def _orderVertices(vertexCoords, vertices):
coordinates = numerix.take(vertexCoords, vertices, axis=1)
centroid = numerix.add.reduce(coordinates, axis=1) / coordinates.shape[1]
coordinates = coordinates - centroid[..., numerix.newaxis]
coordinates = numerix.where(coordinates == 0, 1.e-10, coordinates) ## to prevent division by zero
angles = numerix.arctan(coordinates[1] / coordinates[0]) + numerix.where(coordinates[0] < 0, numerix.pi, 0) ## angles go from -pi / 2 to 3*pi / 2
sortorder = numerix.argsort(angles)
return numerix.take(vertices, sortorder)
def _orderVertices(vertexCoords, vertices):
coordinates = numerix.take(vertexCoords, vertices)
centroid = numerix.add.reduce(coordinates) / coordinates.shape[0]
coordinates = coordinates - centroid
# to prevent division by zero
coordinates = numerix.where(coordinates == 0, 1.e-100, coordinates)
# angles go from -pi / 2 to 3*pi / 2
angles = numerix.arctan(coordinates[:, 1] / coordinates[:, 0]) \
+ numerix.where(coordinates[:, 0] < 0, numerix.pi, 0)
sortorder = numerix.argsort(angles)
return numerix.take(vertices, sortorder)
def _orderVertices(vertexCoords, vertices):
coordinates = numerix.take(vertexCoords, vertices)
centroid = numerix.add.reduce(coordinates) / coordinates.shape[0]
coordinates = coordinates - centroid
# to prevent division by zero
coordinates = numerix.where(coordinates == 0, 1.e-100, coordinates)
# angles go from -pi / 2 to 3*pi / 2
angles = numerix.arctan(coordinates[:, 1] / coordinates[:, 0]) \
+ numerix.where(coordinates[:, 0] < 0, numerix.pi, 0)
sortorder = numerix.argsort(angles)
return numerix.take(vertices, sortorder)
x, y = mesh.getCellCenters()[...,0], mesh.getCellCenters()[...,1]
phase.setValue(1., where=(x - seedCenter[0])**2 + (y - seedCenter[1])**2 < radius**2)
temperature = CellVariable(
name='temperature',
mesh=mesh,
value=initialTemperature,
hasOld=1
)
bench.stop('variables')
bench.start()
from fipy.tools import numerix
mVar = phase - 0.5 - kappa1 / numerix.pi * \
numerix.arctan(kappa2 * temperature)
phaseY = phase.getFaceGrad().dot((0, 1))
phaseX = phase.getFaceGrad().dot((1, 0))
psi = theta + numerix.arctan2(phaseY, phaseX)
Phi = numerix.tan(N * psi / 2)
PhiSq = Phi**2
beta = (1. - PhiSq) / (1. + PhiSq)
betaPsi = -N * 2 * Phi / (1 + PhiSq)
A = alpha**2 * c * (1.+ c * beta) * betaPsi
D = alpha**2 * (1.+ c * beta)**2
dxi = phase.getFaceGrad()._take((1, 0), axis = 1) * (-1, 1)
anisotropySource = (A * dxi).getDivergence()
from fipy.terms.transientTerm import TransientTerm
from fipy.terms.explicitDiffusionTerm import ExplicitDiffusionTerm
from fipy.terms.implicitSourceTerm import ImplicitSourceTerm
def arctan(self):
return self._UnaryOperatorVariable(lambda a: numerix.arctan(a))
x, y = mesh.getCellCenters()[..., 0], mesh.getCellCenters()[..., 1]
phase.setValue(1.,
where=(x - seedCenter[0])**2 +
(y - seedCenter[1])**2 < radius**2)
temperature = CellVariable(name='temperature',
mesh=mesh,
value=initialTemperature,
hasOld=1)
bench.stop('variables')
bench.start()
from fipy.tools import numerix
mVar = phase - 0.5 - kappa1 / numerix.pi * \
numerix.arctan(kappa2 * temperature)
phaseY = phase.getFaceGrad().dot((0, 1))
phaseX = phase.getFaceGrad().dot((1, 0))
psi = theta + numerix.arctan2(phaseY, phaseX)
Phi = numerix.tan(N * psi / 2)
PhiSq = Phi**2
beta = (1. - PhiSq) / (1. + PhiSq)
betaPsi = -N * 2 * Phi / (1 + PhiSq)
A = alpha**2 * c * (1. + c * beta) * betaPsi
D = alpha**2 * (1. + c * beta)**2
dxi = phase.getFaceGrad()._take((1, 0), axis=1) * (-1, 1)
anisotropySource = (A * dxi).getDivergence()
from fipy.terms.transientTerm import TransientTerm
from fipy.terms.explicitDiffusionTerm import ExplicitDiffusionTerm
from fipy.terms.implicitSourceTerm import ImplicitSourceTerm
