def allequal(self, other):
if self.getMesh().communicator.Nproc > 1:
def allequalParallel(a, b):
return self.getMesh().communicator.allequal(a, b)
operatorClass = Variable._OperatorVariableClass(self, baseClass=Variable)
return self._BinaryOperatorVariable(allequalParallel,
other,
operatorClass=operatorClass,
opShape=(),
canInline=False)
else:
return Variable.allequal(self, other)
def allclose(self, other, rtol=1.e-5, atol=1.e-8):
if self.getMesh().communicator.Nproc > 1:
def allcloseParallel(a, b):
return self.getMesh().communicator.allclose(a, b, rtol=rtol, atol=atol)
operatorClass = Variable._OperatorVariableClass(self, baseClass=Variable)
return self._BinaryOperatorVariable(allcloseParallel,
other,
operatorClass=operatorClass,
opShape=(),
canInline=False)
else:
return Variable.allclose(self, other, rtol=rtol, atol=atol)
def allequal(self, other):
if parallel.Nproc > 1:
from mpi4py import MPI
def allequalParallel(a, b):
return MPI.COMM_WORLD.allreduce(numerix.allequal(a, b), op=MPI.LAND)
operatorClass = Variable._OperatorVariableClass(self, baseClass=Variable)
return self._BinaryOperatorVariable(allequalParallel,
other,
operatorClass=operatorClass,
opShape=(),
canInline=False)
else:
return Variable.allequal(self, other)
def allequal(self, other):
if self.mesh.communicator.Nproc > 1:
def allequalParallel(a, b):
return self.mesh.communicator.allequal(a, b)
operatorClass = Variable._OperatorVariableClass(self,
baseClass=Variable)
return self._BinaryOperatorVariable(allequalParallel,
other,
operatorClass=operatorClass,
opShape=(),
canInline=False)
else:
return Variable.allequal(self, other)
def std(self, axis=None, **kwargs):
"""Evaluate standard deviation of all the elements of a `MeshVariable`.
Adapted from http://mpitutorial.com/tutorials/mpi-reduce-and-allreduce/
>>> import fipy as fp
>>> mesh = fp.Grid2D(nx=2, ny=2, dx=2., dy=5.)
>>> var = fp.CellVariable(value=(1., 2., 3., 4.), mesh=mesh)
>>> print (var.std()**2).allclose(1.25)
True
"""
if self.mesh.communicator.Nproc > 1 and (axis is None or axis
== len(self.shape) - 1):
def stdParallel(a):
N = self.mesh.globalNumberOfCells
mean = self.sum(axis=axis).value / N
sq_diff = (self - mean)**2
return numerix.sqrt(sq_diff.sum(axis=axis).value / N)
return self._axisOperator(opname="stdVar",
op=stdParallel,
axis=axis)
else:
return Variable.std(self, axis=axis)
def __init__(self,
surfactantVar = None,
distanceVar = None,
bulkVar = None,
rateConstant = None,
otherVar = None,
otherBulkVar = None,
otherRateConstant = None,
consumptionCoeff = None):
"""
Create a `AdsorbingSurfactantEquation` object.
:Parameters:
- `surfactantVar`: The `SurfactantVariable` to be solved for.
- `distanceVar`: The `DistanceVariable` that marks the interface.
- `bulkVar`: The value of the `surfactantVar` in the bulk.
- `rateConstant`: The adsorption rate of the `surfactantVar`.
- `otherVar`: Another `SurfactantVariable` with more surface affinity.
- `otherBulkVar`: The value of the `otherVar` in the bulk.
- `otherRateConstant`: The adsorption rate of the `otherVar`.
- `consumptionCoeff`: The rate that the `surfactantVar` is consumed during deposition.
"""
self.eq = TransientTerm(coeff = 1) - ExplicitUpwindConvectionTerm(SurfactantConvectionVariable(distanceVar))
self.dt = Variable(0.)
mesh = distanceVar.mesh
adsorptionCoeff = self.dt * bulkVar * rateConstant
spCoeff = adsorptionCoeff * distanceVar._cellInterfaceFlag
scCoeff = adsorptionCoeff * distanceVar.cellInterfaceAreas / mesh.cellVolumes
self.eq += ImplicitSourceTerm(spCoeff) - scCoeff
if otherVar is not None:
otherSpCoeff = self.dt * otherBulkVar * otherRateConstant * distanceVar._cellInterfaceFlag
otherScCoeff = -otherVar.interfaceVar * scCoeff
self.eq += ImplicitSourceTerm(otherSpCoeff) - otherScCoeff
vars = (surfactantVar, otherVar)
else:
vars = (surfactantVar,)
total = 0
for var in vars:
total += var.interfaceVar
maxVar = (total > 1) * distanceVar._cellInterfaceFlag
val = distanceVar.cellInterfaceAreas / mesh.cellVolumes
for var in vars[1:]:
val -= distanceVar._cellInterfaceFlag * var
spMaxCoeff = 1e20 * maxVar
scMaxCoeff = spMaxCoeff * val * (val > 0)
self.eq += ImplicitSourceTerm(spMaxCoeff) - scMaxCoeff - 1e-40
if consumptionCoeff is not None:
self.eq += ImplicitSourceTerm(consumptionCoeff)
def shape(self):
"""
>>> from fipy.meshes import Grid2D
>>> from fipy.variables.cellVariable import CellVariable
>>> mesh = Grid2D(nx=2, ny=3)
>>> var = CellVariable(mesh=mesh)
>>> print numerix.allequal(var.shape, (6,)) # doctest: +PROCESSOR_0
True
>>> print numerix.allequal(var.arithmeticFaceValue.shape, (17,)) # doctest: +PROCESSOR_0
True
>>> print numerix.allequal(var.grad.shape, (2, 6)) # doctest: +PROCESSOR_0
True
>>> print numerix.allequal(var.faceGrad.shape, (2, 17)) # doctest: +PROCESSOR_0
True
Have to account for zero length arrays
>>> from fipy import Grid1D
>>> m = Grid1D(nx=0)
>>> v = CellVariable(mesh=m, elementshape=(2,))
>>> (v * 1).shape
(2, 0)
"""
return (Variable._getShape(self)
or (self.elementshape + self._getShapeFromMesh(self.mesh))
or ())
def __init__(self, coeff=(1., ), var=None):
if self.__class__ is _AbstractDiffusionTerm:
raise AbstractBaseClassError
if type(coeff) not in (type(()), type([])):
coeff = [coeff]
self.order = len(coeff) * 2
if len(coeff) > 0:
self.nthCoeff = coeff[0]
from fipy.variables.variable import Variable
if not isinstance(self.nthCoeff, Variable):
self.nthCoeff = Variable(value=self.nthCoeff)
from fipy.variables.cellVariable import CellVariable
if isinstance(self.nthCoeff, CellVariable):
self.nthCoeff = self.nthCoeff.arithmeticFaceValue
else:
self.nthCoeff = None
_UnaryTerm.__init__(self, coeff=coeff, var=var)
if self.order > 0:
self.lowerOrderDiffusionTerm = self.__class__(coeff=coeff[1:])
def __init__(self, coeff = (1.,)):
"""
Create a `DiffusionTerm`.
:Parameters:
- `coeff`: `Tuple` or `list` of `FaceVariables` or numbers.
"""
if type(coeff) not in (type(()), type([])):
coeff = (coeff,)
self.order = len(coeff) * 2
if len(coeff) > 0:
self.nthCoeff = coeff[0]
from fipy.variables.variable import Variable
if not isinstance(self.nthCoeff, Variable):
self.nthCoeff = Variable(value = self.nthCoeff)
from fipy.variables.cellVariable import CellVariable
if isinstance(self.nthCoeff, CellVariable):
self.nthCoeff = self.nthCoeff.getArithmeticFaceValue()
else:
self.nthCoeff = None
Term.__init__(self, coeff = coeff)
if self.order > 0:
self.lowerOrderDiffusionTerm = DiffusionTerm(coeff = coeff[1:])
def shape(self):
"""
>>> from fipy.meshes import Grid2D
>>> from fipy.variables.cellVariable import CellVariable
>>> mesh = Grid2D(nx=2, ny=3)
>>> var = CellVariable(mesh=mesh)
>>> print numerix.allequal(var.shape, (6,)) # doctest: +PROCESSOR_0
True
>>> print numerix.allequal(var.arithmeticFaceValue.shape, (17,)) # doctest: +PROCESSOR_0
True
>>> print numerix.allequal(var.grad.shape, (2, 6)) # doctest: +PROCESSOR_0
True
>>> print numerix.allequal(var.faceGrad.shape, (2, 17)) # doctest: +PROCESSOR_0
True
Have to account for zero length arrays
>>> from fipy import Grid1D
>>> m = Grid1D(nx=0)
>>> v = CellVariable(mesh=m, elementshape=(2,))
>>> (v * 1).shape
(2, 0)
"""
return (Variable._getShape(self)
or (self.elementshape + self._getShapeFromMesh(self.mesh))
or ())
def _OperatorVariableClass(self, baseClass=None):
baseClass = Variable._OperatorVariableClass(self, baseClass=baseClass)
class _MeshOperatorVariable(baseClass):
def __init__(self, op, var, opShape=None, canInline=True,
*args, **kwargs):
mesh = reduce(lambda a, b: a or b,
[getattr(v, "mesh", None) for v in var])
for shape in [opShape] + [getattr(v, "opShape", None) for v in var]:
if shape is not None:
opShape = shape
break
## opShape = reduce(lambda a, b: a or b,
## [opShape] + [getattr(v, "opShape", None) for v in var])
if opShape is not None:
elementshape = opShape[:-1]
else:
elementshape = reduce(lambda a, b: a or b,
[getattr(v, "elementshape", None) for v in var])
baseClass.__init__(self, mesh=mesh, op=op, var=var,
opShape=opShape, canInline=canInline,
elementshape=elementshape,
*args, **kwargs)
def getRank(self):
return len(self.opShape) - 1
return _MeshOperatorVariable
def min(self, axis=None):
"""
>>> from fipy import Grid2D, CellVariable
>>> mesh = Grid2D(nx=5, ny=5)
>>> x, y = mesh.cellCenters
>>> v = CellVariable(mesh=mesh, value=x*y)
>>> print v.min()
0.25
"""
if self.mesh.communicator.Nproc > 1 and (axis is None or axis
== len(self.shape) - 1):
def minParallel(a):
return self._maxminparallel_(
a=a,
axis=axis,
default=numerix.inf,
fn=a.min,
fnParallel=self.mesh.communicator.MinAll)
return self._axisOperator(opname="minVar",
op=minParallel,
axis=axis)
else:
return Variable.min(self, axis=axis)
def _shapeClassAndOther(self, opShape, operatorClass, other):
"""
Determine the shape of the result, the base class of the result, and (if
necessary) a modified form of `other` that is suitable for the
operation.
By default, returns the result of the generic
`Variable._shapeClassAndOther()`, but if that fails, and if each
dimension of `other` is exactly the `Mesh` dimension, do what the user
probably "meant" and project `other` onto the `Mesh`.
>>> from fipy import *
>>> mesh = Grid1D(nx=5)
>>> A = numerix.arange(5)
>>> B = Variable(1.)
>>> import warnings
>>> savedFilters = list(warnings.filters)
>>> warnings.resetwarnings()
>>> warnings.simplefilter("error", UserWarning, append=True)
>>> C = CellVariable(mesh=mesh) * (A * B)
Traceback (most recent call last):
...
UserWarning: The expression `(multiply([0 1 2 3 4], Variable(value=array(1.0))))` has been cast to a constant `CellVariable`
>>> warnings.filters = savedFilters
"""
otherShape = numerix.getShape(other)
if (not isinstance(other, _MeshVariable) and otherShape is not ()
and otherShape[-1] == self._globalNumberOfElements):
if (isinstance(other, Variable)
and len(other.requiredVariables) > 0):
import warnings
warnings.warn(
"The expression `%s` has been cast to a constant `%s`" %
(repr(other), self._variableClass.__name__),
UserWarning,
stacklevel=4)
other = self._variableClass(value=other, mesh=self.mesh)
newOpShape, baseClass, newOther = Variable._shapeClassAndOther(
self, opShape, operatorClass, other)
if ((newOpShape is None or baseClass is None) and numerix.alltrue(
numerix.array(numerix.getShape(other)) == self.mesh.dim)):
newOpShape, baseClass, newOther = Variable._shapeClassAndOther(
self, opShape, operatorClass, other[..., numerix.newaxis])
return (newOpShape, baseClass, newOther)
def allclose(self, other, rtol=1.e-5, atol=1.e-8):
if self.mesh.communicator.Nproc > 1:
def allcloseParallel(a, b):
return self.mesh.communicator.allclose(a,
b,
rtol=rtol,
atol=atol)
operatorClass = Variable._OperatorVariableClass(self,
baseClass=Variable)
return self._BinaryOperatorVariable(allcloseParallel,
other,
operatorClass=operatorClass,
opShape=(),
canInline=False)
else:
return Variable.allclose(self, other, rtol=rtol, atol=atol)
def setValue(self, value, unit = None, where = None):
if where is not None:
shape = numerix.getShape(where)
if shape != self.shape \
and shape == self._getShapeFromMesh(mesh=self.getMesh()):
for dim in self.elementshape:
where = numerix.repeat(where[numerix.newaxis, ...], repeats=dim, axis=0)
return Variable.setValue(self, value=value, unit=unit, where=where)
def _axisClass(self, axis):
"""
if we operate along the mesh elements, then this is no longer a
`_MeshVariable`, otherwise we get back a `_MeshVariable` of the same
class, but lower rank.
"""
if axis is None or axis == len(self.shape) - 1 or axis == -1:
return Variable._OperatorVariableClass(self, baseClass=Variable)
else:
return self._OperatorVariableClass()
def _axisClass(self, axis):
"""
if we operate along the mesh elements, then this is no longer a
`_MeshVariable`, otherwise we get back a `_MeshVariable` of the same
class, but lower rank.
"""
if axis is None or axis == len(self.shape) - 1 or axis == -1:
return Variable._OperatorVariableClass(self, baseClass=Variable)
else:
return self._OperatorVariableClass()
def _shapeClassAndOther(self, opShape, operatorClass, other):
"""
Determine the shape of the result, the base class of the result, and (if
necessary) a modified form of `other` that is suitable for the
operation.
By default, returns the result of the generic
`Variable._shapeClassAndOther()`, but if that fails, and if each
dimension of `other` is exactly the `Mesh` dimension, do what the user
probably "meant" and project `other` onto the `Mesh`.
>>> from fipy import *
>>> mesh = Grid1D(nx=5)
>>> A = numerix.arange(5)
>>> B = Variable(1.)
>>> import warnings
>>> savedFilters = list(warnings.filters)
>>> warnings.resetwarnings()
>>> warnings.simplefilter("error", UserWarning, append=True)
>>> C = CellVariable(mesh=mesh) * (A * B)
Traceback (most recent call last):
...
UserWarning: The expression `(multiply([0 1 2 3 4], Variable(value=array(1.0))))` has been cast to a constant `CellVariable`
>>> warnings.filters = savedFilters
"""
otherShape = numerix.getShape(other)
if (not isinstance(other, _MeshVariable)
and otherShape is not ()
and otherShape[-1] == self._globalNumberOfElements):
if (isinstance(other, Variable) and len(other.requiredVariables) > 0):
import warnings
warnings.warn("The expression `%s` has been cast to a constant `%s`"
% (repr(other), self._variableClass.__name__),
UserWarning, stacklevel=4)
other = self._variableClass(value=other, mesh=self.mesh)
newOpShape, baseClass, newOther = Variable._shapeClassAndOther(self, opShape, operatorClass, other)
if ((newOpShape is None or baseClass is None)
and numerix.alltrue(numerix.array(numerix.getShape(other)) == self.mesh.dim)):
newOpShape, baseClass, newOther = Variable._shapeClassAndOther(self, opShape, operatorClass, other[..., numerix.newaxis])
return (newOpShape, baseClass, newOther)
def max(self, axis=None):
if self.mesh.communicator.Nproc > 1 and (axis is None or axis == len(self.shape) - 1):
def maxParallel(a):
return self._maxminparallel_(a=a, axis=axis, default=-numerix.inf,
fn=a.max, fnParallel=self.mesh.communicator.MaxAll)
return self._axisOperator(opname="maxVar",
op=maxParallel,
axis=axis)
else:
return Variable.max(self, axis=axis)
def sum(self, axis=None):
if self.mesh.communicator.Nproc > 1 and (axis is None or axis == len(self.shape) - 1):
def sumParallel(a):
a = a[..., self._localNonOverlappingIDs]
return self.mesh.communicator.sum(a, axis=axis)
return self._axisOperator(opname="sumVar",
op=sumParallel,
axis=axis)
else:
return Variable.sum(self, axis=axis)
def min(self, axis=None):
if self.getMesh().communicator.Nproc > 1 and (axis is None or axis == len(self.getShape()) - 1):
def minParallel(a):
return self._maxminparallel_(a=a, axis=axis, default=numerix.inf,
fn=a.min, fnParallel=self.getMesh().communicator.epetra_comm.MinAll)
return self._axisOperator(opname="minVar",
op=minParallel,
axis=axis)
else:
return Variable.min(self, axis=axis)
def sum(self, axis=None):
if self.getMesh().communicator.Nproc > 1 and (axis is None or axis == len(self.getShape()) - 1):
def sumParallel(a):
a = a[self._getLocalNonOverlappingIDs()]
return self.getMesh().communicator.sum(a, axis=axis)
return self._axisOperator(opname="sumVar",
op=sumParallel,
axis=axis)
else:
return Variable.sum(self, axis=axis)
def setValue(self, value, unit=None, where=None):
if where is not None:
shape = numerix.getShape(where)
if shape != self.shape \
and shape == self._getShapeFromMesh(mesh=self.mesh):
for dim in self.elementshape:
where = numerix.repeat(where[numerix.newaxis, ...],
repeats=dim,
axis=0)
return Variable.setValue(self, value=value, unit=unit, where=where)
def any(self, axis=None):
if parallel.Nproc > 1 and (axis is None or axis == len(self.getShape()) - 1):
from mpi4py import MPI
def anyParallel(a):
a = a[self._getLocalNonOverlappingIDs()]
return MPI.COMM_WORLD.allreduce(a.any(axis=axis), op=MPI.LOR)
return self._axisOperator(opname="anyVar",
op=anyParallel,
axis=axis)
else:
return Variable.any(self, axis=axis)
def sum(self, axis=None):
if parallel.Nproc > 1 and (axis is None or axis == len(self.getShape()) - 1):
from PyTrilinos import Epetra
def sumParallel(a):
a = a[self._getLocalNonOverlappingIDs()]
return Epetra.PyComm().SumAll(a.sum(axis=axis))
return self._axisOperator(opname="sumVar",
op=sumParallel,
axis=axis)
else:
return Variable.sum(self, axis=axis)
def _getitemClass(self, index):
if not isinstance(index, tuple):
if isinstance(index, list):
index = tuple(index)
else:
index = (index, )
indexshape = numerix._indexShape(index=index, arrayShape=self.shape)
if (len(indexshape) > 0 and indexshape[-1] == self.shape[-1]
and numerix.obj2sctype(index[-1]) != numerix.obj2sctype(bool)):
return self._OperatorVariableClass()
else:
return Variable._OperatorVariableClass(self, baseClass=Variable)
def min(self, axis=None):
if parallel.Nproc > 1 and (axis is None or axis == len(self.getShape()) - 1):
from PyTrilinos import Epetra
def minParallel(a):
return self._maxminparallel_(a=a, axis=axis, default=numerix.inf,
fn=a.min, fnParallel=Epetra.PyComm().MinAll)
return self._axisOperator(opname="minVar",
op=minParallel,
axis=axis)
else:
return Variable.min(self, axis=axis)
def sum(self, axis=None):
if self.mesh.communicator.Nproc > 1 and (axis is None or axis
== len(self.shape) - 1):
def sumParallel(a):
a = a[..., self._localNonOverlappingIDs]
return self.mesh.communicator.sum(a, axis=axis)
return self._axisOperator(opname="sumVar",
op=sumParallel,
axis=axis)
else:
return Variable.sum(self, axis=axis)
def _getitemClass(self, index):
if not isinstance(index, tuple):
if isinstance(index, list):
index = tuple(index)
else:
index = (index,)
indexshape = numerix._indexShape(index=index, arrayShape=self.shape)
if (len(indexshape) > 0
and indexshape[-1] == self.shape[-1]
and numerix.obj2sctype(index[-1]) != numerix.obj2sctype(bool)):
return self._OperatorVariableClass()
else:
return Variable._OperatorVariableClass(self, baseClass=Variable)
def _shapeClassAndOther(self, opShape, operatorClass, other):
"""
Determine the shape of the result, the base class of the result, and (if
necessary) a modified form of `other` that is suitable for the
operation.
By default, returns the result of the generic
`Variable._shapeClassAndOther()`, but if that fails, and if each
dimension of `other` is exactly the `Mesh` dimension, do what the user
probably "meant" and project `other` onto the `Mesh`.
"""
otherShape = numerix.getShape(other)
if (not isinstance(other, _MeshVariable)
and otherShape is not ()
and otherShape[-1] == self._getGlobalNumberOfElements()):
other = self._getVariableClass()(value=other, mesh=self.getMesh())
newOpShape, baseClass, newOther = Variable._shapeClassAndOther(self, opShape, operatorClass, other)
if ((newOpShape is None or baseClass is None)
and numerix.alltrue(numerix.array(numerix.getShape(other)) == self.getMesh().getDim())):
newOpShape, baseClass, newOther = Variable._shapeClassAndOther(self, opShape, operatorClass, other[..., numerix.newaxis])
return (newOpShape, baseClass, newOther)
def _OperatorVariableClass(self, baseClass=None):
baseClass = Variable._OperatorVariableClass(self, baseClass=baseClass)
class _MeshOperatorVariable(baseClass):
def __init__(self,
op,
var,
opShape=None,
canInline=True,
*args,
**kwargs):
mesh = reduce(lambda a, b: a or b,
[getattr(v, "mesh", None) for v in var])
for shape in [opShape
] + [getattr(v, "opShape", None) for v in var]:
if shape is not None:
opShape = shape
break
## opShape = reduce(lambda a, b: a or b,
## [opShape] + [getattr(v, "opShape", None) for v in var])
if opShape is not None:
elementshape = opShape[:-1]
else:
elementshape = reduce(
lambda a, b: a or b,
[getattr(v, "elementshape", None) for v in var])
baseClass.__init__(self,
mesh=mesh,
op=op,
var=var,
opShape=opShape,
canInline=canInline,
elementshape=elementshape,
*args,
**kwargs)
@getsetDeprecated
def getRank(self):
return self.rank
@property
def rank(self):
return len(self.opShape) - 1
return _MeshOperatorVariable
def max(self, axis=None):
if self.mesh.communicator.Nproc > 1 and (axis is None or axis
== len(self.shape) - 1):
def maxParallel(a):
return self._maxminparallel_(
a=a,
axis=axis,
default=-numerix.inf,
fn=a.max,
fnParallel=self.mesh.communicator.MaxAll)
return self._axisOperator(opname="maxVar",
op=maxParallel,
axis=axis)
else:
return Variable.max(self, axis=axis)
def getShape(self):
"""
>>> from fipy.meshes.grid2D import Grid2D
>>> from fipy.variables.cellVariable import CellVariable
>>> mesh = Grid2D(nx=2, ny=3)
>>> var = CellVariable(mesh=mesh)
>>> from fipy.tools import parallel
>>> print parallel.procID > 0 or numerix.allequal(var.shape, (6,))
True
>>> print parallel.procID > 0 or numerix.allequal(var.getArithmeticFaceValue().shape, (17,))
True
>>> print parallel.procID > 0 or numerix.allequal(var.getGrad().shape, (2, 6))
True
>>> print parallel.procID > 0 or numerix.allequal(var.getFaceGrad().shape, (2, 17))
True
"""
return (Variable.getShape(self)
or (self.elementshape + self._getShapeFromMesh(self.getMesh()))
or ())
def min(self, axis=None):
"""
>>> from fipy import Grid2D, CellVariable
>>> mesh = Grid2D(nx=5, ny=5)
>>> x, y = mesh.cellCenters
>>> v = CellVariable(mesh=mesh, value=x*y)
>>> print v.min()
0.25
"""
if self.mesh.communicator.Nproc > 1 and (axis is None or axis == len(self.shape) - 1):
def minParallel(a):
return self._maxminparallel_(a=a, axis=axis, default=numerix.inf,
fn=a.min, fnParallel=self.mesh.communicator.MinAll)
return self._axisOperator(opname="minVar",
op=minParallel,
axis=axis)
else:
return Variable.min(self, axis=axis)
def std(self, axis=None, **kwargs):
"""Evaluate standard deviation of all the elements of a `MeshVariable`.
Adapted from http://mpitutorial.com/tutorials/mpi-reduce-and-allreduce/
>>> import fipy as fp
>>> mesh = fp.Grid2D(nx=2, ny=2, dx=2., dy=5.)
>>> var = fp.CellVariable(value=(1., 2., 3., 4.), mesh=mesh)
>>> print((var.std()**2).allclose(1.25))
True
"""
if self.mesh.communicator.Nproc > 1 and (axis is None or axis == len(self.shape) - 1):
def stdParallel(a):
N = self.mesh.globalNumberOfCells
mean = self.sum(axis=axis).value / N
sq_diff = (self - mean)**2
return numerix.sqrt(sq_diff.sum(axis=axis).value / N)
return self._axisOperator(opname="stdVar",
op=stdParallel,
axis=axis)
else:
return Variable.std(self, axis=axis)
def __init__(self,
surfactantVar=None,
distanceVar=None,
bulkVar=None,
rateConstant=None,
otherVar=None,
otherBulkVar=None,
otherRateConstant=None,
consumptionCoeff=None):
"""
Create a `AdsorbingSurfactantEquation` object.
:Parameters:
- `surfactantVar`: The `SurfactantVariable` to be solved for.
- `distanceVar`: The `DistanceVariable` that marks the interface.
- `bulkVar`: The value of the `surfactantVar` in the bulk.
- `rateConstant`: The adsorption rate of the `surfactantVar`.
- `otherVar`: Another `SurfactantVariable` with more surface affinity.
- `otherBulkVar`: The value of the `otherVar` in the bulk.
- `otherRateConstant`: The adsorption rate of the `otherVar`.
- `consumptionCoeff`: The rate that the `surfactantVar` is consumed during deposition.
"""
self.eq = TransientTerm(coeff=1) - ExplicitUpwindConvectionTerm(
SurfactantConvectionVariable(distanceVar))
self.dt = Variable(0.)
mesh = distanceVar.mesh
adsorptionCoeff = self.dt * bulkVar * rateConstant
spCoeff = adsorptionCoeff * distanceVar._cellInterfaceFlag
scCoeff = adsorptionCoeff * distanceVar.cellInterfaceAreas / mesh.cellVolumes
self.eq += ImplicitSourceTerm(spCoeff) - scCoeff
if otherVar is not None:
otherSpCoeff = self.dt * otherBulkVar * otherRateConstant * distanceVar._cellInterfaceFlag
otherScCoeff = -otherVar.interfaceVar * scCoeff
self.eq += ImplicitSourceTerm(otherSpCoeff) - otherScCoeff
vars = (surfactantVar, otherVar)
else:
vars = (surfactantVar, )
total = 0
for var in vars:
total += var.interfaceVar
maxVar = (total > 1) * distanceVar._cellInterfaceFlag
val = distanceVar.cellInterfaceAreas / mesh.cellVolumes
for var in vars[1:]:
val -= distanceVar._cellInterfaceFlag * var
spMaxCoeff = 1e20 * maxVar
scMaxCoeff = spMaxCoeff * val * (val > 0)
self.eq += ImplicitSourceTerm(spMaxCoeff) - scMaxCoeff - 1e-40
if consumptionCoeff is not None:
self.eq += ImplicitSourceTerm(consumptionCoeff)
class AdsorbingSurfactantEquation():
r"""
The `AdsorbingSurfactantEquation` object solves the
`SurfactantEquation` but with an adsorbing species from some bulk
value. The equation that describes the surfactant adsorbing is
given by,
.. math::
\dot{\theta} = J v \theta + k c (1 - \theta - \theta_{\text{other}}) - \theta c_{\text{other}} k_{\text{other}} - k^- \theta
where :math:`\theta`, :math:`J`, :math:`v`, :math:`k`, :math:`c`,
:math:`k^-` and :math:`n` represent the surfactant coverage, the curvature,
the interface normal velocity, the adsorption rate, the concentration in the
bulk at the interface, the consumption rate and an exponent of consumption,
respectively. The :math:`\text{other}` subscript refers to another
surfactant with greater surface affinity.
The terms on the RHS of the above equation represent conservation of
surfactant on a non-uniform surface, Langmuir adsorption, removal of
surfactant due to adsorption of the other surfactant onto non-vacant sites
and consumption of the surfactant respectively. The adsorption term is added
to the source by setting :math:` S_c = k c (1 - \theta_{\text{other}})` and
:math:`S_p = -k c`. The other terms are added to the source in a similar
way.
The following is a test case:
>>> from fipy.variables.distanceVariable \
... import DistanceVariable
>>> from fipy import SurfactantVariable
>>> from fipy.meshes import Grid2D
>>> from fipy.tools import numerix
>>> from fipy.variables.cellVariable import CellVariable
>>> dx = .5
>>> dy = 2.3
>>> dt = 0.25
>>> k = 0.56
>>> initialValue = 0.1
>>> c = 0.2
>>> from fipy.meshes import Grid2D
>>> from fipy import serialComm
>>> mesh = Grid2D(dx = dx, dy = dy, nx = 5, ny = 1, communicator=serialComm)
>>> distanceVar = DistanceVariable(mesh = mesh,
... value = (-dx*3/2, -dx/2, dx/2,
... 3*dx/2, 5*dx/2),
... hasOld = 1)
>>> surfactantVar = SurfactantVariable(value = (0, 0, initialValue, 0 ,0),
... distanceVar = distanceVar)
>>> bulkVar = CellVariable(mesh = mesh, value = (c , c, c, c, c))
>>> eqn = AdsorbingSurfactantEquation(surfactantVar = surfactantVar,
... distanceVar = distanceVar,
... bulkVar = bulkVar,
... rateConstant = k)
>>> eqn.solve(surfactantVar, dt = dt)
>>> answer = (initialValue + dt * k * c) / (1 + dt * k * c)
>>> print numerix.allclose(surfactantVar.interfaceVar,
... numerix.array((0, 0, answer, 0, 0)))
1
The following test case is for two surfactant variables. One has more
surface affinity than the other.
>>> from fipy.variables.distanceVariable \
... import DistanceVariable
>>> from fipy import SurfactantVariable
>>> from fipy.meshes import Grid2D
>>> dx = 0.5
>>> dy = 2.73
>>> dt = 0.001
>>> k0 = 1.
>>> k1 = 10.
>>> theta0 = 0.
>>> theta1 = 0.
>>> c0 = 1.
>>> c1 = 1.
>>> totalSteps = 10
>>> mesh = Grid2D(dx = dx, dy = dy, nx = 5, ny = 1, communicator=serialComm)
>>> distanceVar = DistanceVariable(mesh = mesh,
... value = dx * (numerix.arange(5) - 1.5),
... hasOld = 1)
>>> var0 = SurfactantVariable(value = (0, 0, theta0, 0 ,0),
... distanceVar = distanceVar)
>>> var1 = SurfactantVariable(value = (0, 0, theta1, 0 ,0),
... distanceVar = distanceVar)
>>> bulkVar0 = CellVariable(mesh = mesh, value = (c0, c0, c0, c0, c0))
>>> bulkVar1 = CellVariable(mesh = mesh, value = (c1, c1, c1, c1, c1))
>>> eqn0 = AdsorbingSurfactantEquation(surfactantVar = var0,
... distanceVar = distanceVar,
... bulkVar = bulkVar0,
... rateConstant = k0)
>>> eqn1 = AdsorbingSurfactantEquation(surfactantVar = var1,
... distanceVar = distanceVar,
... bulkVar = bulkVar1,
... rateConstant = k1,
... otherVar = var0,
... otherBulkVar = bulkVar0,
... otherRateConstant = k0)
>>> for step in range(totalSteps):
... eqn0.solve(var0, dt = dt)
... eqn1.solve(var1, dt = dt)
>>> answer0 = 1 - numerix.exp(-k0 * c0 * dt * totalSteps)
>>> answer1 = (1 - numerix.exp(-k1 * c1 * dt * totalSteps)) * (1 - answer0)
>>> print numerix.allclose(var0.interfaceVar,
... numerix.array((0, 0, answer0, 0, 0)), rtol = 1e-2)
1
>>> print numerix.allclose(var1.interfaceVar,
... numerix.array((0, 0, answer1, 0, 0)), rtol = 1e-2)
1
>>> dt = 0.1
>>> for step in range(10):
... eqn0.solve(var0, dt = dt)
... eqn1.solve(var1, dt = dt)
>>> x, y = mesh.cellCenters
>>> check = var0.interfaceVar + var1.interfaceVar
>>> answer = CellVariable(mesh=mesh, value=check)
>>> answer[x==1.25] = 1.
>>> print check.allequal(answer)
True
The following test case is to fix a bug where setting the adosrbtion
coefficient to zero leads to the solver not converging and an eventual
failure.
>>> var0 = SurfactantVariable(value = (0, 0, theta0, 0 ,0),
... distanceVar = distanceVar)
>>> bulkVar0 = CellVariable(mesh = mesh, value = (c0, c0, c0, c0, c0))
>>> eqn0 = AdsorbingSurfactantEquation(surfactantVar = var0,
... distanceVar = distanceVar,
... bulkVar = bulkVar0,
... rateConstant = 0)
>>> eqn0.solve(var0, dt = dt)
>>> eqn0.solve(var0, dt = dt)
>>> answer = CellVariable(mesh=mesh, value=var0.interfaceVar)
>>> answer[x==1.25] = 0.
>>> print var0.interfaceVar.allclose(answer)
True
The following test case is to fix a bug that allows the accelerator to
become negative.
>>> nx = 5
>>> ny = 5
>>> dx = 1.
>>> dy = 1.
>>> mesh = Grid2D(dx=dx, dy=dy, nx = nx, ny = ny, communicator=serialComm)
>>> x, y = mesh.cellCenters
>>> disVar = DistanceVariable(mesh=mesh, value=1., hasOld=True)
>>> disVar[y < dy] = -1
>>> disVar[x < dx] = -1
>>> disVar.calcDistanceFunction() #doctest: +LSM
>>> levVar = SurfactantVariable(value = 0.5, distanceVar = disVar)
>>> accVar = SurfactantVariable(value = 0.5, distanceVar = disVar)
>>> levEq = AdsorbingSurfactantEquation(levVar,
... distanceVar = disVar,
... bulkVar = 0,
... rateConstant = 0)
>>> accEq = AdsorbingSurfactantEquation(accVar,
... distanceVar = disVar,
... bulkVar = 0,
... rateConstant = 0,
... otherVar = levVar,
... otherBulkVar = 0,
... otherRateConstant = 0)
>>> extVar = CellVariable(mesh = mesh, value = accVar.interfaceVar)
>>> from fipy import TransientTerm, AdvectionTerm
>>> advEq = TransientTerm() + AdvectionTerm(extVar)
>>> dt = 0.1
>>> for i in range(50):
... disVar.calcDistanceFunction()
... extVar.value = (numerix.array(accVar.interfaceVar))
... disVar.extendVariable(extVar)
... disVar.updateOld()
... advEq.solve(disVar, dt = dt)
... levEq.solve(levVar, dt = dt)
... accEq.solve(accVar, dt = dt) #doctest: +LSM
>>> print (accVar >= -1e-10).all()
True
"""
def __init__(self,
surfactantVar = None,
distanceVar = None,
bulkVar = None,
rateConstant = None,
otherVar = None,
otherBulkVar = None,
otherRateConstant = None,
consumptionCoeff = None):
"""
Create a `AdsorbingSurfactantEquation` object.
:Parameters:
- `surfactantVar`: The `SurfactantVariable` to be solved for.
- `distanceVar`: The `DistanceVariable` that marks the interface.
- `bulkVar`: The value of the `surfactantVar` in the bulk.
- `rateConstant`: The adsorption rate of the `surfactantVar`.
- `otherVar`: Another `SurfactantVariable` with more surface affinity.
- `otherBulkVar`: The value of the `otherVar` in the bulk.
- `otherRateConstant`: The adsorption rate of the `otherVar`.
- `consumptionCoeff`: The rate that the `surfactantVar` is consumed during deposition.
"""
self.eq = TransientTerm(coeff = 1) - ExplicitUpwindConvectionTerm(SurfactantConvectionVariable(distanceVar))
self.dt = Variable(0.)
mesh = distanceVar.mesh
adsorptionCoeff = self.dt * bulkVar * rateConstant
spCoeff = adsorptionCoeff * distanceVar._cellInterfaceFlag
scCoeff = adsorptionCoeff * distanceVar.cellInterfaceAreas / mesh.cellVolumes
self.eq += ImplicitSourceTerm(spCoeff) - scCoeff
if otherVar is not None:
otherSpCoeff = self.dt * otherBulkVar * otherRateConstant * distanceVar._cellInterfaceFlag
otherScCoeff = -otherVar.interfaceVar * scCoeff
self.eq += ImplicitSourceTerm(otherSpCoeff) - otherScCoeff
vars = (surfactantVar, otherVar)
else:
vars = (surfactantVar,)
total = 0
for var in vars:
total += var.interfaceVar
maxVar = (total > 1) * distanceVar._cellInterfaceFlag
val = distanceVar.cellInterfaceAreas / mesh.cellVolumes
for var in vars[1:]:
val -= distanceVar._cellInterfaceFlag * var
spMaxCoeff = 1e20 * maxVar
scMaxCoeff = spMaxCoeff * val * (val > 0)
self.eq += ImplicitSourceTerm(spMaxCoeff) - scMaxCoeff - 1e-40
if consumptionCoeff is not None:
self.eq += ImplicitSourceTerm(consumptionCoeff)
def solve(self, var, boundaryConditions=(), solver=None, dt=None):
"""
Builds and solves the `AdsorbingSurfactantEquation`'s linear system once.
:Parameters:
- `var`: A `SurfactantVariable` to be solved for. Provides the initial condition, the old value and holds the solution on completion.
- `solver`: The iterative solver to be used to solve the linear system of equations.
- `boundaryConditions`: A tuple of boundaryConditions.
- `dt`: The time step size.
"""
self.dt.setValue(dt)
if solver is None:
import fipy.solvers.solver
if fipy.solvers.solver == 'pyamg':
from fipy.solvers.pyAMG.linearGeneralSolver import LinearGeneralSolver
solver = LinearGeneralSolver(tolerance=1e-15, iterations=2000)
else:
from fipy.solvers import LinearPCGSolver
solver = LinearPCGSolver()
if type(boundaryConditions) not in (type(()), type([])):
boundaryConditions = (boundaryConditions,)
var.constrain(0, var.mesh.exteriorFaces)
self.eq.solve(var,
boundaryConditions=boundaryConditions,
solver = solver,
dt=1.)
def sweep(self, var, solver=None, boundaryConditions=(), dt=None, underRelaxation=None, residualFn=None):
r"""
Builds and solves the `AdsorbingSurfactantEquation`'s linear
system once. This method also recalculates and returns the
residual as well as applying under-relaxation.
:Parameters:
- `var`: The variable to be solved for. Provides the initial condition, the old value and holds the solution on completion.
- `solver`: The iterative solver to be used to solve the linear system of equations.
- `boundaryConditions`: A tuple of boundaryConditions.
- `dt`: The time step size.
- `underRelaxation`: Usually a value between `0` and `1` or `None` in the case of no under-relaxation
"""
self.dt.setValue(dt)
if solver is None:
from fipy.solvers import DefaultAsymmetricSolver
solver = DefaultAsymmetricSolver()
if type(boundaryConditions) not in (type(()), type([])):
boundaryConditions = (boundaryConditions,)
var.constrain(0, var.mesh.exteriorFaces)
return self.eq.sweep(var, solver=solver, boundaryConditions=boundaryConditions, underRelaxation=underRelaxation, residualFn=residualFn, dt=1.)
def __init__(self, mesh, name='', value=0., rank=None, elementshape=None,
unit=None, cached=1):
"""
:Parameters:
- `mesh`: the mesh that defines the geometry of this `Variable`
- `name`: the user-readable name of the `Variable`
- `value`: the initial value
- `rank`: the rank (number of dimensions) of each element of this
`Variable`. Default: 0
- `elementshape`: the shape of each element of this variable
Default: `rank * (mesh.getDim(),)`
- `unit`: the physical units of the `Variable`
"""
from fipy.tools import debug
if isinstance(value, (list, tuple)):
value = numerix.array(value)
if isinstance(value, _MeshVariable):
if mesh is None:
mesh = value.mesh
elif mesh != value.mesh:
raise ValueError, "The new 'Variable' must use the same mesh as the supplied value"
self.mesh = mesh
value = self._globalToLocalValue(value)
if value is None:
array = None
elif not isinstance(value, _Constant) and isinstance(value, Variable):
name = name or value.name
unit = None
if isinstance(value, _MeshVariable):
if not isinstance(value, self._getVariableClass()):
raise TypeError, "A '%s' cannot be cast to a '%s'" % (value._getVariableClass().__name__,
self._getVariableClass().__name__)
if elementshape is not None and elementshape != value.shape[:-1]:
raise ValueError, "'elementshape' != shape of elements of 'value'"
if rank is not None and rank != value.getRank():
raise ValueError, "'rank' != rank of 'value'"
elementshape = value.shape[:-1]
array = None
# value = value._copyValue()
if elementshape is None:
valueShape = numerix.getShape(value)
if valueShape != () and valueShape[-1] == self._getShapeFromMesh(mesh)[-1]:
if elementshape is not None and elementshape != valueShape[:-1]:
raise ValueError, "'elementshape' != shape of elements of 'value'"
if rank is not None and rank != len(valueShape[:-1]):
raise ValueError, "'rank' != rank of 'value'"
elementshape = valueShape[:-1]
elif rank is None and elementshape is None:
elementshape = valueShape
if rank is None:
if elementshape is None:
elementshape = ()
elif elementshape is None:
elementshape = rank * (mesh.getDim(),)
elif len(elementshape) != rank:
raise ValueError, 'len(elementshape) != rank'
self.elementshape = elementshape
if not locals().has_key("array"):
if numerix._isPhysical(value):
dtype = numerix.obj2sctype(value.value)
else:
dtype = numerix.obj2sctype(value)
array = numerix.zeros(self.elementshape
+ self._getShapeFromMesh(mesh),
dtype)
if numerix._broadcastShape(array.shape, numerix.shape(value)) is None:
if not isinstance(value, Variable):
value = _Constant(value)
value = value[..., numerix.newaxis]
Variable.__init__(self, name=name, value=value, unit=unit,
array=array, cached=cached)
def __init__(self,
mesh,
name='',
value=0.,
rank=None,
elementshape=None,
unit=None,
cached=1):
"""
:Parameters:
- `mesh`: the mesh that defines the geometry of this `Variable`
- `name`: the user-readable name of the `Variable`
- `value`: the initial value
- `rank`: the rank (number of dimensions) of each element of this
`Variable`. Default: 0
- `elementshape`: the shape of each element of this variable
Default: `rank * (mesh.dim,)`
- `unit`: the physical units of the `Variable`
"""
if isinstance(value, (list, tuple)):
value = numerix.array(value)
if isinstance(value, _MeshVariable):
if mesh is None:
mesh = value.mesh
elif mesh != value.mesh:
raise ValueError, "The new 'Variable' must use the same mesh as the supplied value"
self.mesh = mesh
value = self._globalToLocalValue(value)
if value is None:
array = None
elif not isinstance(value, _Constant) and isinstance(value, Variable):
name = name or value.name
unit = None
if isinstance(value, _MeshVariable):
if not isinstance(value, self._variableClass):
raise TypeError, "A '%s' cannot be cast to a '%s'" % (
value._variableClass.__name__,
self._variableClass.__name__)
if elementshape is not None and elementshape != value.shape[:
-1]:
raise ValueError, "'elementshape' != shape of elements of 'value'"
if rank is not None and rank != value.rank:
raise ValueError, "'rank' != rank of 'value'"
elementshape = value.shape[:-1]
array = None
# value = value._copyValue()
if elementshape is None:
valueShape = numerix.getShape(value)
if valueShape != () and valueShape[-1] == self._getShapeFromMesh(
mesh)[-1]:
if elementshape is not None and elementshape != valueShape[:-1]:
raise ValueError, "'elementshape' != shape of elements of 'value'"
if rank is not None and rank != len(valueShape[:-1]):
raise ValueError, "'rank' != rank of 'value'"
elementshape = valueShape[:-1]
elif rank is None and elementshape is None:
elementshape = valueShape
if rank is None:
if elementshape is None:
elementshape = ()
elif elementshape is None:
elementshape = rank * (mesh.dim, )
elif len(elementshape) != rank:
raise ValueError, 'len(elementshape) != rank'
self.elementshape = elementshape
if not "array" in locals():
if numerix._isPhysical(value):
dtype = numerix.obj2sctype(value.value)
else:
dtype = numerix.obj2sctype(value)
#print "meshvariable elshape: ",self.elementshape
#print "meshvariable _getShapeFromMesh: ",self._getShapeFromMesh(mesh)
array = numerix.zeros(
self.elementshape + self._getShapeFromMesh(mesh), dtype)
if numerix._broadcastShape(array.shape,
numerix.shape(value)) is None:
if not isinstance(value, Variable):
value = _Constant(value)
value = value[..., numerix.newaxis]
Variable.__init__(self,
name=name,
value=value,
unit=unit,
array=array,
cached=cached)
class AdsorbingSurfactantEquation():
r"""
The `AdsorbingSurfactantEquation` object solves the
`SurfactantEquation` but with an adsorbing species from some bulk
value. The equation that describes the surfactant adsorbing is
given by,
.. math::
\dot{\theta} = J v \theta + k c (1 - \theta - \theta_{\text{other}}) - \theta c_{\text{other}} k_{\text{other}} - k^- \theta
where :math:`\theta`, :math:`J`, :math:`v`, :math:`k`, :math:`c`,
:math:`k^-` and :math:`n` represent the surfactant coverage, the curvature,
the interface normal velocity, the adsorption rate, the concentration in the
bulk at the interface, the consumption rate and an exponent of consumption,
respectively. The :math:`\text{other}` subscript refers to another
surfactant with greater surface affinity.
The terms on the RHS of the above equation represent conservation of
surfactant on a non-uniform surface, Langmuir adsorption, removal of
surfactant due to adsorption of the other surfactant onto non-vacant sites
and consumption of the surfactant respectively. The adsorption term is added
to the source by setting :math:` S_c = k c (1 - \theta_{\text{other}})` and
:math:`S_p = -k c`. The other terms are added to the source in a similar
way.
The following is a test case:
>>> from fipy.variables.distanceVariable \
... import DistanceVariable
>>> from fipy import SurfactantVariable
>>> from fipy.meshes import Grid2D
>>> from fipy.tools import numerix
>>> from fipy.variables.cellVariable import CellVariable
>>> dx = .5
>>> dy = 2.3
>>> dt = 0.25
>>> k = 0.56
>>> initialValue = 0.1
>>> c = 0.2
>>> from fipy.meshes import Grid2D
>>> from fipy import serialComm
>>> mesh = Grid2D(dx = dx, dy = dy, nx = 5, ny = 1, communicator=serialComm)
>>> distanceVar = DistanceVariable(mesh = mesh,
... value = (-dx*3/2, -dx/2, dx/2,
... 3*dx/2, 5*dx/2),
... hasOld = 1)
>>> surfactantVar = SurfactantVariable(value = (0, 0, initialValue, 0 ,0),
... distanceVar = distanceVar)
>>> bulkVar = CellVariable(mesh = mesh, value = (c , c, c, c, c))
>>> eqn = AdsorbingSurfactantEquation(surfactantVar = surfactantVar,
... distanceVar = distanceVar,
... bulkVar = bulkVar,
... rateConstant = k)
>>> eqn.solve(surfactantVar, dt = dt)
>>> answer = (initialValue + dt * k * c) / (1 + dt * k * c)
>>> print numerix.allclose(surfactantVar.interfaceVar,
... numerix.array((0, 0, answer, 0, 0)))
1
The following test case is for two surfactant variables. One has more
surface affinity than the other.
>>> from fipy.variables.distanceVariable \
... import DistanceVariable
>>> from fipy import SurfactantVariable
>>> from fipy.meshes import Grid2D
>>> dx = 0.5
>>> dy = 2.73
>>> dt = 0.001
>>> k0 = 1.
>>> k1 = 10.
>>> theta0 = 0.
>>> theta1 = 0.
>>> c0 = 1.
>>> c1 = 1.
>>> totalSteps = 10
>>> mesh = Grid2D(dx = dx, dy = dy, nx = 5, ny = 1, communicator=serialComm)
>>> distanceVar = DistanceVariable(mesh = mesh,
... value = dx * (numerix.arange(5) - 1.5),
... hasOld = 1)
>>> var0 = SurfactantVariable(value = (0, 0, theta0, 0 ,0),
... distanceVar = distanceVar)
>>> var1 = SurfactantVariable(value = (0, 0, theta1, 0 ,0),
... distanceVar = distanceVar)
>>> bulkVar0 = CellVariable(mesh = mesh, value = (c0, c0, c0, c0, c0))
>>> bulkVar1 = CellVariable(mesh = mesh, value = (c1, c1, c1, c1, c1))
>>> eqn0 = AdsorbingSurfactantEquation(surfactantVar = var0,
... distanceVar = distanceVar,
... bulkVar = bulkVar0,
... rateConstant = k0)
>>> eqn1 = AdsorbingSurfactantEquation(surfactantVar = var1,
... distanceVar = distanceVar,
... bulkVar = bulkVar1,
... rateConstant = k1,
... otherVar = var0,
... otherBulkVar = bulkVar0,
... otherRateConstant = k0)
>>> for step in range(totalSteps):
... eqn0.solve(var0, dt = dt)
... eqn1.solve(var1, dt = dt)
>>> answer0 = 1 - numerix.exp(-k0 * c0 * dt * totalSteps)
>>> answer1 = (1 - numerix.exp(-k1 * c1 * dt * totalSteps)) * (1 - answer0)
>>> print numerix.allclose(var0.interfaceVar,
... numerix.array((0, 0, answer0, 0, 0)), rtol = 1e-2)
1
>>> print numerix.allclose(var1.interfaceVar,
... numerix.array((0, 0, answer1, 0, 0)), rtol = 1e-2)
1
>>> dt = 0.1
>>> for step in range(10):
... eqn0.solve(var0, dt = dt)
... eqn1.solve(var1, dt = dt)
>>> x, y = mesh.cellCenters
>>> check = var0.interfaceVar + var1.interfaceVar
>>> answer = CellVariable(mesh=mesh, value=check)
>>> answer[x==1.25] = 1.
>>> print check.allequal(answer)
True
The following test case is to fix a bug where setting the adsorption
coefficient to zero leads to the solver not converging and an eventual
failure.
>>> var0 = SurfactantVariable(value = (0, 0, theta0, 0 ,0),
... distanceVar = distanceVar)
>>> bulkVar0 = CellVariable(mesh = mesh, value = (c0, c0, c0, c0, c0))
>>> eqn0 = AdsorbingSurfactantEquation(surfactantVar = var0,
... distanceVar = distanceVar,
... bulkVar = bulkVar0,
... rateConstant = 0)
>>> eqn0.solve(var0, dt = dt)
>>> eqn0.solve(var0, dt = dt)
>>> answer = CellVariable(mesh=mesh, value=var0.interfaceVar)
>>> answer[x==1.25] = 0.
>>> print var0.interfaceVar.allclose(answer)
True
The following test case is to fix a bug that allows the accelerator to
become negative.
>>> nx = 5
>>> ny = 5
>>> dx = 1.
>>> dy = 1.
>>> mesh = Grid2D(dx=dx, dy=dy, nx = nx, ny = ny, communicator=serialComm)
>>> x, y = mesh.cellCenters
>>> disVar = DistanceVariable(mesh=mesh, value=1., hasOld=True)
>>> disVar[y < dy] = -1
>>> disVar[x < dx] = -1
>>> disVar.calcDistanceFunction() #doctest: +LSM
>>> levVar = SurfactantVariable(value = 0.5, distanceVar = disVar)
>>> accVar = SurfactantVariable(value = 0.5, distanceVar = disVar)
>>> levEq = AdsorbingSurfactantEquation(levVar,
... distanceVar = disVar,
... bulkVar = 0,
... rateConstant = 0)
>>> accEq = AdsorbingSurfactantEquation(accVar,
... distanceVar = disVar,
... bulkVar = 0,
... rateConstant = 0,
... otherVar = levVar,
... otherBulkVar = 0,
... otherRateConstant = 0)
>>> extVar = CellVariable(mesh = mesh, value = accVar.interfaceVar)
>>> from fipy import TransientTerm, AdvectionTerm
>>> advEq = TransientTerm() + AdvectionTerm(extVar)
>>> dt = 0.1
>>> for i in range(50):
... disVar.calcDistanceFunction()
... extVar.value = (numerix.array(accVar.interfaceVar))
... disVar.extendVariable(extVar)
... disVar.updateOld()
... advEq.solve(disVar, dt = dt)
... levEq.solve(levVar, dt = dt)
... accEq.solve(accVar, dt = dt) #doctest: +LSM
>>> # The following test fails sometimes on linux with scipy solvers
>>> # See issue #575. We ignore for now.
>>> print (accVar >= -1e-10).all() #doctest: +NOTLINUXSCIPY
True
"""
def __init__(self,
surfactantVar=None,
distanceVar=None,
bulkVar=None,
rateConstant=None,
otherVar=None,
otherBulkVar=None,
otherRateConstant=None,
consumptionCoeff=None):
"""
Create a `AdsorbingSurfactantEquation` object.
:Parameters:
- `surfactantVar`: The `SurfactantVariable` to be solved for.
- `distanceVar`: The `DistanceVariable` that marks the interface.
- `bulkVar`: The value of the `surfactantVar` in the bulk.
- `rateConstant`: The adsorption rate of the `surfactantVar`.
- `otherVar`: Another `SurfactantVariable` with more surface affinity.
- `otherBulkVar`: The value of the `otherVar` in the bulk.
- `otherRateConstant`: The adsorption rate of the `otherVar`.
- `consumptionCoeff`: The rate that the `surfactantVar` is consumed during deposition.
"""
self.eq = TransientTerm(coeff=1) - ExplicitUpwindConvectionTerm(
SurfactantConvectionVariable(distanceVar))
self.dt = Variable(0.)
mesh = distanceVar.mesh
adsorptionCoeff = self.dt * bulkVar * rateConstant
spCoeff = adsorptionCoeff * distanceVar._cellInterfaceFlag
scCoeff = adsorptionCoeff * distanceVar.cellInterfaceAreas / mesh.cellVolumes
self.eq += ImplicitSourceTerm(spCoeff) - scCoeff
if otherVar is not None:
otherSpCoeff = self.dt * otherBulkVar * otherRateConstant * distanceVar._cellInterfaceFlag
otherScCoeff = -otherVar.interfaceVar * scCoeff
self.eq += ImplicitSourceTerm(otherSpCoeff) - otherScCoeff
vars = (surfactantVar, otherVar)
else:
vars = (surfactantVar, )
total = 0
for var in vars:
total += var.interfaceVar
maxVar = (total > 1) * distanceVar._cellInterfaceFlag
val = distanceVar.cellInterfaceAreas / mesh.cellVolumes
for var in vars[1:]:
val -= distanceVar._cellInterfaceFlag * var
spMaxCoeff = 1e20 * maxVar
scMaxCoeff = spMaxCoeff * val * (val > 0)
self.eq += ImplicitSourceTerm(spMaxCoeff) - scMaxCoeff - 1e-40
if consumptionCoeff is not None:
self.eq += ImplicitSourceTerm(consumptionCoeff)
def solve(self, var, boundaryConditions=(), solver=None, dt=None):
"""
Builds and solves the `AdsorbingSurfactantEquation`'s linear system once.
:Parameters:
- `var`: A `SurfactantVariable` to be solved for. Provides the initial condition, the old value and holds the solution on completion.
- `solver`: The iterative solver to be used to solve the linear system of equations.
- `boundaryConditions`: A tuple of boundaryConditions.
- `dt`: The time step size.
"""
self.dt.setValue(dt)
if solver is None:
import fipy.solvers.solver
if fipy.solvers.solver == 'pyamg':
from fipy.solvers.pyAMG.linearGeneralSolver import LinearGeneralSolver
solver = LinearGeneralSolver(tolerance=1e-15, iterations=2000)
else:
from fipy.solvers import LinearPCGSolver
solver = LinearPCGSolver()
if type(boundaryConditions) not in (type(()), type([])):
boundaryConditions = (boundaryConditions, )
var.constrain(0, var.mesh.exteriorFaces)
self.eq.solve(var,
boundaryConditions=boundaryConditions,
solver=solver,
dt=1.)
def sweep(self,
var,
solver=None,
boundaryConditions=(),
dt=None,
underRelaxation=None,
residualFn=None):
r"""
Builds and solves the `AdsorbingSurfactantEquation`'s linear
system once. This method also recalculates and returns the
residual as well as applying under-relaxation.
:Parameters:
- `var`: The variable to be solved for. Provides the initial condition, the old value and holds the solution on completion.
- `solver`: The iterative solver to be used to solve the linear system of equations.
- `boundaryConditions`: A tuple of boundaryConditions.
- `dt`: The time step size.
- `underRelaxation`: Usually a value between `0` and `1` or `None` in the case of no under-relaxation
"""
self.dt.setValue(dt)
if solver is None:
from fipy.solvers import DefaultAsymmetricSolver
solver = DefaultAsymmetricSolver()
if type(boundaryConditions) not in (type(()), type([])):
boundaryConditions = (boundaryConditions, )
var.constrain(0, var.mesh.exteriorFaces)
return self.eq.sweep(var,
solver=solver,
boundaryConditions=boundaryConditions,
underRelaxation=underRelaxation,
residualFn=residualFn,
dt=1.)
def _isCached(self):
return (Variable._isCached(self)
or (len(self.subscribedVariables) > 1
and not self._cacheNever))
class DiffusionTerm(Term):
r"""
This term represents a higher order diffusion term. The order of the term is determined
by the number of `coeffs`, such that::
DiffusionTerm(D1)
represents a typical 2nd-order diffusion term of the form
.. math::
\nabla\cdot\left(D_1 \nabla \phi\right)
and::
DiffusionTerm((D1,D2))
represents a 4th-order Cahn-Hilliard term of the form
.. math::
\nabla \cdot \left\{ D_1 \nabla \left[ \nabla\cdot\left( D_2 \nabla \phi\right) \right] \right\}
and so on.
"""
def __init__(self, coeff = (1.,)):
"""
Create a `DiffusionTerm`.
:Parameters:
- `coeff`: `Tuple` or `list` of `FaceVariables` or numbers.
"""
if type(coeff) not in (type(()), type([])):
coeff = (coeff,)
self.order = len(coeff) * 2
if len(coeff) > 0:
self.nthCoeff = coeff[0]
from fipy.variables.variable import Variable
if not isinstance(self.nthCoeff, Variable):
self.nthCoeff = Variable(value = self.nthCoeff)
from fipy.variables.cellVariable import CellVariable
if isinstance(self.nthCoeff, CellVariable):
self.nthCoeff = self.nthCoeff.getArithmeticFaceValue()
else:
self.nthCoeff = None
Term.__init__(self, coeff = coeff)
if self.order > 0:
self.lowerOrderDiffusionTerm = DiffusionTerm(coeff = coeff[1:])
def __neg__(self):
"""
Negate the term.
>>> -DiffusionTerm(coeff=[1.])
DiffusionTerm(coeff=[-1.0])
>>> -DiffusionTerm()
DiffusionTerm(coeff=[-1.0])
"""
negatedCoeff = list(self.coeff)
negatedCoeff[0] = -negatedCoeff[0]
return self.__class__(coeff = negatedCoeff)
def _getBoundaryConditions(self, boundaryConditions):
higherOrderBCs = []
lowerOrderBCs = []
for bc in boundaryConditions:
bcDeriv = bc._getDerivative(self.order - 2)
if bcDeriv:
higherOrderBCs.append(bcDeriv)
else:
lowerOrderBCs.append(bc)
return higherOrderBCs, lowerOrderBCs
def _getNormals(self, mesh):
return mesh._getFaceCellToCellNormals()
def _getRotationTensor(self, mesh):
if not hasattr(self, 'rotationTensor'):
from fipy.variables.faceVariable import FaceVariable
rotationTensor = FaceVariable(mesh=mesh, rank=2)
rotationTensor[:, 0] = self._getNormals(mesh)
if mesh.getDim() == 2:
rotationTensor[:,1] = rotationTensor[:,0].dot((((0, 1), (-1, 0))))
elif mesh.getDim() ==3:
epsilon = 1e-20
div = numerix.sqrt(1 - rotationTensor[2,0]**2)
flag = numerix.resize(div > epsilon, (mesh.getDim(), mesh._getNumberOfFaces()))
rotationTensor[0, 1] = 1
rotationTensor[:, 1] = numerix.where(flag,
rotationTensor[:,0].dot((((0, 1, 0), (-1, 0, 0), (0, 0, 0)))) / div,
rotationTensor[:, 1])
rotationTensor[1, 2] = 1
rotationTensor[:, 2] = numerix.where(flag,
rotationTensor[:,0] * rotationTensor[2,0] / div,
rotationTensor[:, 2])
rotationTensor[2, 2] = -div
self.rotationTensor = rotationTensor
return self.rotationTensor
def _treatMeshAsOrthogonal(self, mesh):
return mesh._isOrthogonal()
def _calcAnisotropySource(self, coeff, mesh, var):
if not hasattr(self, 'anisotropySource'):
if len(coeff) > 1:
gradients = var.getGrad().getHarmonicFaceValue().dot(self._getRotationTensor(mesh))
from fipy.variables.addOverFacesVariable import _AddOverFacesVariable
self.anisotropySource = _AddOverFacesVariable(gradients[1:].dot(coeff[1:])) * mesh.getCellVolumes()
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 _getCoefficientMatrix(self, SparseMatrix, mesh, coeff):
interiorCoeff = numerix.array(coeff)
interiorCoeff[mesh.getExteriorFaces().getValue()] = 0
interiorCoeff = numerix.take(interiorCoeff, mesh._getCellFaceIDs())
coefficientMatrix = SparseMatrix(mesh=mesh, bandwidth = mesh._getMaxFacesPerCell() + 1)
coefficientMatrix.addAtDiagonal(numerix.sum(interiorCoeff, 0))
del interiorCoeff
interiorFaces = mesh.getInteriorFaceIDs()
interiorFaceCellIDs = mesh.getInteriorFaceCellIDs()
interiorCoeff = -numerix.take(coeff, interiorFaces, axis=-1)
coefficientMatrix.addAt(interiorCoeff, interiorFaceCellIDs[0], interiorFaceCellIDs[1])
interiorCoeff = -numerix.take(coeff, interiorFaces, axis=-1)
coefficientMatrix.addAt(interiorCoeff, interiorFaceCellIDs[1], interiorFaceCellIDs[0])
return coefficientMatrix
def _bcAdd(self, coefficientMatrix, boundaryB, LLbb):
coefficientMatrix += LLbb[0]
boundaryB += LLbb[1]
def _doBCs(self, SparseMatrix, higherOrderBCs, N, M, coeffs, coefficientMatrix, boundaryB):
for boundaryCondition in higherOrderBCs:
self._bcAdd(coefficientMatrix, boundaryB, boundaryCondition._buildMatrix(SparseMatrix, N, M, coeffs))
return coefficientMatrix, boundaryB
def __add__(self, other):
if isinstance(other, DiffusionTerm):
from fipy.terms.collectedDiffusionTerm import _CollectedDiffusionTerm
if isinstance(other, _CollectedDiffusionTerm):
return other + self
elif other.order == self.order and self.order <= 2:
if self.order == 0:
return self
elif self.order == 2:
return self.__class__(coeff=self.coeff[0] + other.coeff[0])
else:
term = _CollectedDiffusionTerm()
term += self
term += other
return term
else:
return Term.__add__(self, other)
def _buildMatrix(self, var, SparseMatrix, boundaryConditions = (), dt = 1., equation=None):
mesh = var.getMesh()
N = mesh.getNumberOfCells()
M = mesh._getMaxFacesPerCell()
if self.order > 2:
higherOrderBCs, lowerOrderBCs = self._getBoundaryConditions(boundaryConditions)
lowerOrderL, lowerOrderb = self.lowerOrderDiffusionTerm._buildMatrix(var = var, SparseMatrix=SparseMatrix,
boundaryConditions = lowerOrderBCs,
dt = dt,
equation=equation)
del lowerOrderBCs
lowerOrderb = lowerOrderb / mesh.getCellVolumes()
volMatrix = SparseMatrix(mesh=var.getMesh(), bandwidth = 1)
volMatrix.addAtDiagonal(1. / mesh.getCellVolumes() )
lowerOrderL = volMatrix * lowerOrderL
del volMatrix
if not hasattr(self, 'coeffDict'):
coeff = self._getGeomCoeff(mesh)[0]
minusCoeff = -coeff
coeff.dontCacheMe()
minusCoeff.dontCacheMe()
self.coeffDict = {
'cell 1 diag': minusCoeff,
'cell 1 offdiag': coeff
}
del coeff
del minusCoeff
self.coeffDict['cell 2 offdiag'] = self.coeffDict['cell 1 offdiag']
self.coeffDict['cell 2 diag'] = self.coeffDict['cell 1 diag']
mm = self._getCoefficientMatrix(SparseMatrix, mesh, self.coeffDict['cell 1 diag'])
L, b = self._doBCs(SparseMatrix, higherOrderBCs, N, M, self.coeffDict,
mm, numerix.zeros(N,'d'))
del higherOrderBCs
del mm
b = L * lowerOrderb + b
del lowerOrderb
L = L * lowerOrderL
del lowerOrderL
elif self.order == 2:
if not hasattr(self, 'coeffDict'):
coeff = self._getGeomCoeff(mesh)
minusCoeff = -coeff[0]
coeff[0].dontCacheMe()
minusCoeff.dontCacheMe()
self.coeffDict = {
'cell 1 diag': minusCoeff,
'cell 1 offdiag': coeff[0]
}
self.coeffDict['cell 2 offdiag'] = self.coeffDict['cell 1 offdiag']
self.coeffDict['cell 2 diag'] = self.coeffDict['cell 1 diag']
self._calcAnisotropySource(coeff, mesh, var)
del coeff
del minusCoeff
higherOrderBCs, lowerOrderBCs = self._getBoundaryConditions(boundaryConditions)
del lowerOrderBCs
L, b = self._doBCs(SparseMatrix, higherOrderBCs, N, M, self.coeffDict,
self._getCoefficientMatrix(SparseMatrix, mesh, self.coeffDict['cell 1 diag']), numerix.zeros(N,'d'))
if hasattr(self, 'anisotropySource'):
b -= self.anisotropySource
del higherOrderBCs
else:
L = SparseMatrix(mesh=mesh)
L.addAtDiagonal(mesh.getCellVolumes())
b = numerix.zeros((N),'d')
return (L, b)
def _test(self):
r"""
Test, 2nd order, 1 dimension, fixed flux of zero both ends.
>>> from fipy.meshes.grid1D import Grid1D
>>> from fipy.matrices.pysparseMatrix import _PysparseMeshMatrix as SparseMatrix
>>> from fipy.tools import parallel
>>> procID = parallel.procID
>>> mesh = Grid1D(dx = 1., nx = 2)
>>> term = DiffusionTerm(coeff = (1,))
>>> coeff = term._getGeomCoeff(mesh)
>>> M = term._getCoefficientMatrix(SparseMatrix, mesh, coeff[0])
>>> print numerix.allclose(M.getNumpyArray(),
... (( 1., -1.),
... (-1., 1.))) or procID != 0
True
>>> from fipy.variables.cellVariable import CellVariable
>>> L,b = term._buildMatrix(var=CellVariable(mesh=mesh), SparseMatrix=SparseMatrix)
>>> print numerix.allclose(L.getNumpyArray(),
... ((-1., 1.),
... ( 1., -1.))) or procID != 0
True
>>> print numerix.allclose(b, (0., 0.)) or procID != 0
True
The coefficient must be a `FaceVariable`, a `CellVariable` (which will
be interpolated to a `FaceVariable`), or a scalar value
>>> from fipy.variables.faceVariable import FaceVariable
>>> term = DiffusionTerm(coeff=FaceVariable(mesh=mesh, value=1))
>>> coeff = term._getGeomCoeff(mesh)
>>> M = term._getCoefficientMatrix(SparseMatrix, mesh, coeff[0])
>>> print numerix.allclose(M.getNumpyArray(),
... (( 1., -1.),
... (-1., 1.))) or procID != 0
True
>>> L,b = term._buildMatrix(var=CellVariable(mesh=mesh), SparseMatrix=SparseMatrix)
>>> print numerix.allclose(L.getNumpyArray(),
... ((-1., 1.),
... ( 1., -1.))) or procID != 0
True
>>> print numerix.allclose(b, (0., 0.)) or procID != 0
True
>>> term = DiffusionTerm(coeff=CellVariable(mesh=mesh, value=1))
>>> coeff = term._getGeomCoeff(mesh)
>>> M = term._getCoefficientMatrix(SparseMatrix, mesh, coeff[0])
>>> print numerix.allclose(M.getNumpyArray(),
... (( 1., -1.),
... (-1., 1.))) or procID != 0
True
>>> L,b = term._buildMatrix(var=CellVariable(mesh=mesh), SparseMatrix=SparseMatrix)
>>> print numerix.allclose(L.getNumpyArray(),
... ((-1., 1.),
... ( 1., -1.))) or procID != 0
True
>>> print numerix.allclose(b, (0., 0.)) or procID != 0
True
>>> from fipy.variables.variable import Variable
>>> term = DiffusionTerm(coeff = Variable(value = 1))
>>> coeff = term._getGeomCoeff(mesh)
>>> M = term._getCoefficientMatrix(SparseMatrix, mesh, coeff[0])
>>> print numerix.allclose(M.getNumpyArray(),
... (( 1., -1.),
... (-1., 1.))) or procID != 0
True
>>> L,b = term._buildMatrix(var=CellVariable(mesh=mesh), SparseMatrix=SparseMatrix)
>>> print numerix.allclose(L.getNumpyArray(),
... ((-1., 1.),
... ( 1., -1.))) or procID != 0
True
>>> print numerix.allclose(b, (0., 0.)) or procID != 0
True
>>> term = DiffusionTerm(coeff = ((1,2),))
>>> term = DiffusionTerm(coeff = FaceVariable(mesh = mesh, value = (1,), rank=1))
>>> term = DiffusionTerm(coeff = CellVariable(mesh=mesh, value=(1,), rank=1))
Test, 2nd order, 1 dimension, fixed flux 3, fixed value of 4
>>> from fipy.boundaryConditions.fixedFlux import FixedFlux
>>> from fipy.boundaryConditions.fixedValue import FixedValue
>>> bcLeft = FixedFlux(mesh.getFacesLeft(), 3.)
>>> bcRight = FixedValue(mesh.getFacesRight(), 4.)
>>> term = DiffusionTerm(coeff = (1.,))
>>> coeff = term._getGeomCoeff(mesh)
>>> M = term._getCoefficientMatrix(SparseMatrix, mesh, coeff[0])
>>> print numerix.allclose(M.getNumpyArray(),
... (( 1., -1.),
... (-1., 1.))) or procID != 0
True
>>> L,b = term._buildMatrix(var=CellVariable(mesh=mesh),
... SparseMatrix=SparseMatrix ,
... boundaryConditions=(bcLeft, bcRight))
>>> print numerix.allclose(L.getNumpyArray(),
... ((-1., 1.),
... ( 1., -3.))) or procID != 0
True
>>> print numerix.allclose(b, (-3., -8.)) or procID != 0
True
Test, 4th order, 1 dimension, x = 0; fixed flux 3, fixed curvatures 0,
x = 2, fixed value 1, fixed curvature 0
>>> bcLeft1 = FixedFlux(mesh.getFacesLeft(), 3.)
>>> from fipy.boundaryConditions.nthOrderBoundaryCondition \
... import NthOrderBoundaryCondition
>>> bcLeft2 = NthOrderBoundaryCondition(mesh.getFacesLeft(), 0., 2)
>>> bcRight1 = FixedValue(mesh.getFacesRight(), 4.)
>>> bcRight2 = NthOrderBoundaryCondition(mesh.getFacesRight(), 0., 2)
>>> term = DiffusionTerm(coeff = (1., 1.))
>>> coeff = term._getGeomCoeff(mesh)
>>> M = term._getCoefficientMatrix(SparseMatrix, mesh, coeff[0])
>>> print numerix.allclose(M.getNumpyArray(),
... (( 1., -1.),
... (-1., 1.))) or procID != 0
True
>>> L,b = term._buildMatrix(var = CellVariable(mesh = mesh), SparseMatrix=SparseMatrix,
... boundaryConditions = (bcLeft1, bcLeft2,
... bcRight1, bcRight2))
>>> print numerix.allclose(L.getNumpyArray(),
... (( 4., -6.),
... (-4., 10.))) or procID != 0
True
>>> print numerix.allclose(b, (1., 21.)) or procID != 0
True
Test, 4th order, 1 dimension, x = 0; fixed flux 3, fixed curvature 2,
x = 2, fixed value 4, fixed 3rd order -1
>>> bcLeft1 = FixedFlux(mesh.getFacesLeft(), 3.)
>>> bcLeft2 = NthOrderBoundaryCondition(mesh.getFacesLeft(), 2., 2)
>>> bcRight1 = FixedValue(mesh.getFacesRight(), 4.)
>>> bcRight2 = NthOrderBoundaryCondition(mesh.getFacesRight(), -1., 3)
>>> term = DiffusionTerm(coeff = (-1., 1.))
>>> coeff = term._getGeomCoeff(mesh)
>>> M = term._getCoefficientMatrix(SparseMatrix, mesh, coeff[0])
>>> print numerix.allclose(M.getNumpyArray(),
... ((-1., 1.),
... ( 1., -1.))) or procID != 0
True
>>> L,b = term._buildMatrix(var = CellVariable(mesh = mesh),
... SparseMatrix=SparseMatrix,
... boundaryConditions = (bcLeft1, bcLeft2,
... bcRight1, bcRight2))
>>> print numerix.allclose(L.getNumpyArray(),
... ((-4., 6.),
... ( 2., -4.))) or procID != 0
True
>>> print numerix.allclose(b, (3., -4.)) or procID != 0
True
Test when dx = 0.5.
>>> mesh = Grid1D(dx = .5, nx = 2)
>>> bcLeft1 = FixedValue(mesh.getFacesLeft(), 0.)
>>> bcLeft2 = NthOrderBoundaryCondition(mesh.getFacesLeft(), 1., 2)
>>> bcRight1 = FixedFlux(mesh.getFacesRight(), 1.)
>>> bcRight2 = NthOrderBoundaryCondition(mesh.getFacesRight(), 0., 3)
>>> term = DiffusionTerm(coeff = (1., 1.))
>>> coeff = term._getGeomCoeff(mesh)
>>> M = term._getCoefficientMatrix(SparseMatrix, mesh, coeff[0])
>>> print numerix.allclose(M.getNumpyArray(),
... (( 2., -2.),
... (-2., 2.))) or procID != 0
True
>>> L,b = term._buildMatrix(var = CellVariable(mesh = mesh),
... SparseMatrix=SparseMatrix,
... boundaryConditions = (bcLeft1, bcLeft2,
... bcRight1, bcRight2))
>>> print numerix.allclose(L.getNumpyArray(),
... (( 80., -32.),
... (-32., 16.))) or procID != 0
True
>>> print numerix.allclose(b, (-8., 4.)) or procID != 0
True
The following tests are to check that DiffusionTerm can take any of the four
main Variable types.
>>> from fipy.meshes.tri2D import Tri2D
>>> mesh = Tri2D(nx = 1, ny = 1)
>>> term = DiffusionTerm(CellVariable(value = 1, mesh = mesh))
>>> print term._getGeomCoeff(mesh)[0]
[ 6. 6. 6. 6. 1.5 1.5 1.5 1.5]
>>> term = DiffusionTerm(FaceVariable(value = 1, mesh = mesh))
>>> print term._getGeomCoeff(mesh)[0]
[ 6. 6. 6. 6. 1.5 1.5 1.5 1.5]
>>> term = DiffusionTerm(CellVariable(value=(0.5, 1), mesh=mesh, rank=1))
>>> term = DiffusionTerm(CellVariable(value=((0.5,), (1,)), mesh=mesh, rank=1))
>>> print term._getGeomCoeff(mesh)[0]
[ 6. 6. 3. 3. 1.125 1.125 1.125 1.125]
>>> term = DiffusionTerm(FaceVariable(value=(0.5, 1), mesh=mesh, rank=1))
>>> term = DiffusionTerm(FaceVariable(value=((0.5,), (1,)), mesh=mesh, rank=1))
>>> print term._getGeomCoeff(mesh)[0]
[ 6. 6. 3. 3. 1.125 1.125 1.125 1.125]
>>> mesh = Tri2D(nx = 1, ny = 1, dy = 0.1)
>>> term = DiffusionTerm(FaceVariable(value=(0.5, 1), mesh=mesh, rank=1))
>>> term = DiffusionTerm(FaceVariable(value=((0.5,), (1,)), mesh=mesh, rank=1))
>>> val = (60., 60., 0.3, 0.3, 0.22277228, 0.22277228, 0.22277228, 0.22277228)
>>> print numerix.allclose(term._getGeomCoeff(mesh)[0], val)
1
>>> term = DiffusionTerm(((0.5, 1),))
>>> term = DiffusionTerm((((0.5,), (1,)),))
>>> print numerix.allclose(term._getGeomCoeff(mesh)[0], val)
Traceback (most recent call last):
...
IndexError: diffusion coefficent tensor is not an appropriate shape for this mesh
Anisotropy test
>>> from fipy.meshes.tri2D import Tri2D
>>> mesh = Tri2D(nx = 1, ny = 1)
>>> term = DiffusionTerm((((1, 2), (3, 4)),))
>>> print term._getGeomCoeff(mesh)
[[ 24. 24. 6. 6. 0. 7.5
7.5 0. ]
[ -3. -3. 2. 2. -1.41421356
0.70710678 0.70710678 -1.41421356]]
"""
pass
def __init__(self, var):
Variable.__init__(self, unit=var.unit)
self.var = self._requires(var)
def _isCached(self):
return (Variable._isCached(self)
or (len(self.subscribedVariables) > 1 and not self._cacheNever))
def __init__(self, var):
Variable.__init__(self, unit = var.unit)
self.var = self._requires(var)