"""
** Example: meshing four rings & solving the laplace equation
for a space-dependent resistivity that depends on outer parameters
(Presumably, we will encounter bugs at our first try)
**
"""
##### Creating the mesh #####
# For now, we use a very very simple mesh...
rings = nmesh.union([nmesh.difference(nmesh.ellipsoid([3.0,3.0],
transform=[("shift",[-2.5,0.0])]),
[nmesh.ellipsoid([1.5,1.5],
transform=[("shift",[-2.5,0.0])])]),
nmesh.difference(nmesh.ellipsoid([3.0,3.0],
transform=[("shift",[2.5,0.0])]),
[nmesh.ellipsoid([1.5,1.5],
transform=[("shift",[2.5,0.0])])])])
boxed_rings=nmesh.intersect([rings,nmesh.box([-8.0,-2.5],[8.0,2.5])])
N = 100
density = "density=1.;"
the_mesh = nmesh.mesh(objects = [boxed_rings],
cache_name="rings-mesh",
a0=0.3,
bounding_box=[[-10.0,-3.5],[10.0,3.5]],
neigh_force_scale = 1.,
density = density,
{
H_total_Fe(0)=0.0;
H_total_Fe(1)=0.0;
H_total_Fe(2)=0.0;
}
"""
)
mag.set_local_magnetic_coupling(mat_Dy,mat_Fe,-80.0)
mag.defregion("DyFe2",nm.box([1.0],[2.0]),
mag_mat=[mat_Dy,mat_Fe]
)
mag.defregion("YFe2", nm.union([nm.box([0.0],[1.0]),nm.box([2.0],[3.0])]),
mag_mat=mat_Fe # can pass either a material or a list of materials
)
mag.set_meshing_parameters(cache_name="exchange-spring-mesh",
bounding_box=([-1.0],[5.0]),
a0=0.25,
max_steps=100,
)
mag.create_mesh()
def initial_m(dof_name,coords):
print "DDD initial_M(dof_name=\"",dof_name,"\",coords=",coords,")\n"
dir=dof_name[1][0]
if dir==0:
m=[0.0,1.0,0.0]
return m[dof_name_indices[1][0]]
# Note that we can easily also use the 3d differential operators for
# the 2d problems...
diffop_laplace=nfem.diffop("-<d/dxj rho_M||d/dxj phi_M>, j:3")
diffop_div_M=nfem.diffop("<rho_M||d/dxj M(j)>, j:3")
diffop_grad_phi=nfem.diffop("<H(j)||d/dxj phi_M>, j:3")
##### Creating the mesh #####
# For now, we use a very very simple mesh...
double_disc_2d = nmesh.union([nmesh.ellipsoid([3.0,3.0], transform=[("shift",[-1.0,0.0])]),
nmesh.ellipsoid([3.0,3.0], transform=[("shift",[1.0,0.0])])])
double_disc_3d = nmesh.union([nmesh.conic([-1.0,0.0,thickness2d*0.5],3.0,[-1.0,0.0,-thickness2d*0.5],3.0),
nmesh.conic([ 1.0,0.0,thickness2d*0.5],3.0,[ 1.0,0.0,-thickness2d*0.5],3.0)])
density = "density=1.;"
mesh_2d = nmesh.mesh(objects = [double_disc_2d],
cache_name="double-disc-2d",
a0=0.4,
bounding_box=[[-5.0,-5.0],[5.0,5.0]],
neigh_force_scale = 1.,
density = density,
initial_settling_steps = 50,
max_relaxation = 4,
# external ring
R = nmesh.ellipsoid(
[outer_radius, outer_radius],
transform=[("shift",[x*centres_distance, y*centres_distance])]
)
#internal ring
r = nmesh.ellipsoid(
[inner_radius, inner_radius],
transform=[("shift",[x*centres_distance, y*centres_distance])]
)
# take the difference
rings.append(nmesh.difference(R,[r]))
# cut the rings at top and bottom
union_rings = nmesh.union(rings)
rings_array = nmesh.intersect([union_rings,rings_box])
# semiaxis of a rhombus on the diagonals of the array
d = (centres_distance/2.) - Numeric.sqrt(outer_radius**2 - (centres_distance/2.)**2)
# rhombi on the diagonals of the array
for x in range(-3,4,2):
for y in range(-3,4,2):
centre_x = 0.5*x*centres_distance
centre_y = 0.5*y*centres_distance
# centre of the rhombus
c = Numeric.array([centre_x,centre_y])
import nmesh
box = nmesh.box([-4, -2], [4, 2])
ellipsoid = nmesh.ellipsoid([3, 3])
# create union
union = nmesh.union([box, ellipsoid])
bbox = [[-5, -4], [5, 4]]
mesh = nmesh.mesh(objects=[union], bounding_box=bbox)
mesh.save("union.nmesh")
nmesh.visual.plot2d_ps(mesh, "union.ps")
A=4.0,
extra_H="""H_total_Fe(0) -= mag[0]*1.2;
if(X(0)<0.01 || X(0)>3.99) /* pin the M field at boundaries */
{
H_total_Fe(0)=0.0;
H_total_Fe(1)=0.0;
H_total_Fe(2)=0.0;
}
""")
mag.set_local_magnetic_coupling(mat_Dy, mat_Fe, -80.0)
mag.defregion("DyFe2",
nm.union([
nm.box([0.0], [0.5]),
nm.box([1.5], [2.5]),
nm.box([3.5], [4.0])
]),
mag_mat=[mat_Dy, mat_Fe])
mag.defregion(
"YFe2",
nm.union([nm.box([0.5], [1.5]), nm.box([2.5], [3.5])]),
mag_mat=mat_Fe # can pass either a material or a list of materials
)
mag.set_meshing_parameters(
cache_name="exchange-spring-mesh",
bounding_box=([-1.0], [5.0]),
a0=0.1,
max_steps=100,
mat_Fe = mag.MagMaterial("Fe",Ms=1.2,A=4.0,
extra_H="""H_total_Fe(0) -= mag[0]*1.2;
if(X(0)<0.01 || X(0)>3.99) /* pin the M field at boundaries */
{
H_total_Fe(0)=0.0;
H_total_Fe(1)=0.0;
H_total_Fe(2)=0.0;
}
"""
)
mag.set_local_magnetic_coupling(mat_Dy,mat_Fe,-80.0)
mag.defregion("DyFe2",nm.union([nm.box([0.0],[0.5]),
nm.box([1.5],[2.5]),
nm.box([3.5],[4.0])]),
mag_mat=[mat_Dy,mat_Fe]
)
mag.defregion("YFe2", nm.union([nm.box([0.5],[1.5]),
nm.box([2.5],[3.5])]),
mag_mat=mat_Fe # can pass either a material or a list of materials
)
mag.set_meshing_parameters(cache_name="exchange-spring-mesh",
bounding_box=([-1.0],[5.0]),
a0=0.1,
max_steps=100,
)
import nmesh
box = nmesh.box( [-4,-2],[4,2] )
ellipsoid = nmesh.ellipsoid([3,3])
# create union
union = nmesh.union([box,ellipsoid])
bbox = [[-5,-4],[5,4]]
mesh = nmesh.mesh(objects = [union],bounding_box=bbox)
mesh.save("union.nmesh")
nmesh.visual.plot2d_ps(mesh,"union.ps")
import nmesh
nx = 2 #how many ellipsoids in x direction
x0 = 20 #spacing of ellipsoids in x
ny = 2 #how many ellipsoids in y direction
y0 = 20 #spacing of ellipsoids in x
rx, ry = 10.5, 10.5 #radii of ellipsoids
angle = 0 #orientation of ellipsoids
#create list 'objects' with ellipsoids
objects = []
for i in range(nx):
for j in range(ny):
objects.append(
nmesh.ellipsoid([rx, ry], [("rotate2d", angle),
("shift", [i * x0, j * y0])]))
union = nmesh.union(objects)
#bounding box
bbox = [[-15, -15], [(nx - 1) * x0 + 15, (ny - 1) * y0 + 15]]
#create the mesh
mesh = nmesh.mesh(objects=[union], a0=2, bounding_box=bbox)
#save plot to file
nmesh.visual.plot2d_ps(mesh, "mergedspheres.ps")
import nmesh
nx = 2 #how many ellipsoids in x direction
x0 = 20 #spacing of ellipsoids in x
ny = 2 #how many ellipsoids in y direction
y0 = 20 #spacing of ellipsoids in x
rx,ry = 10.5,10.5 #radii of ellipsoids
angle = 0 #orientation of ellipsoids
#create list 'objects' with ellipsoids
objects = []
for i in range(nx):
for j in range(ny):
objects.append( nmesh.ellipsoid([rx,ry], [("rotate2d",angle),
("shift",[i*x0,j*y0])]))
union = nmesh.union(objects)
#bounding box
bbox = [[-15,-15],[(nx-1)*x0+15,(ny-1)*y0+15]]
#create the mesh
mesh = nmesh.mesh(objects=[union],a0=2,bounding_box=bbox)
#save plot to file
nmesh.visual.plot2d_ps(mesh,"mergedspheres.ps")
import nmesh
# create sections of a square ring
bottom = nmesh.box( [2.0,1.0], [4.0,2.0])
right = nmesh.box( [4.0,1.0], [5.0,3.0])
top = nmesh.box( [3.0,3.0], [5.0,4.0])
left = nmesh.box( [2.0,2.0], [3.0,4.0])
# create compound
square_ring = nmesh.union([bottom,right,top,left])
rod= 0.4
bbox = [[-1.,-1.],[7.,6.]]
fixed_points = [[3.0,2.0],[4.0,2.0,],[3.0,3.0],[4.0,3.0]]
# create mesh
mesh_ex = nmesh.mesh(objects = [square_ring], a0=rod, bounding_box=bbox, \
fixed_points=fixed_points,
topology_threshold=0.2, # change the threshold
# for re-triangulation
# during mesh relaxation
time_step_scale=0.1, # change the factor which
# controls the time step
# used to relax the mesh
tolerated_rel_move=0.002,# change the threshold to
# stop the mesh relaxation