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]]))
},
{
'node_list': cn,
'comp': 2,
'value': lambda x: 0.0
},
]
# Symmetry plane
cn = fenode_select(fens, box=numpy.array([W, W, 0, L, 0, H]), inflate=htol)
essential.append({'node_list': cn, 'comp': 0, 'value': lambda x: 0.0})
model_data['boundary_conditions']['essential'] = essential
# Traction on the free end
bfes = mesh_boundary(fes)
fesel = fe_select(fens, bfes, box=[0, W, L, L, 0, H], inflate=htol)
fi = ForceIntensity(magn=lambda x, J: numpy.array([0, 0, magn]))
tsfes = bfes.subset(fesel)
sfemm = FEMMDeforLinear(fes=tsfes, integration_rule=TriRule(npts=3))
traction = [{'femm': sfemm, 'force_intensity': fi}]
model_data['boundary_conditions']['traction'] = traction
# Call the solver
algo_defor_linear.statics(model_data)
for action, time in model_data['timings']:
print(action, time, ' sec')
geom = model_data['geom']
u = model_data['u']
tipn = fenode_select(fens, box=[0, W, L, L, 0, H])
uv = u.values[tipn, :]
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)
start = time.time()
# lu = splu(K)
# T = lu.solve(F)
# T = spsolve(K, F, use_umfpack=True)
T, info = minres(K, F)
print(info)
temp.scatter_sysvec(T)
k = 1.0 # thermal conductivity
m = MatHeatDiff(thermal_conductivity=numpy.array([[k, 0.0], [0.0, k]]))
start = time.time()
N = 50
Length, Width, nL, nW = 1.0, 1.0, N, N
fens, fes = t3_ablock(Length, Width, nL, nW)
fes.other_dimension = lambda conn, N, x: 1.0
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)),
'heat_generation':
ForceIntensity(magn=lambda x, J: -6.0)
}]
bfes = mesh_boundary(fes)
model_data['boundary_conditions'] = {
'essential': [{
'node_list': connected_nodes(bfes),
'value': lambda x: 1.0 + x[0]**2 + 2 * x[1]**2
}]
}
# Call the solver
steady_state(model_data)
for action, time in model_data['timings']:
print(action, time, ' sec')
plot_temperature(model_data)