def _buildMatrix(self, var, SparseMatrix, boundaryConditions=(), dt=None, equation=None, transientGeomCoeff=None, diffusionGeomCoeff=None):
oldArray = var.old
mesh = var.mesh
NCells = mesh.numberOfCells
NCellFaces = mesh._maxFacesPerCell
cellValues = numerix.repeat(oldArray[numerix.newaxis, ...], NCellFaces, axis = 0)
cellIDs = numerix.repeat(numerix.arange(NCells)[numerix.newaxis, ...], NCellFaces, axis = 0)
cellToCellIDs = mesh._cellToCellIDs
if NCells > 0:
cellToCellIDs = MA.where(MA.getmask(cellToCellIDs), cellIDs, cellToCellIDs)
adjacentValues = numerix.take(oldArray, cellToCellIDs)
differences = self._getDifferences(adjacentValues, cellValues, oldArray, cellToCellIDs, mesh)
differences = MA.filled(differences, 0)
minsq = numerix.sqrt(numerix.sum(numerix.minimum(differences, numerix.zeros((NCellFaces, NCells), 'l'))**2, axis=0))
maxsq = numerix.sqrt(numerix.sum(numerix.maximum(differences, numerix.zeros((NCellFaces, NCells), 'l'))**2, axis=0))
coeff = numerix.array(self._getGeomCoeff(var))
coeffXdifferences = coeff * ((coeff > 0.) * minsq + (coeff < 0.) * maxsq)
else:
coeffXdifferences = 0.
return (var, SparseMatrix(mesh=var.mesh), -coeffXdifferences * mesh.cellVolumes)
def _buildMatrix(self, var, SparseMatrix, boundaryConditions=(), dt=None, equation=None, transientGeomCoeff=None, diffusionGeomCoeff=None):
oldArray = var.old
mesh = var.mesh
NCells = mesh.numberOfCells
NCellFaces = mesh._maxFacesPerCell
cellValues = numerix.repeat(oldArray[numerix.newaxis, ...], NCellFaces, axis = 0)
cellIDs = numerix.repeat(numerix.arange(NCells)[numerix.newaxis, ...], NCellFaces, axis = 0)
cellToCellIDs = mesh._cellToCellIDs
if NCells > 0:
cellToCellIDs = MA.where(MA.getmask(cellToCellIDs), cellIDs, cellToCellIDs)
adjacentValues = numerix.take(oldArray, cellToCellIDs)
differences = self._getDifferences(adjacentValues, cellValues, oldArray, cellToCellIDs, mesh)
differences = MA.filled(differences, 0)
minsq = numerix.sqrt(numerix.sum(numerix.minimum(differences, numerix.zeros((NCellFaces, NCells), 'l'))**2, axis=0))
maxsq = numerix.sqrt(numerix.sum(numerix.maximum(differences, numerix.zeros((NCellFaces, NCells), 'l'))**2, axis=0))
coeff = numerix.array(self._getGeomCoeff(var))
coeffXdiffereneces = coeff * ((coeff > 0.) * minsq + (coeff < 0.) * maxsq)
else:
coeffXdiffereneces = 0.
return (var, SparseMatrix(mesh=var.mesh), -coeffXdiffereneces * mesh.cellVolumes)
def _buildMatrix(self, var, SparseMatrix, boundaryCondtions=(), dt=None, equation=None):
oldArray = var.getOld()
mesh = var.getMesh()
NCells = mesh.getNumberOfCells()
NCellFaces = mesh._getMaxFacesPerCell()
cellValues = numerix.repeat(oldArray[numerix.newaxis, ...], NCellFaces, axis = 0)
cellIDs = numerix.repeat(numerix.arange(NCells)[numerix.newaxis, ...], NCellFaces, axis = 0)
cellToCellIDs = mesh._getCellToCellIDs()
if NCells > 0:
cellToCellIDs = MA.where(MA.getmask(cellToCellIDs), cellIDs, cellToCellIDs)
adjacentValues = numerix.take(oldArray, cellToCellIDs)
differences = self._getDifferences(adjacentValues, cellValues, oldArray, cellToCellIDs, mesh)
differences = MA.filled(differences, 0)
minsq = numerix.sqrt(numerix.sum(numerix.minimum(differences, numerix.zeros((NCellFaces, NCells)))**2, axis=0))
maxsq = numerix.sqrt(numerix.sum(numerix.maximum(differences, numerix.zeros((NCellFaces, NCells)))**2, axis=0))
coeff = numerix.array(self._getGeomCoeff(mesh))
coeffXdiffereneces = coeff * ((coeff > 0.) * minsq + (coeff < 0.) * maxsq)
else:
coeffXdiffereneces = 0.
return (SparseMatrix(mesh=var.getMesh()), -coeffXdiffereneces * mesh.getCellVolumes())
def _createVertices(self):
x = self._calcVertexCoordinates(self.dx, self.nx)
x = numerix.resize(x, (self.numberOfVertices,))
y = self._calcVertexCoordinates(self.dy, self.ny)
y = numerix.repeat(y, self.numberOfVerticalColumns)
y = numerix.resize(y, (self.numberOfVertices,))
z = self._calcVertexCoordinates(self.dz, self.nz)
z = numerix.repeat(z, self.numberOfHorizontalRows * self.numberOfVerticalColumns)
z = numerix.resize(z, (self.numberOfVertices,))
return numerix.array((x, y, z))
def _createVertices(self):
x = numerix.arange(self.nx + 1) * self.dx
y = numerix.arange(self.ny + 1) * self.dy
x = numerix.resize(x, (self.numberOfCornerVertices, ))
y = numerix.repeat(y, self.nx + 1)
boxCorners = numerix.array((x, y))
x = numerix.arange(0.5, self.nx + 0.5) * self.dx
y = numerix.arange(0.5, self.ny + 0.5) * self.dy
x = numerix.resize(x, (self.numberOfCenterVertices, ))
y = numerix.repeat(y, self.nx)
boxCenters = numerix.array((x, y))
return numerix.concatenate((boxCorners, boxCenters), axis=1)
def createVertices(dx, dy, dz, nx, ny, nz, numVertices, numHorizRows, numVertCols):
x = _AbstractGridBuilder.calcVertexCoordinates(dx, nx)
x = numerix.resize(x, (numVertices,))
y = _AbstractGridBuilder.calcVertexCoordinates(dy, ny)
y = numerix.repeat(y, numVertCols)
y = numerix.resize(y, (numVertices,))
z = _AbstractGridBuilder.calcVertexCoordinates(dz, nz)
z = numerix.repeat(z, numHorizRows * numVertCols)
z = numerix.resize(z, (numVertices,))
return numerix.array((x, y, z))
def _calcFaceAreas(self):
faceVertexIDs = MA.filled(self.faceVertexIDs, -1)
substitute = numerix.repeat(faceVertexIDs[numerix.newaxis, 0],
faceVertexIDs.shape[0], axis=0)
faceVertexIDs = numerix.where(MA.getmaskarray(self.faceVertexIDs), substitute, faceVertexIDs)
faceVertexCoords = numerix.take(self.vertexCoords, faceVertexIDs, axis=1)
faceOrigins = numerix.repeat(faceVertexCoords[:,0], faceVertexIDs.shape[0], axis=0)
faceOrigins = numerix.reshape(faceOrigins, MA.shape(faceVertexCoords))
faceVertexCoords = faceVertexCoords - faceOrigins
left = range(faceVertexIDs.shape[0])
right = left[1:] + [left[0]]
cross = numerix.sum(numerix.cross(faceVertexCoords, numerix.take(faceVertexCoords, right, 1), axis=0), 1)
self.faceAreas = numerix.sqrtDot(cross, cross) / 2.
def _createVertices(self):
x = numerix.arange(self.nx + 1) * self.dx
y = numerix.arange(self.ny + 1) * self.dy
x = numerix.resize(x, (self.numberOfCornerVertices,))
y = numerix.repeat(y, self.nx + 1)
boxCorners = numerix.array((x, y))
x = numerix.arange(0.5, self.nx + 0.5) * self.dx
y = numerix.arange(0.5, self.ny + 0.5) * self.dy
x = numerix.resize(x, (self.numberOfCenterVertices,))
y = numerix.repeat(y, self.nx)
boxCenters = numerix.array((x, y))
return numerix.concatenate((boxCorners, boxCenters), axis=1)
def createVertices(dx, dy, dz, nx, ny, nz, numVertices, numHorizRows,
numVertCols):
x = _AbstractGridBuilder.calcVertexCoordinates(dx, nx)
x = numerix.resize(x, (numVertices, ))
y = _AbstractGridBuilder.calcVertexCoordinates(dy, ny)
y = numerix.repeat(y, numVertCols)
y = numerix.resize(y, (numVertices, ))
z = _AbstractGridBuilder.calcVertexCoordinates(dz, nz)
z = numerix.repeat(z, numHorizRows * numVertCols)
z = numerix.resize(z, (numVertices, ))
return numerix.array((x, y, z))
def _cellDistances(self):
Hdis = numerix.repeat((self.dy,), self.numberOfHorizontalFaces)
Hdis = numerix.reshape(Hdis, (self.nx, self.numberOfHorizontalRows))
if self.numberOfHorizontalRows > 0:
Hdis[..., 0] = self.dy / 2.
Hdis[..., -1] = self.dy / 2.
Vdis = numerix.repeat((self.dx,), self.numberOfFaces - self.numberOfHorizontalFaces)
Vdis = numerix.reshape(Vdis, (self.numberOfVerticalColumns, self.ny))
if self.numberOfVerticalColumns > 0:
Vdis[0, ...] = self.dx / 2.
Vdis[-1, ...] = self.dx / 2.
return numerix.concatenate((numerix.reshape(numerix.swapaxes(Hdis, 0, 1), (self.numberOfHorizontalFaces,)),
numerix.reshape(numerix.swapaxes(Vdis, 0, 1), (self.numberOfFaces - self.numberOfHorizontalFaces,))))
def _cellInterfaceNormals(self):
"""
Returns the interface normals over the cells.
>>> from fipy.meshes import Grid2D
>>> from fipy.variables.cellVariable import CellVariable
>>> mesh = Grid2D(dx = .5, dy = .5, nx = 2, ny = 2)
>>> distanceVariable = DistanceVariable(mesh = mesh,
... value = (-0.5, 0.5, 0.5, 1.5))
>>> v = 1 / numerix.sqrt(2)
>>> answer = CellVariable(mesh=mesh,
... value=(((0, 0, v, 0),
... (0, 0, 0, 0),
... (0, 0, 0, 0),
... (0, v, 0, 0)),
... ((0, 0, v, 0),
... (0, 0, 0, 0),
... (0, 0, 0, 0),
... (0, v, 0, 0))))
>>> print(numerix.allclose(distanceVariable._cellInterfaceNormals, answer))
True
"""
dim = self.mesh.dim
valueOverFaces = numerix.repeat(self._cellValueOverFaces[numerix.newaxis, ...], dim, axis=0)
cellFaceIDs = self.mesh.cellFaceIDs
if cellFaceIDs.shape[-1] > 0:
interfaceNormals = self._interfaceNormals[..., cellFaceIDs]
else:
interfaceNormals = 0
return MA.where(valueOverFaces < 0, 0, interfaceNormals)
def _getDifferences(self, adjacentValues, cellValues, oldArray, cellToCellIDs, mesh):
dAP = mesh._cellToCellDistances
## adjacentGradient = numerix.take(oldArray.grad, cellToCellIDs)
adjacentGradient = numerix.take(oldArray.grad, mesh._cellToCellIDs, axis=-1)
adjacentNormalGradient = numerix.dot(adjacentGradient, mesh._cellNormals)
adjacentUpValues = cellValues + 2 * dAP * adjacentNormalGradient
cellIDs = numerix.repeat(numerix.arange(mesh.numberOfCells)[numerix.newaxis, ...],
mesh._maxFacesPerCell, axis=0)
cellIDs = MA.masked_array(cellIDs, mask = MA.getmask(mesh._cellToCellIDs))
cellGradient = numerix.take(oldArray.grad, cellIDs, axis=-1)
cellNormalGradient = numerix.dot(cellGradient, mesh._cellNormals)
cellUpValues = adjacentValues - 2 * dAP * cellNormalGradient
cellLaplacian = (cellUpValues + adjacentValues - 2 * cellValues) / dAP**2
adjacentLaplacian = (adjacentUpValues + cellValues - 2 * adjacentValues) / dAP**2
adjacentLaplacian = adjacentLaplacian.filled(0)
cellLaplacian = cellLaplacian.filled(0)
mm = numerix.where(cellLaplacian * adjacentLaplacian < 0.,
0.,
numerix.where(abs(cellLaplacian) > abs(adjacentLaplacian),
adjacentLaplacian,
cellLaplacian))
return FirstOrderAdvectionTerm._getDifferences(self, adjacentValues, cellValues, oldArray, cellToCellIDs, mesh) - mm * dAP / 2.
def _cellValueOverFaces(self):
"""
Returns the cells values at the faces.
>>> from fipy.meshes import Grid2D
>>> from fipy.variables.cellVariable import CellVariable
>>> mesh = Grid2D(dx = .5, dy = .5, nx = 2, ny = 2)
>>> distanceVariable = DistanceVariable(mesh = mesh,
... value = (-0.5, 0.5, 0.5, 1.5))
>>> answer = CellVariable(mesh=mesh,
... value=((-.5, .5, .5, 1.5),
... (-.5, .5, .5, 1.5),
... (-.5, .5, .5, 1.5),
... (-.5, .5, .5, 1.5)))
>>> print numerix.allclose(distanceVariable._cellValueOverFaces, answer)
True
"""
M = self.mesh._maxFacesPerCell
N = self.mesh.numberOfCells
return numerix.reshape(
numerix.repeat(numerix.array(self._value)[numerix.newaxis, ...],
M,
axis=0), (M, N))
def _cellInterfaceNormals(self):
"""
Returns the interface normals over the cells.
>>> from fipy.meshes import Grid2D
>>> from fipy.variables.cellVariable import CellVariable
>>> mesh = Grid2D(dx = .5, dy = .5, nx = 2, ny = 2)
>>> distanceVariable = DistanceVariable(mesh = mesh,
... value = (-0.5, 0.5, 0.5, 1.5))
>>> v = 1 / numerix.sqrt(2)
>>> answer = CellVariable(mesh=mesh,
... value=(((0, 0, v, 0),
... (0, 0, 0, 0),
... (0, 0, 0, 0),
... (0, v, 0, 0)),
... ((0, 0, v, 0),
... (0, 0, 0, 0),
... (0, 0, 0, 0),
... (0, v, 0, 0))))
>>> print numerix.allclose(distanceVariable._cellInterfaceNormals, answer)
True
"""
dim = self.mesh.dim
valueOverFaces = numerix.repeat(self._cellValueOverFaces[numerix.newaxis, ...], dim, axis=0)
cellFaceIDs = self.mesh.cellFaceIDs
if cellFaceIDs.shape[-1] > 0:
interfaceNormals = self._interfaceNormals[...,cellFaceIDs]
else:
interfaceNormals = 0
return MA.where(valueOverFaces < 0, 0, interfaceNormals)
def _calcValue(self):
Nfaces = self.mesh.numberOfFaces
M = self.mesh._maxFacesPerCell
dim = self.mesh.dim
cellFaceIDs = self.mesh.cellFaceIDs
faceNormalAreas = self.distanceVar._levelSetNormals * self.mesh._faceAreas
cellFaceNormalAreas = numerix.array(MA.filled(numerix.take(faceNormalAreas, cellFaceIDs, axis=-1), 0))
norms = numerix.array(MA.filled(MA.array(self.mesh._cellNormals), 0))
alpha = numerix.dot(cellFaceNormalAreas, norms)
alpha = numerix.where(alpha > 0, alpha, 0)
alphasum = numerix.sum(alpha, axis=0)
alphasum += (alphasum < 1e-100) * 1.0
alpha = alpha / alphasum
phi = numerix.repeat(self.distanceVar[numerix.newaxis, ...], M, axis=0)
alpha = numerix.where(phi > 0., 0, alpha)
volumes = numerix.array(self.mesh.cellVolumes)
alpha = alpha * volumes * norms
value = numerix.zeros((dim, Nfaces), 'd')
vector._putAdd(value, cellFaceIDs, alpha, mask=MA.getmask(MA.array(cellFaceIDs)))
## value = numerix.reshape(value, (dim, Nfaces, dim))
return -value / self.mesh._faceAreas
def _interfaceNormals(self):
"""
Returns the normals on the boundary faces only, the other are set to zero.
>>> from fipy.meshes import Grid2D
>>> from fipy.variables.faceVariable import FaceVariable
>>> mesh = Grid2D(dx = .5, dy = .5, nx = 2, ny = 2)
>>> distanceVariable = DistanceVariable(mesh = mesh,
... value = (-0.5, 0.5, 0.5, 1.5))
>>> v = 1 / numerix.sqrt(2)
>>> answer = FaceVariable(mesh=mesh,
... value=((0, 0, v, 0, 0, 0, 0, v, 0, 0, 0, 0),
... (0, 0, v, 0, 0, 0, 0, v, 0, 0, 0, 0)))
>>> print numerix.allclose(distanceVariable._interfaceNormals, answer)
True
"""
M = self.mesh.dim
interfaceFlag = numerix.repeat(self._interfaceFlag[numerix.newaxis,
...],
M,
axis=0)
return numerix.where(interfaceFlag, self._levelSetNormals, 0)
def _cellToCellIDsFilled(self):
N = self.numberOfCells
M = self._maxFacesPerCell
cellIDs = numerix.repeat(numerix.arange(N)[numerix.newaxis, ...],
M,
axis=0)
cellToCellIDs = self._cellToCellIDs
return MA.where(MA.getmaskarray(cellToCellIDs), cellIDs, cellToCellIDs)
def _calcFaceAreas(self):
faceVertexIDs = MA.filled(self.faceVertexIDs, -1)
substitute = numerix.repeat(faceVertexIDs[numerix.newaxis, 0],
faceVertexIDs.shape[0], axis=0)
faceVertexIDs = numerix.where(MA.getmaskarray(self.faceVertexIDs),
substitute, faceVertexIDs)
faceVertexCoords = numerix.take(self.vertexCoords, faceVertexIDs, axis=1)
faceOrigins = numerix.repeat(faceVertexCoords[:,0], faceVertexIDs.shape[0], axis=0)
faceOrigins = numerix.reshape(faceOrigins, MA.shape(faceVertexCoords))
faceVertexCoords = faceVertexCoords - faceOrigins
left = range(faceVertexIDs.shape[0])
right = left[1:] + [left[0]]
cross = numerix.sum(numerix.cross(faceVertexCoords,
numerix.take(faceVertexCoords, right, 1),
axis=0),
1)
return numerix.sqrtDot(cross, cross) / 2.
def _createVertices(self):
x = self._calcVertexCoordinates(self.dx, self.nx)
x = numerix.resize(x, (self.numberOfVertices,))
y = self._calcVertexCoordinates(self.dy, self.ny)
y = numerix.repeat(y, self.numberOfVerticalColumns)
return numerix.array((x, y))
def createVertices(nx, ny, dx, dy, numVerts, numVertCols):
x = _AbstractGridBuilder.calcVertexCoordinates(dx, nx)
x = numerix.resize(x, (numVerts,))
y = _AbstractGridBuilder.calcVertexCoordinates(dy, ny)
y = numerix.repeat(y, numVertCols)
return numerix.array((x, y))
def createVertices(nx, ny, dx, dy, numVerts, numVertCols):
x = _AbstractGridBuilder.calcVertexCoordinates(dx, nx)
x = numerix.resize(x, (numVerts, ))
y = _AbstractGridBuilder.calcVertexCoordinates(dy, ny)
y = numerix.repeat(y, numVertCols)
return numerix.array((x, y))
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 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 _calcCellNormals(self):
cellNormals = numerix.take(self._getFaceNormals(), self._getCellFaceIDs(), axis=1)
cellFaceCellIDs = numerix.take(self.faceCellIDs[0], self.cellFaceIDs)
cellIDs = numerix.repeat(numerix.arange(self.getNumberOfCells())[numerix.newaxis,...],
self._getMaxFacesPerCell(),
axis=0)
direction = (cellFaceCellIDs == cellIDs) * 2 - 1
if self._getMaxFacesPerCell() > 0:
self.cellNormals = direction[numerix.newaxis, ...] * cellNormals
else:
self.cellNormals = cellNormals
def _calcCellNormals(self):
cellNormals = numerix.take(self.faceNormals, self.cellFaceIDs, axis=1)
cellFaceCellIDs = numerix.take(self.faceCellIDs[0], self.cellFaceIDs)
cellIDs = numerix.repeat(numerix.arange(self.numberOfCells)[numerix.newaxis,...],
self._maxFacesPerCell,
axis=0)
direction = (cellFaceCellIDs == cellIDs) * 2 - 1
if self._maxFacesPerCell > 0:
return direction[numerix.newaxis, ...] * cellNormals
else:
return cellNormals
def _iadd(self, other, sign=1):
if hasattr(other, "matrix"):
self.matrix = self.matrix + (sign * other.matrix)
elif type(other) in [float, int]:
fillVec = numerix.repeat(other, self.matrix.nnz)
self.matrix = self.matrix \
+ sp.csr_matrix((fillVec, self.matrix.nonzero()),
self.matrix.shape)
else:
self.matrix = self.matrix + (sign * other)
return self
def _iadd(self, other, sign=1):
if hasattr(other, "matrix"):
self.matrix = self.matrix + (sign * other.matrix)
elif type(other) in [float, int]:
fillVec = numerix.repeat(other, self.matrix.nnz)
self.matrix = self.matrix \
+ sp.csr_matrix((fillVec, self.matrix.nonzero()),
self.matrix.shape)
else:
self.matrix = self.matrix + (sign * other)
return self
def _calcFaceCenters(self):
maskedFaceVertexIDs = MA.filled(self.faceVertexIDs, 0)
faceVertexCoords = numerix.take(self.vertexCoords, maskedFaceVertexIDs, axis=1)
if MA.getmask(self.faceVertexIDs) is False:
faceVertexCoordsMask = numerix.zeros(numerix.shape(faceVertexCoords), 'l')
else:
faceVertexCoordsMask = \
numerix.repeat(MA.getmaskarray(self.faceVertexIDs)[numerix.newaxis,...],
self.dim, axis=0)
faceVertexCoords = MA.array(data=faceVertexCoords, mask=faceVertexCoordsMask)
return MA.filled(MA.average(faceVertexCoords, axis=1))
def putDiagonal(self, vector):
"""
Put elements of `vector` along diagonal of matrix
>>> L = _ScipyMatrixFromShape(size=3)
>>> L.putDiagonal([3., 10., numerix.pi])
>>> print(L)
3.000000 --- ---
--- 10.000000 ---
--- --- 3.141593
>>> L.putDiagonal([10., 3.])
>>> print(L)
10.000000 --- ---
--- 3.000000 ---
--- --- 3.141593
"""
if type(vector) in [int, float]:
vector = numerix.repeat(vector, self._shape[0])
self.matrix.setdiag(vector)
def putDiagonal(self, vector):
"""
Put elements of `vector` along diagonal of matrix
>>> L = _ScipyMatrixFromShape(size=3)
>>> L.putDiagonal([3.,10.,numerix.pi])
>>> print L
3.000000 --- ---
--- 10.000000 ---
--- --- 3.141593
>>> L.putDiagonal([10.,3.])
>>> print L
10.000000 --- ---
--- 3.000000 ---
--- --- 3.141593
"""
if type(vector) in [int, float]:
vector = numerix.repeat(vector, self._shape[0])
self.matrix.setdiag(vector)
def _getDifferences(self, adjacentValues, cellValues, oldArray,
cellToCellIDs, mesh):
dAP = mesh._cellToCellDistances
## adjacentGradient = numerix.take(oldArray.grad, cellToCellIDs)
adjacentGradient = numerix.take(oldArray.grad,
mesh._cellToCellIDs,
axis=-1)
adjacentNormalGradient = numerix.dot(adjacentGradient,
mesh._cellNormals)
adjacentUpValues = cellValues + 2 * dAP * adjacentNormalGradient
cellIDs = numerix.repeat(numerix.arange(
mesh.numberOfCells)[numerix.newaxis, ...],
mesh._maxFacesPerCell,
axis=0)
cellIDs = MA.masked_array(cellIDs,
mask=MA.getmask(mesh._cellToCellIDs))
cellGradient = numerix.take(oldArray.grad, cellIDs, axis=-1)
cellNormalGradient = numerix.dot(cellGradient, mesh._cellNormals)
cellUpValues = adjacentValues - 2 * dAP * cellNormalGradient
cellLaplacian = (cellUpValues + adjacentValues -
2 * cellValues) / dAP**2
adjacentLaplacian = (adjacentUpValues + cellValues -
2 * adjacentValues) / dAP**2
adjacentLaplacian = adjacentLaplacian.filled(0)
cellLaplacian = cellLaplacian.filled(0)
mm = numerix.where(
cellLaplacian * adjacentLaplacian < 0., 0.,
numerix.where(
abs(cellLaplacian) > abs(adjacentLaplacian), adjacentLaplacian,
cellLaplacian))
return FirstOrderAdvectionTerm._getDifferences(
self, adjacentValues, cellValues, oldArray, cellToCellIDs,
mesh) - mm * dAP / 2.
def _interfaceNormals(self):
"""
Returns the normals on the boundary faces only, the other are set to zero.
>>> from fipy.meshes import Grid2D
>>> from fipy.variables.faceVariable import FaceVariable
>>> mesh = Grid2D(dx = .5, dy = .5, nx = 2, ny = 2)
>>> distanceVariable = DistanceVariable(mesh = mesh,
... value = (-0.5, 0.5, 0.5, 1.5))
>>> v = 1 / numerix.sqrt(2)
>>> answer = FaceVariable(mesh=mesh,
... value=((0, 0, v, 0, 0, 0, 0, v, 0, 0, 0, 0),
... (0, 0, v, 0, 0, 0, 0, v, 0, 0, 0, 0)))
>>> print numerix.allclose(distanceVariable._interfaceNormals, answer)
True
"""
M = self.mesh.dim
interfaceFlag = numerix.repeat(self._interfaceFlag[numerix.newaxis, ...], M, axis=0)
return numerix.where(interfaceFlag, self._levelSetNormals, 0)
def _cellValueOverFaces(self):
"""
Returns the cells values at the faces.
>>> from fipy.meshes import Grid2D
>>> from fipy.variables.cellVariable import CellVariable
>>> mesh = Grid2D(dx = .5, dy = .5, nx = 2, ny = 2)
>>> distanceVariable = DistanceVariable(mesh = mesh,
... value = (-0.5, 0.5, 0.5, 1.5))
>>> answer = CellVariable(mesh=mesh,
... value=((-.5, .5, .5, 1.5),
... (-.5, .5, .5, 1.5),
... (-.5, .5, .5, 1.5),
... (-.5, .5, .5, 1.5)))
>>> print numerix.allclose(distanceVariable._cellValueOverFaces, answer)
True
"""
M = self.mesh._maxFacesPerCell
N = self.mesh.numberOfCells
return numerix.reshape(numerix.repeat(numerix.array(self._value)[numerix.newaxis, ...], M, axis=0), (M, N))
def _getCellInterfaceNormals(self):
"""
Returns the interface normals over the cells.
>>> from fipy.meshes.grid2D import Grid2D
>>> from fipy.variables.cellVariable import CellVariable
>>> mesh = Grid2D(dx = .5, dy = .5, nx = 2, ny = 2)
>>> distanceVariable = DistanceVariable(mesh = mesh,
... value = (-0.5, 0.5, 0.5, 1.5))
>>> v = 1 / numerix.sqrt(2)
>>> answer = CellVariable(mesh=mesh,
... value=(((0, 0, v, 0),
... (0, 0, 0, 0),
... (0, 0, 0, 0),
... (0, v, 0, 0)),
... ((0, 0, v, 0),
... (0, 0, 0, 0),
... (0, 0, 0, 0),
... (0, v, 0, 0))))
>>> print numerix.allclose(distanceVariable._getCellInterfaceNormals(), answer)
True
"""
N = self.mesh.getNumberOfCells()
M = self.mesh._getMaxFacesPerCell()
dim = self.mesh.getDim()
valueOverFaces = numerix.repeat(self._getCellValueOverFaces()[numerix.newaxis, ...], dim, axis=0)
if self.cellFaceIDs.shape[-1] > 0:
interfaceNormals = self._getInterfaceNormals()[...,self.cellFaceIDs]
else:
interfaceNormals = 0
from fipy.tools.numerix import MA
return MA.where(valueOverFaces < 0, 0, interfaceNormals)
def addAtDiagonal(self, vector):
if type(vector) in [type(1), type(1.)]:
vector = numerix.repeat(vector, self._shape[0])
ids = numerix.arange(len(vector))
self.addAt(vector, ids, ids)
def _faceAreas(self):
return numerix.concatenate((numerix.repeat((self.dx * self.dy,), self.numberOfXYFaces),
numerix.repeat((self.dx * self.dz,), self.numberOfXZFaces),
numerix.repeat((self.dy * self.dz,), self.numberOfYZFaces)))
def addAtDiagonal(self, vector):
if isinstance(vector, (int, float)):
vector = numerix.repeat(vector, self._shape[0])
ids = numerix.arange(len(vector))
self.addAt(vector, ids, ids)
def addAtDiagonal(self, vector):
if type(vector) in [type(1), type(1.)]:
vector = numerix.repeat(vector, self._shape[0])
ids = numerix.arange(len(vector))
self.addAt(vector, ids, ids)
def _faceAreas(self):
return numerix.concatenate((numerix.repeat((self.dx * self.dy,), self.numberOfXYFaces),
numerix.repeat((self.dx * self.dz,), self.numberOfXZFaces),
numerix.repeat((self.dy * self.dz,), self.numberOfYZFaces)))
def _cellToCellIDsFilled(self):
N = self.numberOfCells
M = self._maxFacesPerCell
cellIDs = numerix.repeat(numerix.arange(N)[numerix.newaxis, ...], M, axis=0)
cellToCellIDs = self._cellToCellIDs
return MA.where(MA.getmaskarray(cellToCellIDs), cellIDs, cellToCellIDs)
def _calcCellToCellIDsFilled(self):
N = self.getNumberOfCells()
M = self._getMaxFacesPerCell()
cellIDs = numerix.repeat(numerix.arange(N)[numerix.newaxis, ...], M, axis=0)
cellToCellIDs = self._getCellToCellIDs()
self.cellToCellIDsFilled = MA.where(MA.getmaskarray(cellToCellIDs), cellIDs, cellToCellIDs)