def _calcGeomCoeff(self, var):
mesh = var.mesh
if self.nthCoeff is not None:
coeff = self.nthCoeff
shape = numerix.getShape(coeff)
if isinstance(coeff, FaceVariable):
rank = coeff.rank
else:
rank = len(shape)
if var.rank == 0:
anisotropicRank = rank
elif var.rank == 1:
anisotropicRank = rank - 2
else:
raise IndexError('the solution variable has the wrong rank')
if anisotropicRank == 0 and self._treatMeshAsOrthogonal(mesh):
if coeff.shape != () and not isinstance(coeff, FaceVariable):
coeff = coeff[..., numerix.newaxis]
tmpBop = (coeff *
FaceVariable(mesh=mesh, value=mesh._faceAreas) /
mesh._cellDistances)[numerix.newaxis, :]
else:
if anisotropicRank == 1 or anisotropicRank == 0:
coeff = coeff * numerix.identity(mesh.dim)
if anisotropicRank > 0:
shape = numerix.getShape(coeff)
if mesh.dim != shape[0] or mesh.dim != shape[1]:
raise IndexError(
'diffusion coefficient tensor is not an appropriate shape for this mesh'
)
faceNormals = FaceVariable(mesh=mesh,
rank=1,
value=mesh.faceNormals)
rotationTensor = self.__getRotationTensor(mesh)
rotationTensor[:,
0] = rotationTensor[:, 0] / mesh._cellDistances
tmpBop = faceNormals.dot(coeff).dot(
rotationTensor) * mesh._faceAreas
return tmpBop
else:
return None
def _calcGeomCoeff(self, var):
mesh = var.mesh
if self.nthCoeff is not None:
coeff = self.nthCoeff
shape = numerix.getShape(coeff)
if isinstance(coeff, FaceVariable):
rank = coeff.rank
else:
rank = len(shape)
if var.rank == 0:
anisotropicRank = rank
elif var.rank == 1:
anisotropicRank = rank - 2
else:
raise IndexError, 'the solution variable has the wrong rank'
if anisotropicRank == 0 and self._treatMeshAsOrthogonal(mesh):
if coeff.shape != () and not isinstance(coeff, FaceVariable):
coeff = coeff[...,numerix.newaxis]
tmpBop = (coeff * FaceVariable(mesh=mesh, value=mesh._faceAreas) / mesh._cellDistances)[numerix.newaxis, :]
else:
if anisotropicRank == 1 or anisotropicRank == 0:
coeff = coeff * numerix.identity(mesh.dim)
if anisotropicRank > 0:
shape = numerix.getShape(coeff)
if mesh.dim != shape[0] or mesh.dim != shape[1]:
raise IndexError, 'diffusion coefficent tensor is not an appropriate shape for this mesh'
faceNormals = FaceVariable(mesh=mesh, rank=1, value=mesh.faceNormals)
rotationTensor = self.__getRotationTensor(mesh)
rotationTensor[:,0] = rotationTensor[:,0] / mesh._cellDistances
tmpBop = faceNormals.dot(coeff).dot(rotationTensor) * mesh._faceAreas
return tmpBop
else:
return None
def _calcGeomCoeff(self, mesh):
if self.nthCoeff is not None:
coeff = self.nthCoeff
shape = numerix.getShape(coeff)
from fipy.variables.faceVariable import FaceVariable
if isinstance(coeff, FaceVariable):
rank = coeff.getRank()
else:
rank = len(shape)
if rank == 0 and self._treatMeshAsOrthogonal(mesh):
tmpBop = (coeff * mesh._getFaceAreas() / mesh._getCellDistances())[numerix.newaxis, :]
else:
if rank == 1 or rank == 0:
coeff = coeff * numerix.identity(mesh.getDim())
if rank > 0:
shape = numerix.getShape(coeff)
if mesh.getDim() != shape[0] or mesh.getDim() != shape[1]:
raise IndexError, 'diffusion coefficent tensor is not an appropriate shape for this mesh'
faceNormals = FaceVariable(mesh=mesh, rank=1, value=mesh._getFaceNormals())
rotationTensor = self._getRotationTensor(mesh)
rotationTensor[:,0] = rotationTensor[:,0] / mesh._getCellDistances()
tmpBop = faceNormals.dot(coeff).dot(rotationTensor) * mesh._getFaceAreas()
return tmpBop
else:
return None
def _buildMatrix(self,
var,
SparseMatrix,
boundaryConditions=(),
dt=None,
transientGeomCoeff=None,
diffusionGeomCoeff=None):
"""
Test to ensure that a changing coefficient influences the boundary conditions.
>>> from fipy import *
>>> m = Grid2D(nx=2, ny=2)
>>> v = CellVariable(mesh=m)
>>> c0 = Variable(1.)
>>> v.constrain(c0, where=m.facesLeft)
Diffusion will only be in the y-direction
>>> coeff = Variable([[0. , 0.], [0. , 1.]])
>>> eq = DiffusionTerm(coeff)
>>> eq.solve(v, solver=DummySolver())
>>> print v
[ 0. 0. 0. 0.]
Change the coefficient.
>>> coeff[0, 0] = 1.
>>> eq.solve(v)
>>> print v
[ 1. 1. 1. 1.]
Change the constraints.
>>> c0.setValue(2.)
>>> v.constrain(3., where=m.facesRight)
>>> print v.faceValue.constraintMask
[False False False False False False True False True True False True]
>>> eq.solve(v)
>>> print v
[ 2.25 2.75 2.25 2.75]
"""
var, L, b = self.__higherOrderbuildMatrix(
var,
SparseMatrix,
boundaryConditions=boundaryConditions,
dt=dt,
transientGeomCoeff=transientGeomCoeff,
diffusionGeomCoeff=diffusionGeomCoeff)
mesh = var.mesh
if self.order == 2:
if (not hasattr(self, 'constraintL')) or (not hasattr(
self, 'constraintB')):
normals = FaceVariable(mesh=mesh,
rank=1,
value=mesh._orientedFaceNormals)
if len(var.shape) == 1 and len(self.nthCoeff.shape) > 1:
nthCoeffFaceGrad = var.faceGrad.dot(self.nthCoeff)
normalsNthCoeff = normals.dot(self.nthCoeff)
else:
if self.nthCoeff.shape != () and not isinstance(
self.nthCoeff, FaceVariable):
coeff = self.nthCoeff[..., numerix.newaxis]
else:
coeff = self.nthCoeff
nthCoeffFaceGrad = coeff[
numerix.newaxis] * var.faceGrad[:, numerix.newaxis]
s = (slice(0, None, None), ) + (numerix.newaxis, ) * (
len(coeff.shape) - 1) + (slice(0, None, None), )
normalsNthCoeff = coeff[numerix.newaxis] * normals[s]
self.constraintB = -(
var.faceGrad.constraintMask *
nthCoeffFaceGrad).divergence * mesh.cellVolumes
constrainedNormalsDotCoeffOverdAP = var.arithmeticFaceValue.constraintMask * \
normalsNthCoeff / mesh._cellDistances
self.constraintB -= (
constrainedNormalsDotCoeffOverdAP *
var.arithmeticFaceValue).divergence * mesh.cellVolumes
ids = self._reshapeIDs(var, numerix.arange(mesh.numberOfCells))
self.constraintL = -constrainedNormalsDotCoeffOverdAP.divergence * mesh.cellVolumes
ids = self._reshapeIDs(var, numerix.arange(mesh.numberOfCells))
L.addAt(self.constraintL.ravel(), ids.ravel(),
ids.swapaxes(0, 1).ravel())
b += numerix.reshape(self.constraintB.ravel(),
ids.shape).sum(-2).ravel()
return (var, L, b)
def _buildMatrix(self, var, SparseMatrix, boundaryConditions=(), dt=None, transientGeomCoeff=None, diffusionGeomCoeff=None):
"""
Test to ensure that a changing coefficient influences the boundary conditions.
>>> from fipy import *
>>> m = Grid2D(nx=2, ny=2)
>>> v = CellVariable(mesh=m)
>>> c0 = Variable(1.)
>>> v.constrain(c0, where=m.facesLeft)
Diffusion will only be in the y-direction
>>> coeff = Variable([[0. , 0.], [0. , 1.]])
>>> eq = DiffusionTerm(coeff)
>>> eq.solve(v, solver=DummySolver())
>>> print v
[ 0. 0. 0. 0.]
Change the coefficient.
>>> coeff[0, 0] = 1.
>>> eq.solve(v)
>>> print v
[ 1. 1. 1. 1.]
Change the constraints.
>>> c0.setValue(2.)
>>> v.constrain(3., where=m.facesRight)
>>> print v.faceValue.constraintMask
[False False False False False False True False True True False True]
>>> eq.solve(v)
>>> print v
[ 2.25 2.75 2.25 2.75]
"""
var, L, b = self.__higherOrderbuildMatrix(var, SparseMatrix, boundaryConditions=boundaryConditions, dt=dt, transientGeomCoeff=transientGeomCoeff, diffusionGeomCoeff=diffusionGeomCoeff)
mesh = var.mesh
if self.order == 2:
if (not hasattr(self, 'constraintL')) or (not hasattr(self, 'constraintB')):
normals = FaceVariable(mesh=mesh, rank=1, value=mesh._orientedFaceNormals)
if len(var.shape) == 1 and len(self.nthCoeff.shape) > 1:
nthCoeffFaceGrad = var.faceGrad.dot(self.nthCoeff)
normalsNthCoeff = normals.dot(self.nthCoeff)
else:
if self.nthCoeff.shape != () and not isinstance(self.nthCoeff, FaceVariable):
coeff = self.nthCoeff[...,numerix.newaxis]
else:
coeff = self.nthCoeff
nthCoeffFaceGrad = coeff[numerix.newaxis] * var.faceGrad[:,numerix.newaxis]
s = (slice(0,None,None),) + (numerix.newaxis,) * (len(coeff.shape) - 1) + (slice(0,None,None),)
normalsNthCoeff = coeff[numerix.newaxis] * normals[s]
self.constraintB = -(var.faceGrad.constraintMask * nthCoeffFaceGrad).divergence * mesh.cellVolumes
constrainedNormalsDotCoeffOverdAP = var.arithmeticFaceValue.constraintMask * \
normalsNthCoeff / mesh._cellDistances
self.constraintB -= (constrainedNormalsDotCoeffOverdAP * var.arithmeticFaceValue).divergence * mesh.cellVolumes
ids = self._reshapeIDs(var, numerix.arange(mesh.numberOfCells))
self.constraintL = -constrainedNormalsDotCoeffOverdAP.divergence * mesh.cellVolumes
ids = self._reshapeIDs(var, numerix.arange(mesh.numberOfCells))
L.addAt(self.constraintL.ravel(), ids.ravel(), ids.swapaxes(0,1).ravel())
b += numerix.reshape(self.constraintB.ravel(), ids.shape).sum(-2).ravel()
return (var, L, b)