def test_heat_transfer_4():
def solution(x, q0=1., k=1., N=20):
def fun(n):
al = .5 * (2. * n - 1.) * pi
top = (-1)**n*cos(al*x[:,1])*cosh(al*x[:,0])
bot = al**3*cosh(al)
return top / bot
return q0/2/k*((1-x[:,1]**2)+4.*sum([fun(n) for n in range(1,N)], 0))
random.seed(190) # Always the same results
fd = lambda p: dm.drectangle(p, 0, 1, 0, 1)
fh = dm.huniform
coord, elecon = dm.distmesh2d(fd, fh, .025, (0, 0, 1, 1),
[(0, 0),(0, 1),(1, 0),(1, 1)])
V = fe_model()
V.create_mesh(p=coord, t=elecon)
V.create_material('Material-1')
V.materials['Material-1'].isotropic_thermal_conductivity(1.)
V.create_element_block('ElementBlock1', ALL)
V.assign_properties('ElementBlock1', DC2D3, 'Material-1')
stage = V.create_heat_transfer_stage()
stage.assign_prescribed_bc(IHI, T)
stage.assign_prescribed_bc(JHI, T)
stage.HeatGeneration(ALL, 1)
stage.run()
Tn = solution(V.mesh.coord)
err = sqrt(mean((stage.dofs.flatten()-Tn)**2)) / sqrt(mean(Tn**2))
assert err < 1e-4
def test_heat_transfer_3():
def solution(x, N=20):
def fun(n):
return sin(2.*n*pi/3.)/n**2/sinh(n*pi)*sin(n*pi*x[:,0])*sinh(n*pi*x[:,1])
return 450./pi**2*sum([fun(n) for n in range(1, N)], 0)
random.seed(190) # Always the same results
fd = lambda p: dm.drectangle(p, 0, 1, 0, 1)
fh = dm.huniform
coord, elecon = dm.distmesh2d(fd, fh, .05, (0, 0, 1, 1),
[(0, 0),(0, 1),(1, 0),(1, 1)])
f2 = lambda x: where(x[:,0] <= 2./3., 75*x[:,0], 150*(1-x[:,0]))
V = FiniteElementModel()
V.Mesh(p=coord, t=elecon)
V.Material('Material-1')
V.materials['Material-1'].IsotropicThermalConductivity(1.)
V.ElementBlock('ElementBlock1', ALL)
V.AssignProperties('ElementBlock1', DiffussiveHeatTransfer2D3, 'Material-1')
step = V.HeatTransferStep()
step.PrescribedBC(JLO, T, 0)
step.PrescribedBC(JHI, T, f2)
step.PrescribedBC(ILO, T, 0)
step.PrescribedBC(IHI, T, 0)
step.HeatGeneration(ALL, 0)
step.run()
Tn = solution(V.mesh.coord)
err = sqrt(mean((step.dofs.flatten()-Tn)**2)) / sqrt(mean(Tn**2))
assert err < 5e-3
def plate_with_hole(size=.05):
fd = lambda p: dm.ddiff(dm.drectangle(p, -1, 1, -1, 1),
dm.dcircle(p, 0, 0, 0.5))
fh = lambda p: 0.05 + 0.3 * dm.dcircle(p, 0, 0, 0.5)
p, t = dm.distmesh2d(fd, fh, size, (-1, -1, 1, 1), [(-1, -1), (-1, 1),
(1, -1), (1, 1)])
return p, t
def rectangle_with_circular_hole():
"""Rectangle with circular hole, refined at circle boundary"""
fd = lambda p: dm.ddiff(dm.drectangle(p, -1, 1, -1, 1),
dm.dcircle(p, 0, 0, 0.5))
fh = lambda p: 0.05 + 0.3 * dm.dcircle(p, 0, 0, 0.5)
return dm.distmesh2d(fd, fh, 0.05, (-1, -1, 1, 1), [(-1, -1), (-1, 1),
(1, -1), (1, 1)])
def test_heat_transfer_5():
def solution(x, q0=1., k=1., N=20):
def fun(n):
al = .5 * (2. * n - 1.) * pi
top = (-1)**n*cos(al*x[:,1])*cosh(al*x[:,0])
bot = al**3*cosh(al)
return top / bot
return q0/2/k*((1-x[:,1]**2)+4.*sum([fun(n) for n in range(1,N)], 0))
random.seed(190) # Always the same results
fd = lambda p: dm.drectangle(p, 0, 1, 0, 1)
fh = dm.huniform
coord, elecon = dm.distmesh2d(fd, fh, .025, (0, 0, 1, 1),
[(0, 0),(0, 1),(1, 0),(1, 1)])
V = FiniteElementModel()
V.Mesh(p=coord, t=elecon)
V.Material('Material-1')
V.materials['Material-1'].IsotropicThermalConductivity(1.)
V.ElementBlock('ElementBlock1', ALL)
V.AssignProperties('ElementBlock1', DiffussiveHeatTransfer2D3, 'Material-1')
step = V.HeatTransferStep()
step.PrescribedBC(IHI, T)
step.PrescribedBC(JHI, T)
step.HeatGeneration(ALL, 1)
step.run()
Tn = solution(V.mesh.coord)
err = sqrt(mean((step.dofs.flatten()-Tn)**2)) / sqrt(mean(Tn**2))
assert err < 1e-4
def square():
"""Square, with size function point and line sources"""
fd = lambda p: dm.drectangle(p,0,1,0,1)
fh = lambda p: np.minimum(np.minimum(
0.01+0.3*abs(dm.dcircle(p,0,0,0)),
0.025+0.3*abs(dm.dpoly(p,[(0.3,0.7),(0.7,0.5)]))), 0.15)
return dm.distmesh2d(fd, fh, 0.01, (0,0,1,1), [(0,0), (1,0), (0,1), (1,1)])
def plate_with_hole(size=.05):
fd = lambda p: dm.ddiff(dm.drectangle(p,-1,1,-1,1),
dm.dcircle(p,0,0,0.5))
fh = lambda p: 0.05+0.3*dm.dcircle(p,0,0,0.5)
p, t = dm.distmesh2d(fd, fh, size, (-1,-1,1,1),
[(-1,-1),(-1,1),(1,-1),(1,1)])
return p, t
def square():
"""Square, with size function point and line sources"""
fd = lambda p: dm.drectangle(p, 0, 1, 0, 1)
fh = lambda p: np.minimum(
np.minimum(0.01 + 0.3 * abs(dm.dcircle(p, 0, 0, 0)), 0.025 + 0.3 * abs(
dm.dpoly(p, [(0.3, 0.7), (0.7, 0.5)]))), 0.15)
return dm.distmesh2d(fd, fh, 0.01, (0, 0, 1, 1), [(0, 0), (1, 0), (0, 1),
(1, 1)])
def test_write_fe_results():
from distmesh import drectangle, distmesh2d, huniform
random.seed(190) # Always the same results
fd = lambda p: drectangle(p, -1, 1, -1, 1)
fh = huniform
coord, elecon = distmesh2d(fd, fh, .1, (-1, -1, 1, 1),
[(-1, -1),(-1, 1),(1, -1),(1, 1)])
jobid = 'Job'
nodlab = range(coord.shape[0])
nodmap = dict([(n,n) for n in nodlab])
elelab = range(elecon.shape[0])
elemap = dict([(n,n) for n in elelab])
eletyp = [element_family(2,3)] * elecon.shape[0]
scal = random.rand(coord.shape[0])
vect = random.rand(coord.shape[0]*2).reshape(-1,2)
tens = random.rand(elecon.shape[0]*9).reshape(-1,9)
symt = random.rand(elecon.shape[0]*6).reshape(-1,6)
kwds = dict(scal=scal,vect=vect,tens=tens,symt=symt)
u = zeros_like(coord)
u[:,0] = 1
WriteFEResults(jobid, coord, nodmap, elemap, eletyp, elecon, u=u, **kwds)
filename = jobid+'.vtu'
WriteVTUMesh(filename, coord, nodlab, elelab, eletyp, elecon, check=1)
os.remove(filename)
def test_write_fe_results():
from distmesh import drectangle, distmesh2d, huniform
random.seed(190) # Always the same results
fd = lambda p: drectangle(p, -1, 1, -1, 1)
fh = huniform
coord, elecon = distmesh2d(fd, fh, .1, (-1, -1, 1, 1),
[(-1, -1),(-1, 1),(1, -1),(1, 1)])
jobid = 'Job'
nodlab = range(coord.shape[0])
nodmap = dict([(n,n) for n in nodlab])
elelab = range(elecon.shape[0])
elemap = dict([(n,n) for n in elelab])
eletyp = [ElementFamily(2,3)] * elecon.shape[0]
scal = random.rand(coord.shape[0])
vect = random.rand(coord.shape[0]*2).reshape(-1,2)
tens = random.rand(elecon.shape[0]*9).reshape(-1,9)
symt = random.rand(elecon.shape[0]*6).reshape(-1,6)
kwds = dict(scal=scal,vect=vect,tens=tens,symt=symt)
u = zeros_like(coord)
u[:,0] = 1
WriteFEResults(jobid, coord, nodmap, elemap, eletyp, elecon, u=u, **kwds)
filename = jobid+'.vtu'
WriteVTUMesh(filename, coord, nodlab, elelab, eletyp, elecon, check=1)
os.remove(filename)
def rectangle_with_circle_at_centre():
# Does not terminate!
fd = lambda p: dm.ddiff(dm.drectangle(p, 0, 20, 0, 12),
dm.dcircle(p, 10, 6, 4))
return dm.distmesh2d(fd, dm.huniform, 0.5, (0, 0, 20, 12), max_iter=100)
def rectangle_with_circle_at_corner():
# Does not terminate!
fd = lambda p: dm.ddiff(dm.drectangle(p, 0, 10, 0, 6),
dm.dcircle(p, 10, 0, 4))
return dm.distmesh2d(fd, dm.huniform, 0.9, (0, 0, 10, 6))
def rectangle_with_circle_at_centre():
# Does not terminate!
fd = lambda p: dm.ddiff(dm.drectangle(p,0,20,0,12), dm.dcircle(p,10,6,4))
return dm.distmesh2d(fd, dm.huniform, 0.5, (0, 0, 20, 12), max_iter=100)
def fdout(p):
return dm.dunion(dm.dunion(dm.dcircle(p,0,0,rad), dm.drectangle(p,0.0,2*rad, -rad,rad)), dm.dcircle(p,2*rad,0,rad))
def __init__(self, lx, ly, cx, cy, r): fd = lambda p: dm.ddiff(dm.drectangle(p,-lx,lx,-ly,ly), dm.dcircle(p,cx,cx,r)) fh = lambda p: 0.05+0.03*dm.dcircle(p,cx,cy,r) p, t = dm.distmeshnd(fd, fh, 0.5, (-lx,-ly,lx,ly),[(-lx,-ly),(-lx,ly),(lx,-ly),(lx,ly)]) self.nodes = p self.conn = t
def uniform_plate(size=.05):
fd = lambda p: dm.drectangle(p, -1, 1, -1, 1)
fh = dm.huniform
p, t = dm.distmesh2d(fd, fh, size, (-1, -1, 1, 1), [(-1, -1), (-1, 1),
(1, -1), (1, 1)])
return p, t
def simple_rect():
fd = lambda p: dm.drectangle(p,0,1,0,1)
return dm.distmesh2d(fd, dm.huniform, 0.1, (0, 0, 1, 1), max_iter=100)
def rectangle_with_circle_at_corner():
# Does not terminate!
fd = lambda p: dm.ddiff(dm.drectangle(p,0,10,0,6), dm.dcircle(p,10,0,4))
return dm.distmesh2d(fd, dm.huniform, 0.9, (0, 0, 10, 6))
def uniform_plate(size=.05):
fd = lambda p: dm.drectangle(p, -1, 1, -1, 1)
fh = dm.huniform
p, t = dm.distmesh2d(fd, fh, size, (-1, -1, 1, 1),
[(-1, -1),(-1, 1),(1, -1),(1, 1)])
return p, t
def simple_rect():
fd = lambda p: dm.drectangle(p, 0, 1, 0, 1)
return dm.distmesh2d(fd, dm.huniform, 0.1, (0, 0, 1, 1), max_iter=100)
import distmesh as dm fd = lambda p: dm.ddiff(dm.drectangle(p,-1,1,-1,1), dm.dcircle(p,0,0,0.5)) fh = lambda p: 0.05+0.3*dm.dcircle(p,0,0,0.5) p, t = dm.distmesh2d(fd, fh, 0.05, (-1,-1,1,1), [(-1,-1),(-1,1),(1,-1),(1,1)])
def rectangle_with_circular_hole():
"""Rectangle with circular hole, refined at circle boundary"""
fd = lambda p: dm.ddiff(dm.drectangle(p,-1,1,-1,1), dm.dcircle(p,0,0,0.5))
fh = lambda p: 0.05+0.3*dm.dcircle(p,0,0,0.5)
return dm.distmesh2d(fd, fh, 0.05, (-1,-1,1,1),
[(-1,-1),(-1,1),(1,-1),(1,1)])