def test_first_example(self):
import math
import numpy
from numpy import array
from spyfe.materials.mat_heatdiff import MatHeatDiff
from spyfe.fesets.surfacelike import FESetT3
from spyfe.femms.femm_heatdiff import FEMMHeatDiff
from spyfe.fields.nodal_field import NodalField
from spyfe.integ_rules import TriRule
from spyfe.fenode_set import FENodeSet
# These are the constants in the problem, k is kappa
a = 2.5 # radius on the columnthe
dy = a / 2 * math.sin(15. / 180 * math.pi)
dx = a / 2 * math.cos(15. / 180 * math.pi)
Q = 4.5 # internal heat generation rate
k = 1.8 # thermal conductivity
m = MatHeatDiff(thermal_conductivity=array([[k, 0.0], [0.0, k]]))
Dz = 1.0 # thickness of the slice
xall = array([[0, 0], [dx, -dy], [dx, dy], [2 * dx, -2 * dy],
[2 * dx, 2 * dy]])
fes = FESetT3(array([[1, 2, 3], [2, 4, 5], [2, 5, 3]]) - 1)
femm = FEMMHeatDiff(material=m,
fes=fes,
integration_rule=TriRule(npts=1))
fens = FENodeSet(xyz=xall)
geom = NodalField(fens=fens)
temp = NodalField(nfens=xall.shape[0], dim=1)
temp.set_ebc([3, 4])
temp.apply_ebc()
temp.numberdofs(node_perm=[1, 2, 0, 4, 3])
print(temp.dofnums)
K = femm.conductivity(geom, temp)
print(K)
def test_Poisson_t3(self):
from context import spyfe
from spyfe.meshing.generators.triangles import t3_ablock
from spyfe.meshing.modification import mesh_boundary
from spyfe.meshing.selection import connected_nodes
from numpy import array
from spyfe.materials.mat_heatdiff import MatHeatDiff
from spyfe.femms.femm_heatdiff import FEMMHeatDiff
from spyfe.fields.nodal_field import NodalField
from spyfe.integ_rules import TriRule
from spyfe.force_intensity import ForceIntensity
from scipy.sparse.linalg import spsolve
import time
from spyfe.meshing.exporters.vtkexporter import vtkexport
start0 = time.time()
# These are the constants in the problem, k is kappa
boundaryf = lambda x, y: 1.0 + x**2 + 2 * y**2
Q = -6 # internal heat generation rate
k = 1.0 # thermal conductivity
m = MatHeatDiff(thermal_conductivity=array([[k, 0.0], [0.0, k]]))
Dz = 1.0 # thickness of the slice
start = time.time()
N = 5
Length, Width, nL, nW = 1.0, 1.0, N, N
fens, fes = t3_ablock(Length, Width, nL, nW)
print('Mesh generation', time.time() - start)
bfes = mesh_boundary(fes)
cn = connected_nodes(bfes)
geom = NodalField(fens=fens)
temp = NodalField(nfens=fens.count(), dim=1)
for index in cn:
temp.set_ebc([index],
val=boundaryf(fens.xyz[index, 0], fens.xyz[index, 1]))
temp.apply_ebc()
temp.numberdofs()
femm = FEMMHeatDiff(material=m,
fes=fes,
integration_rule=TriRule(npts=1))
start = time.time()
fi = ForceIntensity(magn=lambda x, J: Q)
F = femm.distrib_loads(geom, temp, fi, 3)
print('Heat generation load', time.time() - start)
start = time.time()
F += femm.nz_ebc_loads_conductivity(geom, temp)
print('NZ EBC load', time.time() - start)
start = time.time()
K = femm.conductivity(geom, temp)
print('Matrix assembly', time.time() - start)
start = time.time()
temp.scatter_sysvec(spsolve(K, F))
print('Solution', time.time() - start)
print(temp.values)
print('Done', time.time() - start0)
from numpy.testing import assert_array_almost_equal
assert_array_almost_equal(temp.values[-4:-1],
array([[3.16], [3.36], [3.64]]))
fens, fes = h8_to_h20(fens, fes)
fes.gradbfunpar(numpy.array([0, 0, 0]))
geom = NodalField(fens=fens)
vtkexport("Poisson_fe_H20_mesh", fes, geom)
print('Mesh generation', time.time() - start)
bfes = mesh_boundary(fes)
cn = connected_nodes(bfes)
temp = NodalField(nfens=fens.count(), dim=1)
for j in cn:
temp.set_ebc([j],
val=boundaryf(fens.xyz[j, 0], fens.xyz[j, 1], fens.xyz[j, 2]))
temp.apply_ebc()
femm = FEMMHeatDiff(material=m,
fes=fes,
integration_rule=GaussRule(dim=3, order=3))
S = femm.connection_matrix(geom)
perm = reverse_cuthill_mckee(S, symmetric_mode=True)
temp.numberdofs(node_perm=perm)
# temp.numberdofs()
start = time.time()
fi = ForceIntensity(magn=lambda x, J: Q)
F = femm.distrib_loads(geom, temp, fi, 3)
print('Heat generation load', time.time() - start)
start = time.time()
F += femm.nz_ebc_loads_conductivity(geom, temp)
print('NZ EBC load', time.time() - start)
start = time.time()
K = femm.conductivity(geom, temp)
print('Matrix assembly', time.time() - start)
Dz = 1.0 # thickness of the slice
start = time.time()
N = 5
Length, Width, nL, nW = 1.0, 1.0, N, N
fens, fes = t3_ablock(Length, Width, nL, nW)
print('Mesh generation', time.time() - start)
bfes = mesh_boundary(fes)
cn = connected_nodes(bfes)
geom = NodalField(fens=fens)
temp = NodalField(nfens=fens.count(), dim=1)
for index in cn:
temp.set_ebc([index],
val=boundaryf(fens.xyz[index, 0], fens.xyz[index, 1]))
temp.apply_ebc()
temp.numberdofs()
femm = FEMMHeatDiff(material=m, fes=fes, integration_rule=TriRule(npts=1))
start = time.time()
fi = ForceIntensity(magn=lambda x, J: Q)
F = femm.distrib_loads(geom, temp, fi, 3)
print('Heat generation load', time.time() - start)
start = time.time()
F += femm.nz_ebc_loads_conductivity(geom, temp)
print('NZ EBC load', time.time() - start)
start = time.time()
K = femm.conductivity(geom, temp)
print('Matrix assembly', time.time() - start)
start = time.time()
temp.scatter_sysvec(spsolve(K, F))
print('Solution', time.time() - start)
print(temp.values)
print('Done', time.time() - start0)
right = fe_select(fens,
bfes,
facing=True,
direction=lambda x: numpy.array([1.0, 0.0]),
tolerance=0.99)
top = fe_select(fens,
bfes,
facing=True,
direction=lambda x: numpy.array([0.0, +1.0]),
tolerance=0.99)
topright = numpy.concatenate((top, right))
print('Mesh generation', time.time() - start)
model_data = {}
model_data['fens'] = fens
model_data['regions'] \
= [{'femm': FEMMHeatDiff(material=m, fes=fes,
integration_rule=TriRule(npts=1))}
]
model_data['boundary_conditions'] \
= {'essential': [{'node_list': connected_nodes(bfes.subset(bottom)),
'temperature': lambda x: 100.0
}],
'surface_transfer': [{'femm': FEMMHeatDiffSurface(fes=bfes.subset(topright),
integration_rule=GaussRule(dim=1, order=1),
surface_transfer_coeff=lambda x: 750.0),
'ambient_temperature': lambda x: 0.0
}]
}
# Call the solver
steady_state(model_data)
print(model_data['timings'])