fipy.meshes.tri2D¶

Classes

Tri2D([dx, dy, nx, ny, ...])

This class creates a mesh made out of triangles.

class fipy.meshes.tri2D.Tri2D(dx=1.0, dy=1.0, nx=1, ny=1, _RepresentationClass=<class 'fipy.meshes.representations.gridRepresentation._Grid2DRepresentation'>, _TopologyClass=<class 'fipy.meshes.topologies.meshTopology._Mesh2DTopology'>)¶

Bases: Mesh2D

This class creates a mesh made out of triangles. It does this by starting with a standard Cartesian mesh (Grid2D) and dividing each cell in that mesh (hereafter referred to as a “box”) into four equal parts with the dividing lines being the diagonals.

Creates a 2D triangular mesh with horizontal faces numbered first then vertical faces, then diagonal faces. Vertices are numbered starting with the vertices at the corners of boxes and then the vertices at the centers of boxes. Cells on the right of boxes are numbered first, then cells on the top of boxes, then cells on the left of boxes, then cells on the bottom of boxes. Within each of the “sub-categories” in the above, the vertices, cells and faces are numbered in the usual way.

Parameters:

dx (float) – The X and Y dimensions of each “box”. If dx <> dy, the line segments connecting the cell centers will not be orthogonal to the faces.
dy (float) – The X and Y dimensions of each “box”. If dx <> dy, the line segments connecting the cell centers will not be orthogonal to the faces.
nx (int) – The number of boxes in the X direction and the Y direction. The total number of boxes will be equal to nx * ny, and the total number of cells will be equal to 4 * nx * ny.
ny (int) – The number of boxes in the X direction and the Y direction. The total number of boxes will be equal to nx * ny, and the total number of cells will be equal to 4 * nx * ny.

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶: Coordinates of geometric centers of cells

property cellFaceIDs¶

extrude(extrudeFunc=<function Mesh2D.<lambda>>, layers=1)¶

This function returns a new 3D mesh. The 2D mesh is extruded using the extrudeFunc and the number of layers.

>>> from fipy.meshes.nonUniformGrid2D import NonUniformGrid2D
>>> print(NonUniformGrid2D(nx=2, ny=2).extrude(layers=2).cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]]

>>> from fipy.meshes.tri2D import Tri2D
>>> print(Tri2D().extrude(layers=2).cellCenters.allclose([[ 0.83333333, 0.5,        0.16666667, 0.5,       0.83333333, 0.5,
...                                                      0.16666667, 0.5       ],
...                                                       [ 0.5,        0.83333333, 0.5,        0.16666667, 0.5,        0.83333333,
...                                                      0.5,        0.16666667],
...                                                      [ 0.5,        0.5,        0.5,        0.5,        1.5,        1.5,        1.5,
...                                                      1.5       ]]))
True

Parameters:

extrudeFunc (function) – Takes the vertex coordinates and returns the displaced values
layers (int) – Number of layers in the extruded mesh (number of times extrudeFunc will be called)

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property physicalShape¶: Return physical dimensions of Grid2D.

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

Last updated on Nov 20, 2024. Created using Sphinx 7.1.2.