discretize.TensorMesh¶

class
discretize.
TensorMesh
(*args, **kwargs)[source]¶ Bases:
discretize.base.base_tensor_mesh.BaseTensorMesh
,discretize.base.base_mesh.BaseRectangularMesh
,discretize.View.TensorView
,discretize.DiffOperators.DiffOperators
,discretize.InnerProducts.InnerProducts
,discretize.MeshIO.TensorMeshIO
TensorMesh is a mesh class that deals with tensor product meshes.
Any Mesh that has a constant width along the entire axis such that it can defined by a single width vector, called ‘h’.
import discretize hx = np.array([1, 1, 1]) hy = np.array([1, 2]) hz = np.array([1, 1, 1, 1]) mesh = discretize.TensorMesh([hx, hy, hz]) mesh.plotGrid()
(Source code, png, pdf)
Example of a padded tensor mesh using
discretize.utils.meshTensor()
:import discretize mesh = discretize.TensorMesh([ [(10, 10, 1.3), (10, 40), (10, 10, 1.3)], [(10, 10, 1.3), (10, 20)] ]) mesh.plotGrid()
(Source code, png, pdf)
For a quick tensor mesh on a (10x12x15) unit cube
import discretize mesh = discretize.TensorMesh([10, 12, 15])
Required Properties:
axis_u (
Vector3
): Vector orientation of udirection. For more details see the docs for therotation_matrix
property., a 3D Vector of <class ‘float’> with shape (3), Default: Xaxis_v (
Vector3
): Vector orientation of vdirection. For more details see the docs for therotation_matrix
property., a 3D Vector of <class ‘float’> with shape (3), Default: Yaxis_w (
Vector3
): Vector orientation of wdirection. For more details see the docs for therotation_matrix
property., a 3D Vector of <class ‘float’> with shape (3), Default: Zh (a list of
Array
): h is a list containing the cell widths of the tensor mesh in each dimension., a list (each item is a list or numpy array of <class ‘float’> with shape (*)) with length between 0 and 3reference_system (
String
): The type of coordinate reference frame. Can take on the values cartesian, cylindrical, or spherical. Abbreviations of these are allowed., a unicode string, Default: cartesianx0 (
Array
): origin of the mesh (dim, ), a list or numpy array of <class ‘float’>, <class ‘int’> with shape (*)
 Attributes
area
Construct face areas of the 3D model as 1d array.
areaFx
Area of the xfaces
areaFy
Area of the yfaces
areaFz
Area of the zfaces
aveCC2F
Construct the averaging operator on cell centers to faces.
aveCCV2F
Construct the averaging operator on cell centers to faces as a vector.
aveE2CC
Construct the averaging operator on cell edges to cell centers.
aveE2CCV
Construct the averaging operator on cell edges to cell centers.
aveEx2CC
Construct the averaging operator on cell edges in the x direction to cell centers.
aveEy2CC
Construct the averaging operator on cell edges in the y direction to cell centers.
aveEz2CC
Construct the averaging operator on cell edges in the z direction to cell centers.
aveF2CC
Construct the averaging operator on cell faces to cell centers.
aveF2CCV
Construct the averaging operator on cell faces to cell centers.
aveFx2CC
Construct the averaging operator on cell faces in the x direction to cell centers.
aveFy2CC
Construct the averaging operator on cell faces in the y direction to cell centers.
aveFz2CC
Construct the averaging operator on cell faces in the z direction to cell centers.
aveN2CC
Construct the averaging operator on cell nodes to cell centers.
aveN2E
Construct the averaging operator on cell nodes to cell edges, keeping each dimension separate.
aveN2F
Construct the averaging operator on cell nodes to cell faces, keeping each dimension separate.
axis_u
axis_u (
Vector3
): Vector orientation of udirection. For more details see the docs for therotation_matrix
property., a 3D Vector of <class ‘float’> with shape (3), Default: Xaxis_v
axis_v (
Vector3
): Vector orientation of vdirection. For more details see the docs for therotation_matrix
property., a 3D Vector of <class ‘float’> with shape (3), Default: Yaxis_w
axis_w (
Vector3
): Vector orientation of wdirection. For more details see the docs for therotation_matrix
property., a 3D Vector of <class ‘float’> with shape (3), Default: ZcellBoundaryInd
Find indices of boundary faces in each direction
cellGrad
The cell centered Gradient, takes you to cell faces.
cellGradBC
The cell centered Gradient boundary condition matrix
cellGradx
Cell centered Gradient in the x dimension.
 cellGrady
cellGradz
Cell centered Gradient in the x dimension.
dim
The dimension of the mesh (1, 2, or 3).
edge
Construct edge legnths of the 3D model as 1d array.
edgeCurl
Construct the 3D curl operator.
edgeEx
xedge lengths
edgeEy
yedge lengths
edgeEz
zedge lengths
faceBoundaryInd
Find indices of boundary faces in each direction
faceDiv
Construct divergence operator (facestg to cellcentres).
faceDivx
Construct divergence operator in the x component (facestg to cellcentres).
 faceDivy
faceDivz
Construct divergence operator in the z component (facestg to cellcenters).
gridCC
Cellcentered grid.
gridEx
Edge staggered grid in the x direction.
gridEy
Edge staggered grid in the y direction.
gridEz
Edge staggered grid in the z direction.
gridFx
Face staggered grid in the x direction.
gridFy
Face staggered grid in the y direction.
gridFz
Face staggered grid in the z direction.
gridN
Nodal grid.
h
h (a list of
Array
): h is a list containing the cell widths of the tensor mesh in each dimension., a list (each item is a list or numpy array of <class ‘float’> with shape (*)) with length between 0 and 3h_gridded
Returns an (nC, dim) numpy array with the widths of all cells in order
hx
Width of cells in the x direction
hy
Width of cells in the y direction
hz
Width of cells in the z direction
nC
Total number of cells
nCx
Number of cells in the x direction
nCy
Number of cells in the y direction
nCz
Number of cells in the z direction
nE
Total number of edges.
nEx
Number of xedges
nEy
Number of yedges
nEz
Number of zedges
nF
Total number of faces.
nFx
Number of xfaces
nFy
Number of yfaces
nFz
Number of zfaces
nN
Total number of nodes
nNx
Number of nodes in the xdirection
nNy
Number of nodes in the ydirection
nNz
Number of nodes in the zdirection
nodalGrad
Construct gradient operator (nodes to edges).
nodalLaplacian
Construct laplacian operator (nodes to edges).
normals
Face Normals
reference_is_rotated
True if the axes are rotated from the traditional <X,Y,Z> system
reference_system
reference_system (
String
): The type of coordinate reference frame. Can take on the values cartesian, cylindrical, or spherical. Abbreviations of these are allowed., a unicode string, Default: cartesianrotation_matrix
Builds a rotation matrix to transform coordinates from their coordinate system into a conventional cartesian system.
tangents
Edge Tangents
vectorCCx
Cellcentered grid vector (1D) in the x direction.
vectorCCy
Cellcentered grid vector (1D) in the y direction.
vectorCCz
Cellcentered grid vector (1D) in the z direction.
vectorNx
Nodal grid vector (1D) in the x direction.
vectorNy
Nodal grid vector (1D) in the y direction.
vectorNz
Nodal grid vector (1D) in the z direction.
vnC
Total number of cells in each direction
vnE
Total number of edges in each direction
vnEx
Number of xedges in each direction
vnEy
Number of yedges in each direction
vnEz
Number of zedges in each direction
vnF
Total number of faces in each direction
vnFx
Number of xfaces in each direction
vnFy
Number of yfaces in each direction
vnFz
Number of zfaces in each direction
vnN
Total number of nodes in each direction
vol
Construct cell volumes of the 3D model as 1d array.
x0
x0 (
Array
): origin of the mesh (dim, ), a list or numpy array of <class ‘float’>, <class ‘int’> with shape (*)
Methods
Generic (shallow and deep) copying operations.
Attributes¶

TensorMesh.
area
¶ Construct face areas of the 3D model as 1d array.

TensorMesh.
areaFx
¶ Area of the xfaces

TensorMesh.
areaFy
¶ Area of the yfaces

TensorMesh.
areaFz
¶ Area of the zfaces

TensorMesh.
aveCC2F
¶ Construct the averaging operator on cell centers to faces.

TensorMesh.
aveCCV2F
¶ Construct the averaging operator on cell centers to faces as a vector.

TensorMesh.
aveE2CC
¶ Construct the averaging operator on cell edges to cell centers.

TensorMesh.
aveE2CCV
¶ Construct the averaging operator on cell edges to cell centers.

TensorMesh.
aveEx2CC
¶ Construct the averaging operator on cell edges in the x direction to cell centers.

TensorMesh.
aveEy2CC
¶ Construct the averaging operator on cell edges in the y direction to cell centers.

TensorMesh.
aveEz2CC
¶ Construct the averaging operator on cell edges in the z direction to cell centers.

TensorMesh.
aveF2CC
¶ Construct the averaging operator on cell faces to cell centers.

TensorMesh.
aveF2CCV
¶ Construct the averaging operator on cell faces to cell centers.

TensorMesh.
aveFx2CC
¶ Construct the averaging operator on cell faces in the x direction to cell centers.

TensorMesh.
aveFy2CC
¶ Construct the averaging operator on cell faces in the y direction to cell centers.

TensorMesh.
aveFz2CC
¶ Construct the averaging operator on cell faces in the z direction to cell centers.

TensorMesh.
aveN2CC
¶ Construct the averaging operator on cell nodes to cell centers.

TensorMesh.
aveN2E
¶ Construct the averaging operator on cell nodes to cell edges, keeping each dimension separate.

TensorMesh.
aveN2F
¶ Construct the averaging operator on cell nodes to cell faces, keeping each dimension separate.

TensorMesh.
axis_u
¶ axis_u (
Vector3
): Vector orientation of udirection. For more details see the docs for therotation_matrix
property., a 3D Vector of <class ‘float’> with shape (3), Default: X

TensorMesh.
axis_v
¶ axis_v (
Vector3
): Vector orientation of vdirection. For more details see the docs for therotation_matrix
property., a 3D Vector of <class ‘float’> with shape (3), Default: Y

TensorMesh.
axis_w
¶ axis_w (
Vector3
): Vector orientation of wdirection. For more details see the docs for therotation_matrix
property., a 3D Vector of <class ‘float’> with shape (3), Default: Z

TensorMesh.
cellBoundaryInd
¶ Find indices of boundary faces in each direction

TensorMesh.
cellGrad
¶ The cell centered Gradient, takes you to cell faces.

TensorMesh.
cellGradBC
¶ The cell centered Gradient boundary condition matrix

TensorMesh.
cellGradx
¶ Cell centered Gradient in the x dimension. Has neumann boundary conditions.

TensorMesh.
cellGrady
¶

TensorMesh.
cellGradz
¶ Cell centered Gradient in the x dimension. Has neumann boundary conditions.

TensorMesh.
dim
¶ The dimension of the mesh (1, 2, or 3).
 Returns
 int
dimension of the mesh

TensorMesh.
edge
¶ Construct edge legnths of the 3D model as 1d array.

TensorMesh.
edgeCurl
¶ Construct the 3D curl operator.

TensorMesh.
edgeEx
¶ xedge lengths

TensorMesh.
edgeEy
¶ yedge lengths

TensorMesh.
edgeEz
¶ zedge lengths

TensorMesh.
faceBoundaryInd
¶ Find indices of boundary faces in each direction

TensorMesh.
faceDiv
¶ Construct divergence operator (facestg to cellcentres).

TensorMesh.
faceDivx
¶ Construct divergence operator in the x component (facestg to cellcentres).

TensorMesh.
faceDivy
¶

TensorMesh.
faceDivz
¶ Construct divergence operator in the z component (facestg to cellcenters).

TensorMesh.
gridCC
¶ Cellcentered grid.

TensorMesh.
gridEx
¶ Edge staggered grid in the x direction.

TensorMesh.
gridEy
¶ Edge staggered grid in the y direction.

TensorMesh.
gridEz
¶ Edge staggered grid in the z direction.

TensorMesh.
gridFx
¶ Face staggered grid in the x direction.

TensorMesh.
gridFy
¶ Face staggered grid in the y direction.

TensorMesh.
gridFz
¶ Face staggered grid in the z direction.

TensorMesh.
gridN
¶ Nodal grid.

TensorMesh.
h
¶ h (a list of
Array
): h is a list containing the cell widths of the tensor mesh in each dimension., a list (each item is a list or numpy array of <class ‘float’> with shape (*)) with length between 0 and 3

TensorMesh.
h_gridded
¶ Returns an (nC, dim) numpy array with the widths of all cells in order

TensorMesh.
hx
¶ Width of cells in the x direction

TensorMesh.
hy
¶ Width of cells in the y direction

TensorMesh.
hz
¶ Width of cells in the z direction

TensorMesh.
nE
¶ Total number of edges.
 Returns
 nEint = sum([nEx, nEy, nEz])

TensorMesh.
nodalGrad
¶ Construct gradient operator (nodes to edges).

TensorMesh.
nodalLaplacian
¶ Construct laplacian operator (nodes to edges).

TensorMesh.
normals
¶ Face Normals
 Return type
 Returns
normals, (sum(nF), dim)

TensorMesh.
reference_is_rotated
¶ True if the axes are rotated from the traditional <X,Y,Z> system with vectors of \((1,0,0)\), \((0,1,0)\), and \((0,0,1)\)

TensorMesh.
reference_system
¶ reference_system (
String
): The type of coordinate reference frame. Can take on the values cartesian, cylindrical, or spherical. Abbreviations of these are allowed., a unicode string, Default: cartesian

TensorMesh.
rotation_matrix
¶ Builds a rotation matrix to transform coordinates from their coordinate system into a conventional cartesian system. This is built off of the three axis_u, axis_v, and axis_w properties; these mapping coordinates use the letters U, V, and W (the three letters preceding X, Y, and Z in the alphabet) to define the projection of the X, Y, and Z durections. These UVW vectors describe the placement and transformation of the mesh’s coordinate sytem assuming at most 3 directions.
Why would you want to use these UVW mapping vectors the this rotation_matrix property? They allow us to define the realationship between local and global coordinate systems and provide a tool for switching between the two while still maintaing the connectivity of the mesh’s cells. For a visual example of this, please see the figure in the docs for the
InterfaceVTK
.

TensorMesh.
tangents
¶ Edge Tangents
 Return type
 Returns
normals, (sum(nE), dim)

TensorMesh.
vectorCCx
¶ Cellcentered grid vector (1D) in the x direction.

TensorMesh.
vectorCCy
¶ Cellcentered grid vector (1D) in the y direction.

TensorMesh.
vectorCCz
¶ Cellcentered grid vector (1D) in the z direction.

TensorMesh.
vectorNx
¶ Nodal grid vector (1D) in the x direction.

TensorMesh.
vectorNy
¶ Nodal grid vector (1D) in the y direction.

TensorMesh.
vectorNz
¶ Nodal grid vector (1D) in the z direction.

TensorMesh.
vnC
¶ Total number of cells in each direction
 Return type
 Returns
[nCx, nCy, nCz]

TensorMesh.
vnE
¶ Total number of edges in each direction
 Returns
 vnEnumpy.ndarray = [nEx, nEy, nEz], (dim, )
import discretize import numpy as np M = discretize.TensorMesh([np.ones(n) for n in [2,3]]) M.plotGrid(edges=True, show_it=True)
(Source code, png, pdf)

TensorMesh.
vnEx
¶ Number of xedges in each direction
 Return type
 Returns
vnEx

TensorMesh.
vnEy
¶ Number of yedges in each direction
 Return type
 Returns
vnEy or None if dim < 2

TensorMesh.
vnEz
¶ Number of zedges in each direction
 Return type
 Returns
vnEz or None if dim < 3

TensorMesh.
vnF
¶ Total number of faces in each direction
 Return type
 Returns
[nFx, nFy, nFz], (dim, )
import discretize import numpy as np M = discretize.TensorMesh([np.ones(n) for n in [2,3]]) M.plotGrid(faces=True, show_it=True)
(Source code, png, pdf)

TensorMesh.
vnFx
¶ Number of xfaces in each direction
 Return type
 Returns
vnFx

TensorMesh.
vnFy
¶ Number of yfaces in each direction
 Return type
 Returns
vnFy or None if dim < 2

TensorMesh.
vnFz
¶ Number of zfaces in each direction
 Return type
 Returns
vnFz or None if dim < 3

TensorMesh.
vnN
¶ Total number of nodes in each direction
 Return type
 Returns
[nNx, nNy, nNz]

TensorMesh.
vol
¶ Construct cell volumes of the 3D model as 1d array.
Methods¶

TensorMesh.
copy
()¶ Make a copy of the current mesh

classmethod
TensorMesh.
deserialize
(value, trusted=False, strict=False, assert_valid=False, **kwargs)¶ Creates HasProperties instance from serialized dictionary
This uses the Property deserializers to deserialize all JSONcompatible dictionary values into their corresponding Property values on a new instance of a HasProperties class. Extra keys in the dictionary that do not correspond to Properties will be ignored.
Parameters:
value  Dictionary to deserialize new instance from.
trusted  If True (and if the input dictionary has
'__class__'
keyword and this class is in the registry), the new HasProperties class will come from the dictionary. If False (the default), only the HasProperties class this method is called on will be constructed.strict  Requires
'__class__'
, if present on the input dictionary, to match the deserialized instance’s class. Also disallows unused properties in the input dictionary. Default is False.assert_valid  Require deserialized instance to be valid. Default is False.
Any other keyword arguments will be passed through to the Property deserializers.

TensorMesh.
equal
(other)¶ Determine if two HasProperties instances are equivalent
Equivalence is determined by checking if all Property values on two instances are equal, using
Property.equal
.

static
TensorMesh.
from_omf
(element)¶ Convert an OMF element to it’s proper
discretize
type. Automatically determines the output type. Returns both the mesh and a dictionary of model arrays.

TensorMesh.
getBCProjWF
(BC, discretization='CC')¶ The weak form boundary condition projection matrices.
Examples
# Neumann in all directions BC = 'neumann' # 3D, Dirichlet in y Neumann else BC = ['neumann', 'dirichlet', 'neumann'] # 3D, Neumann in x on bottom of domain, Dirichlet else BC = [['neumann', 'dirichlet'], 'dirichlet', 'dirichlet']

TensorMesh.
getBCProjWF_simple
(discretization='CC')¶ The weak form boundary condition projection matrices when mixed boundary condition is used

TensorMesh.
getEdgeInnerProduct
(prop=None, invProp=False, invMat=False, doFast=True)¶ Generate the edge inner product matrix
 Parameters
 propnumpy.ndarray
material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
 invPropbool
inverts the material property
 invMatbool
inverts the matrix
 doFastbool
do a faster implementation if available.
 Returns
 scipy.sparse.csr_matrix
M, the inner product matrix (nE, nE)

TensorMesh.
getEdgeInnerProductDeriv
(prop, doFast=True, invProp=False, invMat=False)¶  Parameters
 propnumpy.ndarray
material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
 doFastbool
do a faster implementation if available.
 invPropbool
inverts the material property
 invMatbool
inverts the matrix
 Returns
 scipy.sparse.csr_matrix
dMdm, the derivative of the inner product matrix (nE, nC*nA)

TensorMesh.
getFaceInnerProduct
(prop=None, invProp=False, invMat=False, doFast=True)¶ Generate the face inner product matrix
 Parameters
 propnumpy.ndarray
material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
 invPropbool
inverts the material property
 invMatbool
inverts the matrix
 doFastbool
do a faster implementation if available.
 Returns
 scipy.sparse.csr_matrix
M, the inner product matrix (nF, nF)

TensorMesh.
getFaceInnerProductDeriv
(prop, doFast=True, invProp=False, invMat=False)¶  Parameters
 propnumpy.ndarray
material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
 doFast :
bool do a faster implementation if available.
 invPropbool
inverts the material property
 invMatbool
inverts the matrix
 Returns
 scipy.sparse.csr_matrix
dMdmu(u), the derivative of the inner product matrix for a certain u

TensorMesh.
getInterpolationMat
(loc, locType='CC', zerosOutside=False)¶ Produces interpolation matrix
 Parameters
 locnumpy.ndarray
Location of points to interpolate to
 locTypestr
What to interpolate (see below)
locType can be:
'Ex' > xcomponent of field defined on edges 'Ey' > ycomponent of field defined on edges 'Ez' > zcomponent of field defined on edges 'Fx' > xcomponent of field defined on faces 'Fy' > ycomponent of field defined on faces 'Fz' > zcomponent of field defined on faces 'N' > scalar field defined on nodes 'CC' > scalar field defined on cell centers 'CCVx' > xcomponent of vector field defined on cell centers 'CCVy' > ycomponent of vector field defined on cell centers 'CCVz' > zcomponent of vector field defined on cell centers
 Returns
 scipy.sparse.csr_matrix
M, the interpolation matrix

TensorMesh.
getTensor
(key)¶ Returns a tensor list.
 Parameters
 keystr
Which tensor (see below)
key can be:
'CC' > scalar field defined on cell centers 'N' > scalar field defined on nodes 'Fx' > xcomponent of field defined on faces 'Fy' > ycomponent of field defined on faces 'Fz' > zcomponent of field defined on faces 'Ex' > xcomponent of field defined on edges 'Ey' > ycomponent of field defined on edges 'Ez' > zcomponent of field defined on edges
 Returns
 list
list of the tensors that make up the mesh.

TensorMesh.
isInside
(pts, locType='N')¶ Determines if a set of points are inside a mesh.
 Parameters
pts (numpy.ndarray) – Location of points to test
 Return type
 Returns
inside, numpy array of booleans

TensorMesh.
plotGrid
(ax=None, nodes=False, faces=False, centers=False, edges=False, lines=True, show_it=False, **kwargs)¶ Plot the nodal, cellcentered and staggered grids for 1,2 and 3 dimensions.
 Parameters
import discretize import numpy as np h1 = np.linspace(.1, .5, 3) h2 = np.linspace(.1, .5, 5) mesh = discretize.TensorMesh([h1, h2]) mesh.plotGrid(nodes=True, faces=True, centers=True, lines=True, show_it=True)
(Source code, png, pdf)
import discretize import numpy as np h1 = np.linspace(.1, .5, 3) h2 = np.linspace(.1, .5, 5) h3 = np.linspace(.1, .5, 3) mesh = discretize.TensorMesh([h1, h2, h3]) mesh.plotGrid(nodes=True, faces=True, centers=True, lines=True, show_it=True)
(Source code, png, pdf)

TensorMesh.
plotImage
(v)¶ Plots scalar fields on the given mesh.
Input:
 Parameters
v (numpy.ndarray) – vector
Optional Inputs:
 Parameters
v_type (str) – type of vector (‘CC’, ‘N’, ‘F’, ‘Fx’, ‘Fy’, ‘Fz’, ‘E’, ‘Ex’, ‘Ey’, ‘Ez’)
ax (matplotlib.axes.Axes) – axis to plot to
show_it (bool) – call plt.show()
3D Inputs:
 Parameters
import discretize import numpy as np M = discretize.TensorMesh([20, 20]) v = np.sin(M.gridCC[:, 0]*2*np.pi)*np.sin(M.gridCC[:, 1]*2*np.pi) M.plotImage(v, show_it=True)
(Source code, png, pdf)
import discretize import numpy as np M = discretize.TensorMesh([20, 20, 20]) v = np.sin(M.gridCC[:, 0]*2*np.pi)*np.sin(M.gridCC[:, 1]*2*np.pi)*np.sin(M.gridCC[:, 2]*2*np.pi) M.plotImage(v, annotation_color='k', show_it=True)
(Source code, png, pdf)

TensorMesh.
plotSlice
(v, v_type='CC', normal='Z', ind=None, grid=False, view='real', ax=None, clim=None, show_it=False, pcolor_opts=None, stream_opts=None, grid_opts=None, range_x=None, range_y=None, sample_grid=None, stream_threshold=None, stream_thickness=None, **kwargs)¶ Plots a slice of a 3D mesh.
import discretize from pymatsolver import Solver import numpy as np hx = [(5, 2, 1.3), (2, 4), (5, 2, 1.3)] hy = [(2, 2, 1.3), (2, 6), (2, 2, 1.3)] hz = [(2, 2, 1.3), (2, 6), (2, 2, 1.3)] M = discretize.TensorMesh([hx, hy, hz]) q = np.zeros(M.vnC) q[[4, 4], [4, 4], [2, 6]]=[1, 1] q = discretize.utils.mkvc(q) A = M.faceDiv * M.cellGrad b = Solver(A) * (q) M.plotSlice(M.cellGrad*b, 'F', view='vec', grid=True, show_it=True, pcolor_opts={'alpha':0.8})
(Source code, png, pdf)

TensorMesh.
plot_3d_slicer
(v, xslice=None, yslice=None, zslice=None, v_type='CC', view='real', axis='xy', transparent=None, clim=None, xlim=None, ylim=None, zlim=None, aspect='auto', grid=[2, 2, 1], pcolor_opts=None, fig=None, **kwargs)¶ Plot slices of a 3D volume, interactively (scroll wheel).
If called from a notebook, make sure to set
%matplotlib notebook
See the class discretize.View.Slicer for more information.
It returns nothing. However, if you need the different figure handles you can get it via
fig = plt.gcf()
and subsequently its children via
fig.get_children()
and recursively deeper, e.g.,
fig.get_children()[0].get_children().
One can also provide an existing figure instance, which can be useful for interactive widgets in Notebooks. The provided figure is cleared first.

TensorMesh.
projectEdgeVector
(eV)¶ Given a vector, eV, in cartesian coordinates, this will project it onto the mesh using the tangents
 Parameters
eV (numpy.ndarray) – edge vector with shape (nE, dim)
 Return type
 Returns
projected edge vector, (nE, )

TensorMesh.
projectFaceVector
(fV)¶ Given a vector, fV, in cartesian coordinates, this will project it onto the mesh using the normals
 Parameters
fV (numpy.ndarray) – face vector with shape (nF, dim)
 Return type
 Returns
projected face vector, (nF, )

TensorMesh.
r
(x, xType='CC', outType='CC', format='V')¶ r is a quick reshape command that will do the best it can at giving you what you want.
For example, you have a face variable, and you want the x component of it reshaped to a 3D matrix.
r can fulfil your dreams:
mesh.r(V, 'F', 'Fx', 'M')        {    How: 'M' or ['V'] for a matrix    (ndgrid style) or a vector (n x dim)    }   {   What you want: ['CC'], 'N',   'F', 'Fx', 'Fy', 'Fz',   'E', 'Ex', 'Ey', or 'Ez'   }  {  What is it: ['CC'], 'N',  'F', 'Fx', 'Fy', 'Fz',  'E', 'Ex', 'Ey', or 'Ez'  } { The input: as a list or ndarray }
For example:
# Separates each component of the Ex grid into 3 matrices Xex, Yex, Zex = r(mesh.gridEx, 'Ex', 'Ex', 'M') # Given an edge vector, return just the x edges as a vector XedgeVector = r(edgeVector, 'E', 'Ex', 'V') # Separates each component of the edgeVector into 3 vectors eX, eY, eZ = r(edgeVector, 'E', 'E', 'V')

TensorMesh.
readModelUBC
(fileName, directory='')¶  Read UBC 2D or 3D Tensor mesh model
and generate Tensor mesh model
Input: :param str fileName: path to the UBC GIF mesh file to read or just its name if directory is specified :param str directory: directory where the UBC GIF file lives
Output: :rtype: numpy.ndarray :return: model with TensorMesh ordered

classmethod
TensorMesh.
readUBC
(fileName, directory='')¶ Wrapper to Read UBC GIF 2D and 3D tensor mesh and generate same dimension TensorMesh.
Input: :param str fileName: path to the UBC GIF mesh file or just its name if directory is specified :param str directory: directory where the UBC GIF file lives
Output: :rtype: TensorMesh :return: The tensor mesh for the fileName.

classmethod
TensorMesh.
readVTK
(filename, directory='')¶ Read VTK Rectilinear (vtr xml file) and return Tensor mesh and model
 Parameters
 filenamestr
path to the vtr model file to read or just its name if directory is specified
 directorystr
directory where the UBC GIF file lives
 Returns
 tuple
(TensorMesh, modelDictionary)

classmethod
TensorMesh.
read_vtk
(filename, directory='')¶ Read VTK Rectilinear (vtr xml file) and return Tensor mesh and model
 Parameters
 filenamestr
path to the vtr model file to read or just its name if directory is specified
 directorystr
directory where the UBC GIF file lives
 Returns
 tuple
(TensorMesh, modelDictionary)

TensorMesh.
save
(filename='mesh.json', verbose=False)¶ Save the mesh to json :param str file: filename for saving the casing properties :param str directory: working directory for saving the file

TensorMesh.
serialize
(include_class=True, save_dynamic=False, **kwargs)¶ Serializes a HasProperties instance to dictionary
This uses the Property serializers to serialize all Property values to a JSONcompatible dictionary. Properties that are undefined are not included. If the HasProperties instance contains a reference to itself, a
properties.SelfReferenceError
will be raised.Parameters:
include_class  If True (the default), the name of the class will also be saved to the serialized dictionary under key
'__class__'
save_dynamic  If True, dynamic properties are written to the serialized dict (default: False).
Any other keyword arguments will be passed through to the Property serializers.

TensorMesh.
setCellGradBC
(BC)¶ Function that sets the boundary conditions for cellcentred derivative operators.
Examples
..code:: python
# Neumann in all directions BC = ‘neumann’
# 3D, Dirichlet in y Neumann else BC = [‘neumann’, ‘dirichlet’, ‘neumann’]
# 3D, Neumann in x on bottom of domain, Dirichlet else BC = [[‘neumann’, ‘dirichlet’], ‘dirichlet’, ‘dirichlet’]

TensorMesh.
toVTK
(models=None)¶ Convert this mesh object to it’s proper VTK or
pyvista
data object with the given model dictionary as the cell data of that dataset. Parameters
 modelsdict(numpy.ndarray)
Name(‘s) and array(‘s). Match number of cells

TensorMesh.
to_omf
(models=None)¶ Convert this mesh object to it’s proper
omf
data object with the given model dictionary as the cell data of that dataset. Parameters
 modelsdict(numpy.ndarray)
Name(‘s) and array(‘s). Match number of cells

TensorMesh.
to_vtk
(models=None)¶ Convert this mesh object to it’s proper VTK or
pyvista
data object with the given model dictionary as the cell data of that dataset. Parameters
 modelsdict(numpy.ndarray)
Name(‘s) and array(‘s). Match number of cells

TensorMesh.
validate
()¶ Call all registered class validator methods
These are all methods decorated with
@properties.validator
. Validator methods are expected to raise a ValidationError if they fail.

classmethod
TensorMesh.
vtk_to_tensor_mesh
(vtrGrid)¶ Converts a
vtkRectilinearGrid
orpyvista.RectilinearGrid
to adiscretize.TensorMesh
object.

TensorMesh.
writeModelUBC
(fileName, model, directory='')¶ Writes a model associated with a TensorMesh to a UBCGIF format model file.
Input: :param str fileName: File to write to or just its name if directory is specified :param str directory: directory where the UBC GIF file lives :param numpy.ndarray model: The model

TensorMesh.
writeUBC
(fileName, models=None, directory='', comment_lines='')¶ Writes a TensorMesh to a UBCGIF format mesh file.
Input: :param str fileName: File to write to :param str directory: directory where to save model :param dict models: A dictionary of the models :param str comment_lines: comment lines preceded with ‘!’ to add

TensorMesh.
writeVTK
(filename, models=None, directory='')¶ Makes and saves a VTK object from this mesh and given models
 Parameters
 filenamestr
path to the output vtk file or just its name if directory is specified
 modelsdict
dictionary of numpy.array  Name(‘s) and array(‘s). Match number of cells
 directorystr
directory where the UBC GIF file lives

TensorMesh.
write_vtk
(filename, models=None, directory='')¶ Makes and saves a VTK object from this mesh and given models
 Parameters
 filenamestr
path to the output vtk file or just its name if directory is specified
 modelsdict
dictionary of numpy.array  Name(‘s) and array(‘s). Match number of cells
 directorystr
directory where the UBC GIF file lives