubDomain("near(x[1], 0.0) && on_boundary")
gamma_bottom.mark(facet_marker, BoundaryMarkers.bottom.value)
elif dim == 3:
gamma_top = dlfn.CompiledSubDomain("near(x[2], height) && on_boundary",
height=height)
gamma_top.mark(facet_marker, BoundaryMarkers.top.value)
gamma_bottom = dlfn.CompiledSubDomain("near(x[2], 0.0) && on_boundary")
gamma_bottom.mark(facet_marker, BoundaryMarkers.bottom.value)
return mesh, facet_marker
from finmag.energies import Demag
from finmag import Simulation as Sim
# #############################################
# ###### MESH GENERATOR
# LENGTHS
lex = 5.76 # nm (Exchange length)
L = 2000. # nm
r_ext = 3 * lex # External diameter in nm
r_int = 0.8 * r_ext
# Define the geometric structures to be processed
ntube = (Cylinder(
df.Point(0., 0., 0.),
df.Point(0., 0., L),
r_ext,
r_ext,
) - Cylinder(
df.Point(0., 0., 0.),
df.Point(0., 0., L),
r_int,
r_int,
))
# Create the mesh
diag = np.sqrt(L**2 + (3 * lex)**2)
resolut = diag / 3.
mesh = mshr.generate_mesh(ntube, resolut)
# Output Mesh
outp = file('mesh_info.dat', 'w')
import matplotlib
matplotlib.use("TkAgg")
import matplotlib.pyplot as plt
import fenics as fe
from mshr import Box, Cylinder, generate_mesh, Rectangle, Circle
BOX_SIZE = 1
CYL_X, CYL_Y, CYL_Z1, CYL_Z2 = 0.5, 0.5, 0.2, 0.6
CYL_R = 0.1
MESH_PTS = 40
CONDUCTIVITY = 30 # S/m
CURRENT = 0.01 # idk what units
# Define solution domain
box = Box(fe.Point(0, 0, 0), fe.Point(BOX_SIZE, BOX_SIZE, BOX_SIZE))
cylinder = Cylinder(fe.Point(CYL_X, CYL_Y, CYL_Z1), fe.Point(CYL_X, CYL_Y, CYL_Z2), CYL_R, CYL_R)
# DEBUG
# box = Rectangle(fe.Point(0, 0), fe.Point(BOX_SIZE, BOX_SIZE))
# cylinder = Circle(fe.Point(CYL_X, CYL_Y), CYL_R)
# END DEBUG
domain = box - cylinder
# Generate and display the mesh
mesh = generate_mesh(domain, MESH_PTS)
# fe.plot(mesh, "3D Mesh")
# plt.show()
# Variables defined below are named exactly as in eq (A.1) (see comment at top of file)
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with mshr. If not, see <http://www.gnu.org/licenses/>.
#
import dolfin
from mshr import Sphere, Cylinder, CSGCGALDomain3D, generate_mesh
# dolfin.set_log_level(dolfin.TRACE)
dolfin.set_log_active(True)
dolfin.set_log_level(4)
# Define 3D geometry
sphere = Sphere(dolfin.Point(0, 0, 0), 0.5)
cone = Cylinder(dolfin.Point(0, 0, 0), dolfin.Point(0, 0, -1), .35, .1)
geometry = cone + sphere
# Geometry surfaces can be saved to off files
# which can be viewed by eg. MeshLab
meshing_domain = CSGCGALDomain3D(geometry)
meshing_domain.remove_degenerate_facets(1e-12)
meshing_domain.save("icecream.off")
# Test printing
dolfin.info("\nCompact output of 3D geometry:")
dolfin.info(geometry)
dolfin.info("\nVerbose output of 3D geometry:")
dolfin.info(geometry, True)
def _create_mesh(self):
return generate_mesh(
Cylinder(Point(0.0, 0.0, 0.0), Point(0.0, 0.0, self.H), self.R,
self.R), 100)
# Geometry and material properties dim = 3 # number of dimensions R = 0.005 L = 0.05 rho = 3000 E = 4000000 nu = 0.3 mu = Constant(E / (2.0 * (1.0 + nu))) lambda_ = Constant(E * nu / ((1.0 + nu) * (1.0 - 2.0 * nu))) # create Mesh outer_tube = Cylinder(Point(0, 0, L), Point(0, 0, 0), R + 0.001, R + 0.001) inner_tube = Cylinder(Point(0, 0, L), Point(0, 0, 0), R, R) mesh = generate_mesh(outer_tube - inner_tube, 20) # create Function Space V = VectorFunctionSpace(mesh, 'P', 2) # Trial and Test Functions du = TrialFunction(V) v = TestFunction(V) u_np1 = Function(V) saved_u_old = Function(V) u_delta = Function(V) # function known from previous timestep
def _create_mesh(self):
L = 0.2
R = 1.0
self.mesh = generate_mesh(
Cylinder(Point(0.0, 0.0, L), Point(0.0, 0.0, 0.0), R, R), 64)
File("../output/elasticity/mesh.xml") << self.mesh
def get(self):
"""Use mshr Cylinder, though centers seem to not work."""
h, b, t, n, k = self.pad(self.values)
from mshr import Cylinder
c = Cylinder(Point(0, 0, 0), Point(0, 0, h), b, t, n)
return generate_mesh(c, k)
tmax = 2.0*np.pi/omega*args.simTime t_vec = np.arange((args.steps+1)*dt, tmax, dt) #Set up mesh tankHeight = args.height if(args.geometry == 'rectangle'): dim=1 #dimension of the surface tankWidth = args.width tankLength = args.length meshHeight=tankHeight mesh=RectangleMesh(Point(0.0,0.0), Point(tankLength,tankHeight),args.xmesh, args.zmesh, 'right/left') elif (args.geometry == 'cylinder'): dim=2 #dimension of the surface tankRadius = args.radius meshHeight = args.zmesh/args.xmesh*tankRadius cylinder=Cylinder(Point(0.0,0.0,0.0),Point(0.0,0.0,meshHeight),tankRadius,tankRadius) mesh=generate_mesh(cylinder,args.xmesh) elif (args.geometry == 'box'): dim=2 #dimension of the surface tankWidth = args.width tankLength = args.length meshHeight=tankHeight mesh=BoxMesh(Point(0.0,0.0), Point(tankLength,tankWidth,tankHeight),args.xmesh, args.ymesh,args.zmesh) #Refine the top cells def refine_top(mesh): topvertices = np.array(np.where(np.abs(mesh.coordinates()[:,dim]-meshHeight)< 10*DOLFIN_EPS)[0]) topcells=[] for i in range(len(mesh.cells())): for vertex in mesh.cells()[i]: if(np.any(topvertices==vertex)):