discretize.TensorMesh

class discretize.TensorMesh(h, origin=None, **kwargs)

Bases: discretize.base.BaseTensorMesh, discretize.base.BaseRectangularMesh, discretize.operators.DiffOperators, discretize.operators.InnerProducts, discretize.mixins.mesh_io.TensorMeshIO, discretize.mixins.InterfaceMixins

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.plot_grid()

(Source code, png, pdf)

../../_images/discretize-TensorMesh-1.png

Example of a padded tensor mesh using discretize.utils.unpack_widths():

import discretize
mesh = discretize.TensorMesh([
    [(10, 10, -1.3), (10, 40), (10, 10, 1.3)],
    [(10, 10, -1.3), (10, 20)]
])
mesh.plot_grid()

(Source code, png, pdf)

../../_images/discretize-TensorMesh-2.png

For a quick tensor mesh on a (10x12x15) unit cube

import discretize
mesh = discretize.TensorMesh([10, 12, 15])
Attributes
area

area has been deprecated. See face_areas for documentation

areaFx

areaFx has been deprecated. See face_x_areas for documentation

areaFy

areaFy has been deprecated. See face_y_areas for documentation

areaFz

areaFz has been deprecated. See face_z_areas for documentation

average_cell_to_edge
average_cell_to_face

Construct the averaging operator on cell centers to faces.

average_cell_vector_to_face

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

average_edge_to_cell

Construct the averaging operator on cell edges to cell centers.

average_edge_to_cell_vector

Construct the averaging operator on cell edges to cell centers.

average_edge_to_face_vector
average_edge_x_to_cell

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

average_edge_y_to_cell

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

average_edge_z_to_cell

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

average_face_to_cell

Construct the averaging operator on cell faces to cell centers.

average_face_to_cell_vector

Construct the averaging operator on cell faces to cell centers.

average_face_x_to_cell

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

average_face_y_to_cell

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

average_face_z_to_cell

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

average_node_to_cell

Construct the averaging operator on cell nodes to cell centers.

average_node_to_edge

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

average_node_to_face

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

axis_u

Deprecated since version 0.7.0.

axis_v

Deprecated since version 0.7.0.

axis_w

Deprecated since version 0.7.0.

boundary_edge_vector_integral

Represents the operation of integrating a vector function on the boundary

boundary_edges

Boundary edge locations

boundary_face_outward_normals

Outward directed normal vectors for the boundary faces

boundary_face_scalar_integral

Represents the operation of integrating a scalar function on the boundary

boundary_faces

Boundary face locations

boundary_node_vector_integral

Represents the operation of integrating a vector function dotted with the boundary normal

boundary_nodes

Boundary node locations

cellBoundaryInd

cellBoundaryInd has been deprecated. See cell_boundary_indices for documentation

cellGrad

cellGrad has been deprecated. See cell_gradient for documentation

cellGradBC

cellGradBC has been deprecated. See cell_gradient_BC for documentation

cellGradx

cellGradx has been deprecated. See cell_gradient_x for documentation

cellGrady

cellGrady has been deprecated. See cell_gradient_y for documentation

cellGradz

cellGradz has been deprecated. See cell_gradient_z for documentation

cell_boundary_indices

Find indices of boundary faces in each direction

cell_centers

Cell-centered grid.

cell_centers_x

Cell-centered grid vector (1D) in the x direction.

cell_centers_y

Cell-centered grid vector (1D) in the y direction.

cell_centers_z

Cell-centered grid vector (1D) in the z direction.

cell_gradient

The cell centered Gradient, takes you to cell faces.

cell_gradient_BC

The cell centered Gradient boundary condition matrix

cell_gradient_x

Cell centered Gradient in the x dimension.

cell_gradient_y
cell_gradient_z

Cell centered Gradient in the x dimension.

cell_volumes

Construct cell volumes of the 3D model as 1d array.

dim

The dimension of the mesh (1, 2, or 3).

edge

edge has been deprecated. See edge_lengths for documentation

edgeCurl

edgeCurl has been deprecated. See edge_curl for documentation

edgeEx

edgeEx has been deprecated. See edge_x_lengths for documentation

edgeEy

edgeEy has been deprecated. See edge_y_lengths for documentation

edgeEz

edgeEz has been deprecated. See edge_z_lengths for documentation

edge_curl

Construct the 3D curl operator.

edge_lengths

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

edge_tangents

Edge Tangents

edge_x_lengths

x-edge lengths

edge_y_lengths

y-edge lengths

edge_z_lengths

z-edge lengths

edges

Edge grid

edges_x

Edge staggered grid in the x direction.

edges_y

Edge staggered grid in the y direction.

edges_z

Edge staggered grid in the z direction.

faceBoundaryInd

faceBoundaryInd has been deprecated. See face_boundary_indices for documentation

faceDiv

faceDiv has been deprecated. See face_divergence for documentation

faceDivx

faceDivx has been deprecated. See face_x_divergence for documentation

faceDivy

faceDivy has been deprecated. See face_y_divergence for documentation

faceDivz

faceDivz has been deprecated. See face_z_divergence for documentation

face_areas

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

face_boundary_indices

Find indices of boundary faces in each direction

face_divergence

Construct divergence operator (face-stg to cell-centres).

face_normals

Face Normals

face_x_areas

Area of the x-faces

face_x_divergence

Construct divergence operator in the x component (face-stg to cell-centres).

face_y_areas

Area of the y-faces

face_y_divergence
face_z_areas

Area of the z-faces

face_z_divergence

Construct divergence operator in the z component (face-stg to cell-centers).

faces

Face grid

faces_x

Face staggered grid in the x direction.

faces_y

Face staggered grid in the y direction.

faces_z

Face staggered grid in the z direction.

h
h_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

nCx

Number of cells in the x direction

nCy

Number of cells in the y direction

nCz

Number of cells in the z direction

nNx

Number of nodes in the x-direction

nNy

Number of nodes in the y-direction

nNz

Number of nodes in the z-direction

n_cells

Total number of cells in the mesh.

n_edges

Total number of edges.

n_edges_per_direction

The number of edges in each direction

n_edges_x

Number of x-edges

n_edges_y

Number of y-edges

n_edges_z

Number of z-edges

n_faces

Total number of faces.

n_faces_per_direction

The number of faces in each direction

n_faces_x

Number of x-faces

n_faces_y

Number of y-faces

n_faces_z

Number of z-faces

n_nodes

Total number of nodes

nodalGrad

nodalGrad has been deprecated. See nodal_gradient for documentation

nodalLaplacian

nodalLaplacian has been deprecated. See nodal_laplacian for documentation

nodal_gradient

Construct gradient operator (nodes to edges).

nodal_laplacian

Construct laplacian operator (nodes to edges).

nodes

Nodal grid.

nodes_x

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

nodes_y

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

nodes_z

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

normals

normals has been deprecated. See face_normals for documentation

orientation
origin

Origin of the mesh

project_edge_to_boundary_edge

Projects values defined on all edges to the boundary edges

project_face_to_boundary_face

Projects values defined on all faces to the boundary faces

project_node_to_boundary_node

Projects values defined on all edges to the boundary edges

reference_is_rotated

True if the axes are rotated from the traditional <X,Y,Z> system

reference_system

The type of coordinate reference frame.

rotation_matrix

Builds a rotation matrix to transform coordinates from their coordinate system into a conventional cartesian system.

shape_cells

The number of cells in each direction

shape_edges_x

Number of x-edges in each direction

shape_edges_y

Number of y-edges in each direction

shape_edges_z

Number of z-edges in each direction

shape_faces_x

Number of x-faces in each direction

shape_faces_y

Number of y-faces in each direction

shape_faces_z

Number of z-faces in each direction

shape_nodes

Number of nodes in each direction

stencil_cell_gradient
stencil_cell_gradient_x
stencil_cell_gradient_y
stencil_cell_gradient_z
tangents

tangents has been deprecated. See edge_tangents for documentation

vectorCCx

vectorCCx has been deprecated. See cell_centers_x for documentation

vectorCCy

vectorCCy has been deprecated. See cell_centers_y for documentation

vectorCCz

vectorCCz has been deprecated. See cell_centers_z for documentation

vectorNx

vectorNx has been deprecated. See nodes_x for documentation

vectorNy

vectorNy has been deprecated. See nodes_y for documentation

vectorNz

vectorNz has been deprecated. See nodes_z for documentation

vol

vol has been deprecated. See cell_volumes for documentation

x0

Methods

cell_gradient_weak_form_robin([alpha, beta, …])

Robin boundary condition for the weak formulation of the cell gradient

copy()

Make a copy of the current mesh

edge_divergence_weak_form_robin([alpha, …])

Robin boundary condition for the weak formulation of the edge divergence

from_omf(element)

Convert an OMF element to it’s proper discretize type.

getBCProjWF(*args, **kwargs)

getBCProjWF has been deprecated.

getBCProjWF_simple(*args, **kwargs)

getBCProjWF_simple has been deprecated.

getEdgeInnerProduct(*args, **kwargs)

getEdgeInnerProduct has been deprecated.

getEdgeInnerProductDeriv(*args, **kwargs)

getEdgeInnerProductDeriv has been deprecated.

getFaceInnerProduct(*args, **kwargs)

getFaceInnerProduct has been deprecated.

getFaceInnerProductDeriv(*args, **kwargs)

getFaceInnerProductDeriv has been deprecated.

getInterpolationMat(*args, **kwargs)

getInterpolationMat has been deprecated.

getTensor(*args, **kwargs)

getTensor has been deprecated.

get_BC_projections(BC[, discretization])

The weak form boundary condition projection matrices.

get_BC_projections_simple([discretization])

The weak form boundary condition projection matrices when mixed boundary condition is used

get_edge_inner_product([model, …])

Generate the edge inner product matrix

get_edge_inner_product_deriv(model[, …])

Parameters

get_face_inner_product([model, …])

Generate the face inner product matrix

get_face_inner_product_deriv(model[, …])

Parameters

get_interpolation_matrix(loc[, …])

Produces linear interpolation matrix

get_tensor(key)

Returns a tensor list.

isInside(*args, **kwargs)

isInside has been deprecated.

is_inside(pts[, location_type])

Determines if a set of points are inside a mesh.

plotGrid(*args, **kwargs)

plotGrid has been deprecated.

plotImage(*args, **kwargs)

plotImage has been deprecated.

plotSlice(*args, **kwargs)

plotSlice has been deprecated.

plot_3d_slicer(v[, xslice, yslice, zslice, …])

Plot slices of a 3D volume, interactively (scroll wheel).

plot_grid([ax, nodes, faces, centers, …])

Plot the nodal, cell-centered and staggered grids.

plot_image(v[, v_type, grid, view, ax, …])

Plots fields on the given mesh.

plot_slice(v[, v_type, normal, ind, …])

Plots slice of fields on the given 3D mesh.

projectEdgeVector(*args, **kwargs)

projectEdgeVector has been deprecated.

projectFaceVector(*args, **kwargs)

projectFaceVector has been deprecated.

project_edge_vector(edge_vector)

Project vectors onto the edges of the mesh

project_face_vector(face_vector)

Project vectors onto the faces of the mesh.

r(*args, **kwargs)

r has been deprecated.

readModelUBC(*args, **kwargs)

readModelUBC has been deprecated.

readUBC(file_name[, directory])

readVTK(file_name[, directory])

Read VTK Rectilinear (vtr xml file) and return Tensor mesh and model

read_UBC(file_name[, directory])

Wrapper to Read UBC GIF 2D and 3D tensor mesh and generate same dimension TensorMesh.

read_model_UBC(file_name[, directory])

Read UBC 2D or 3D Tensor mesh model

read_vtk(file_name[, directory])

Read VTK Rectilinear (vtr xml file) and return Tensor mesh and model

reshape(x[, x_type, out_type, format])

A quick reshape command that will do the best it can at giving you what you want.

save([file_name, verbose])

Save the mesh to json :param str file: file_name for saving the casing properties :param str directory: working directory for saving the file

setCellGradBC(*args, **kwargs)

setCellGradBC has been deprecated.

set_cell_gradient_BC(BC)

Function that sets the boundary conditions for cell-centred derivative operators.

toVTK([models])

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.

to_omf([models])

Convert this mesh object to it’s proper omf data object with the given model dictionary as the cell data of that dataset.

to_vtk([models])

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.

validate()

Every object will be valid upon initialization

vtk_to_tensor_mesh(vtrGrid)

Converts a vtkRectilinearGrid or pyvista.RectilinearGrid to a discretize.TensorMesh object.

writeModelUBC(*args, **kwargs)

writeModelUBC has been deprecated.

writeUBC(*args, **kwargs)

writeUBC has been deprecated.

writeVTK(file_name[, models, directory])

Makes and saves a VTK object from this mesh and given models

write_UBC(file_name[, models, directory, …])

Writes a TensorMesh to a UBC-GIF format mesh file.

write_model_UBC(file_name, model[, directory])

Writes a model associated with a TensorMesh to a UBC-GIF format model file.

write_vtk(file_name[, models, directory])

Makes and saves a VTK object from this mesh and given models

deserialize

equals

serialize

to_dict

Attributes

TensorMesh.area

area has been deprecated. See face_areas for documentation

TensorMesh.areaFx

areaFx has been deprecated. See face_x_areas for documentation

TensorMesh.areaFy

areaFy has been deprecated. See face_y_areas for documentation

TensorMesh.areaFz

areaFz has been deprecated. See face_z_areas for documentation

TensorMesh.average_cell_to_edge
TensorMesh.average_cell_to_face

Construct the averaging operator on cell centers to faces.

TensorMesh.average_cell_vector_to_face

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

TensorMesh.average_edge_to_cell

Construct the averaging operator on cell edges to cell centers.

TensorMesh.average_edge_to_cell_vector

Construct the averaging operator on cell edges to cell centers.

TensorMesh.average_edge_to_face_vector
TensorMesh.average_edge_x_to_cell

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

TensorMesh.average_edge_y_to_cell

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

TensorMesh.average_edge_z_to_cell

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

TensorMesh.average_face_to_cell

Construct the averaging operator on cell faces to cell centers.

TensorMesh.average_face_to_cell_vector

Construct the averaging operator on cell faces to cell centers.

TensorMesh.average_face_x_to_cell

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

TensorMesh.average_face_y_to_cell

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

TensorMesh.average_face_z_to_cell

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

TensorMesh.average_node_to_cell

Construct the averaging operator on cell nodes to cell centers.

TensorMesh.average_node_to_edge

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

TensorMesh.average_node_to_face

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

TensorMesh.axis_u

Deprecated since version 0.7.0: axis_u will be removed in discretize 1.0.0, it is replaced by mesh.orientation for better mesh orientation validation.

See also

orientation
TensorMesh.axis_v

Deprecated since version 0.7.0: axis_v will be removed in discretize 1.0.0, it is replaced by mesh.orientation for better mesh orientation validation.

See also

orientation
TensorMesh.axis_w

Deprecated since version 0.7.0: axis_w will be removed in discretize 1.0.0, it is replaced by mesh.orientation for better mesh orientation validation.

See also

orientation
TensorMesh.boundary_edge_vector_integral

Represents the operation of integrating a vector function on the boundary

This matrix represents the boundary surface integral of a vector function multiplied with a finite volume test function on the mesh.

In 1D and 2D, the operation assumes that the right array contains only a single component of the vector u. In 3D, however, we must assume that u will contain each of the three vector components, and it must be ordered as, [edges_1_x, ... ,edge_N_x, edge_1_y, ..., edge_N_y, edge_1_z, ..., edge_N_z] , where N is the number of boundary edges.

Returns
scipy.sparse.csr_matrix

Sparse matrix of shape (n_edges, n_boundary_edges) for 1D or 2D mesh, (n_edges, 3*n_boundary_edges) for a 3D mesh.

Notes

The integral we are representing on the boundary of the mesh is

\[\int_{\Omega} \vec{w} \cdot (\vec{u} \times \hat{n}) \partial \Omega\]

In discrete form this is:

\[w^T * P * u_b\]

where w is defined on all edges, and u_b is all three components defined on boundary edges.

TensorMesh.boundary_edges

Boundary edge locations

Returns
np.ndarray of float

location array of shape (mesh.n_boundary_edges, dim)

TensorMesh.boundary_face_outward_normals

Outward directed normal vectors for the boundary faces

Returns
np.ndarray of float

Array of vectors of shape (mesh.n_boundary_faces, dim)

TensorMesh.boundary_face_scalar_integral

Represents the operation of integrating a scalar function on the boundary

This matrix represents the boundary surface integral of a scalar function multiplied with a finite volume test function on the mesh.

Returns
scipy.sparse.csr_matrix

Sparse matrix of shape (n_faces, n_boundary_faces)

Notes

The integral we are representing on the boundary of the mesh is

\[\int_{\Omega} u\vec{w} \cdot \hat{n} \partial \Omega\]

In discrete form this is:

\[w^T * P * u_b\]

where w is defined on all faces, and u_b is defined on boundary faces.

TensorMesh.boundary_faces

Boundary face locations

Returns
np.ndarray of float

location array of shape (mesh.n_boundary_faces, dim)

TensorMesh.boundary_node_vector_integral

Represents the operation of integrating a vector function dotted with the boundary normal

This matrix represents the boundary surface integral of a vector function dotted with the boundary normal and multiplied with a scalar finite volume test function on the mesh.

Returns
scipy.sparse.csr_matrix

Sparse matrix of shape (n_nodes, ndim * n_boundary_nodes).

Notes

The integral we are representing on the boundary of the mesh is

\[\int_{\Omega} (w \vec{u}) \cdot \hat{n} \partial \Omega\]

In discrete form this is:

\[w^T * P * u_b\]

where w is defined on all nodes, and u_b is all three components defined on boundary nodes.

TensorMesh.boundary_nodes

Boundary node locations

Returns
np.ndarray of float

location array of shape (mesh.n_boundary_nodes, dim)

TensorMesh.cellBoundaryInd

cellBoundaryInd has been deprecated. See cell_boundary_indices for documentation

TensorMesh.cellGrad

cellGrad has been deprecated. See cell_gradient for documentation

TensorMesh.cellGradBC

cellGradBC has been deprecated. See cell_gradient_BC for documentation

TensorMesh.cellGradx

cellGradx has been deprecated. See cell_gradient_x for documentation

TensorMesh.cellGrady

cellGrady has been deprecated. See cell_gradient_y for documentation

TensorMesh.cellGradz

cellGradz has been deprecated. See cell_gradient_z for documentation

TensorMesh.cell_boundary_indices

Find indices of boundary faces in each direction

TensorMesh.cell_centers

Cell-centered grid.

TensorMesh.cell_centers_x

Cell-centered grid vector (1D) in the x direction.

TensorMesh.cell_centers_y

Cell-centered grid vector (1D) in the y direction.

TensorMesh.cell_centers_z

Cell-centered grid vector (1D) in the z direction.

TensorMesh.cell_gradient

The cell centered Gradient, takes you to cell faces.

TensorMesh.cell_gradient_BC

The cell centered Gradient boundary condition matrix

TensorMesh.cell_gradient_x

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

TensorMesh.cell_gradient_y
TensorMesh.cell_gradient_z

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

TensorMesh.cell_volumes

Construct cell volumes of the 3D model as 1d array.

TensorMesh.dim

The dimension of the mesh (1, 2, or 3).

Returns
int

dimension of the mesh

TensorMesh.edge

edge has been deprecated. See edge_lengths for documentation

TensorMesh.edgeCurl

edgeCurl has been deprecated. See edge_curl for documentation

TensorMesh.edgeEx

edgeEx has been deprecated. See edge_x_lengths for documentation

TensorMesh.edgeEy

edgeEy has been deprecated. See edge_y_lengths for documentation

TensorMesh.edgeEz

edgeEz has been deprecated. See edge_z_lengths for documentation

TensorMesh.edge_curl

Construct the 3D curl operator.

TensorMesh.edge_lengths

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

TensorMesh.edge_tangents

Edge Tangents

Returns
numpy.ndarray

normals, (n_edges, dim)

TensorMesh.edge_x_lengths

x-edge lengths

TensorMesh.edge_y_lengths

y-edge lengths

TensorMesh.edge_z_lengths

z-edge lengths

TensorMesh.edges

Edge grid

TensorMesh.edges_x

Edge staggered grid in the x direction.

TensorMesh.edges_y

Edge staggered grid in the y direction.

TensorMesh.edges_z

Edge staggered grid in the z direction.

TensorMesh.faceBoundaryInd

faceBoundaryInd has been deprecated. See face_boundary_indices for documentation

TensorMesh.faceDiv

faceDiv has been deprecated. See face_divergence for documentation

TensorMesh.faceDivx

faceDivx has been deprecated. See face_x_divergence for documentation

TensorMesh.faceDivy

faceDivy has been deprecated. See face_y_divergence for documentation

TensorMesh.faceDivz

faceDivz has been deprecated. See face_z_divergence for documentation

TensorMesh.face_areas

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

TensorMesh.face_boundary_indices

Find indices of boundary faces in each direction

TensorMesh.face_divergence

Construct divergence operator (face-stg to cell-centres).

TensorMesh.face_normals

Face Normals

Returns
numpy.ndarray

normals, (n_faces, dim)

TensorMesh.face_x_areas

Area of the x-faces

TensorMesh.face_x_divergence

Construct divergence operator in the x component (face-stg to cell-centres).

TensorMesh.face_y_areas

Area of the y-faces

TensorMesh.face_y_divergence
TensorMesh.face_z_areas

Area of the z-faces

TensorMesh.face_z_divergence

Construct divergence operator in the z component (face-stg to cell-centers).

TensorMesh.faces

Face grid

TensorMesh.faces_x

Face staggered grid in the x direction.

TensorMesh.faces_y

Face staggered grid in the y direction.

TensorMesh.faces_z

Face staggered grid in the z direction.

TensorMesh.h
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

Returns
numpy.ndarray

Deprecated since version 0.5.0: hx will be removed in discretize 1.0.0 to reduce namespace clutter, please use mesh.h[0].

TensorMesh.hy

Width of cells in the y direction

Returns
numpy.ndarray or None

Deprecated since version 0.5.0: hy will be removed in discretize 1.0.0 to reduce namespace clutter, please use mesh.h[1].

TensorMesh.hz

Width of cells in the z direction

Returns
numpy.ndarray or None

Deprecated since version 0.5.0: hz will be removed in discretize 1.0.0 to reduce namespace clutter, please use mesh.h[2].

TensorMesh.nCx

Number of cells in the x direction

Returns
int

Deprecated since version 0.5.0: nCx will be removed in discretize 1.0.0, it is replaced by mesh.shape_cells[0] to reduce namespace clutter.

TensorMesh.nCy

Number of cells in the y direction

Returns
int or None

None if dim < 2

Deprecated since version 0.5.0: nCy will be removed in discretize 1.0.0, it is replaced by mesh.shape_cells[1] to reduce namespace clutter.

TensorMesh.nCz

Number of cells in the z direction

Returns
int or None

None if dim < 3

Deprecated since version 0.5.0: nCz will be removed in discretize 1.0.0, it is replaced by mesh.shape_cells[2] to reduce namespace clutter.

TensorMesh.nNx

Number of nodes in the x-direction

Returns
int

Deprecated since version 0.5.0: nNx will be removed in discretize 1.0.0, it is replaced by mesh.shape_nodes[0] to reduce namespace clutter.

TensorMesh.nNy

Number of nodes in the y-direction

Returns
int or None

None if dim < 2

Deprecated since version 0.5.0: nNy will be removed in discretize 1.0.0, it is replaced by mesh.shape_nodes[1] to reduce namespace clutter.

TensorMesh.nNz

Number of nodes in the z-direction

Returns
int or None

None if dim < 3

Deprecated since version 0.5.0: nNz will be removed in discretize 1.0.0, it is replaced by mesh.shape_nodes[2] to reduce namespace clutter.

TensorMesh.n_cells
TensorMesh.n_edges

Total number of edges.

Returns
int

sum([n_edges_x, n_edges_y, n_edges_z])

Notes

Also accessible as nE.

TensorMesh.n_edges_per_direction

The number of edges in each direction

Returns
n_edges_per_directiontuple

[n_edges_x, n_edges_y, n_edges_z], (dim, )

Notes

Also accessible as vnE.

Examples

>>> import discretize
>>> import matplotlib.pyplot as plt
>>> import numpy as np
>>> M = discretize.TensorMesh([np.ones(n) for n in [2,3]])
>>> M.plot_grid(edges=True, show_it=True)

(Source code, png, pdf)

../../_images/discretize-TensorMesh-3.png
TensorMesh.n_edges_x
TensorMesh.n_edges_y
TensorMesh.n_edges_z
TensorMesh.n_faces

Total number of faces.

Returns
int

sum([n_faces_x, n_faces_y, n_faces_z])

Notes

Also accessible as nF.

TensorMesh.n_faces_per_direction

The number of faces in each direction

Returns
n_faces_per_directiontuple

[n_faces_x, n_faces_y, n_faces_z], (dim, )

Notes

Also accessible as vnF.

Examples

>>> import discretize
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> M = discretize.TensorMesh([np.ones(n) for n in [2,3]])
>>> M.plot_grid(faces=True, show_it=True)

(Source code, png, pdf)

../../_images/discretize-TensorMesh-4.png
TensorMesh.n_faces_x
TensorMesh.n_faces_y
TensorMesh.n_faces_z
TensorMesh.n_nodes
TensorMesh.nodalGrad

nodalGrad has been deprecated. See nodal_gradient for documentation

TensorMesh.nodalLaplacian

nodalLaplacian has been deprecated. See nodal_laplacian for documentation

TensorMesh.nodal_gradient

Construct gradient operator (nodes to edges).

TensorMesh.nodal_laplacian

Construct laplacian operator (nodes to edges).

TensorMesh.nodes

Nodal grid.

TensorMesh.nodes_x

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

TensorMesh.nodes_y

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

TensorMesh.nodes_z

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

TensorMesh.normals

normals has been deprecated. See face_normals for documentation

TensorMesh.orientation
TensorMesh.origin

Origin of the mesh

TensorMesh.project_edge_to_boundary_edge

Projects values defined on all edges to the boundary edges

Returns
scipy.sparse.csr_matrix

Projection matrix with shape (n_boundary_edges, n_edges)

TensorMesh.project_face_to_boundary_face

Projects values defined on all faces to the boundary faces

Returns
scipy.sparse.csr_matrix

Projection matrix with shape (n_boundary_faces, n_faces)

TensorMesh.project_node_to_boundary_node

Projects values defined on all edges to the boundary edges

Returns
scipy.sparse.csr_matrix

Projection matrix with shape (n_boundary_nodes, n_nodes)

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

The type of coordinate reference frame. Can take on the values

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 relationship 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.shape_cells

The number of cells in each direction

Returns
tuple of ints

Notes

Also accessible as vnC.

TensorMesh.shape_edges_x

Number of x-edges in each direction

Returns
tuple of int

(nx_cells, ny_nodes, nz_nodes)

Notes

Also accessible as vnEx.

TensorMesh.shape_edges_y

Number of y-edges in each direction

Returns
tuple of int or None

(nx_nodes, ny_cells, nz_nodes), None if dim < 2

Notes

Also accessible as vnEy.

TensorMesh.shape_edges_z

Number of z-edges in each direction

Returns
tuple of int or None

(nx_nodes, ny_nodes, nz_cells), None if dim < 3

Notes

Also accessible as vnEz.

TensorMesh.shape_faces_x

Number of x-faces in each direction

Returns
tuple of int

(nx_nodes, ny_cells, nz_cells)

Notes

Also accessible as vnFx.

TensorMesh.shape_faces_y

Number of y-faces in each direction

Returns
tuple of int or None

(nx_cells, ny_nodes, nz_cells), None if dim < 2

Notes

Also accessible as vnFy.

TensorMesh.shape_faces_z

Number of z-faces in each direction

Returns
tuple of int or None

(nx_cells, ny_cells, nz_nodes), None if dim < 3

Notes

Also accessible as vnFz.

TensorMesh.shape_nodes

Number of nodes in each direction

Returns
tuple of int

Notes

Also accessible as vnN.

TensorMesh.stencil_cell_gradient
TensorMesh.stencil_cell_gradient_x
TensorMesh.stencil_cell_gradient_y
TensorMesh.stencil_cell_gradient_z
TensorMesh.tangents

tangents has been deprecated. See edge_tangents for documentation

TensorMesh.vectorCCx

vectorCCx has been deprecated. See cell_centers_x for documentation

TensorMesh.vectorCCy

vectorCCy has been deprecated. See cell_centers_y for documentation

TensorMesh.vectorCCz

vectorCCz has been deprecated. See cell_centers_z for documentation

TensorMesh.vectorNx

vectorNx has been deprecated. See nodes_x for documentation

TensorMesh.vectorNy

vectorNy has been deprecated. See nodes_y for documentation

TensorMesh.vectorNz

vectorNz has been deprecated. See nodes_z for documentation

TensorMesh.vol

vol has been deprecated. See cell_volumes for documentation

TensorMesh.x0

Methods

TensorMesh.cell_gradient_weak_form_robin(alpha=1.0, beta=0.0, gamma=0.0)

Robin boundary condition for the weak formulation of the cell gradient

This function returns the necessary parts for the weak form of the cell gradient operator to represent the Robin boundary conditions.

The implementation assumes a ghost cell that mirrors the boundary cells across the boundary faces, with a piecewise linear approximation to the values at the ghost cell centers.

The parameters can either be defined as a constant applied to the entire boundary, or as arrays that represent those values on the discretize.base.BaseTensorMesh.boundary_faces().

The returned arrays represent the proper boundary conditions on a solution u such that the inner product of the gradient of u with a test function y would be <y, gradient*u> = y.dot((-face_divergence.T*cell_volumes + A)*u + y.dot(b).

The default values will produce a zero-dirichlet boundary condition.

Parameters
alpha, betascalar or array_like

Parameters for the Robin boundary condition. array_like must be defined on each boundary face.

gamma: scalar or array_like

right hand side boundary conditions. If this parameter is array like, it can be fed either a (n_boundary_faces,) shape array or an (n_boundary_faces, n_rhs) shape array if multiple systems have the same alpha and beta parameters.

Returns
Ascipy.sparse.csr_matrix

Matrix to add to (-face_divergence.T * cell_volumes)

bnumpy.ndarray

Array to add to the result of the (-face_divergence.T * cell_volumes + A) @ u.

Notes

The weak form is obtained by multiplying the gradient by a (piecewise-constant) test function, and integrating over the cell, i.e.

(1)\[\int_V \vec{y} \cdot \nabla u \partial V\]

This equation can be transformed to reduce the differentiability requirement on u to be,

(2)\[-\int_V u (\nabla \cdot \vec{y}) \partial V + \int_{dV} u \vec{y} \partial V.\]

The first term in equation :eq:transformed is constructed using the matrix operators defined on this mesh as D = discretize.operators.DiffOperators.face_divergence() and V, a diagonal matrix of discretize.base.BaseMesh.cell_volumes(), as

\[-(D*y)^T*V*u.\]

This function returns the necessary matrices to complete the transformation of equation :eq:transformed. The second part of equation :eq:transformed becomes,

(3)\[\int_V \nabla \cdot (\phi u) \partial V = \int_{\partial\Omega} \phi\vec{u}\cdot\hat{n} \partial a\]

which is then approximated with the matrices returned here such that the full form of the weak formulation in a discrete form would be.

\[y^T(-D^T V + B)u + y^Tb\]

Examples

We first create a very simple 2D tensor mesh on the [0, 1] boundary:

>>> import matplotlib.pyplot as plt
>>> import scipy.sparse as sp
>>> import discretize
>>> mesh = discretize.TensorMesh([32, 32])

Define the alpha, beta, and gamma parameters for a zero - Dirichlet condition on the boundary, this corresponds to setting:

>>> alpha = 1.0
>>> beta = 0.0
>>> gamma = 0.0
>>> A, b = mesh.cell_gradient_weak_form_robin(alpha, beta, gamma)

We can then represent the operation of taking the weak form of the gradient of a function defined on cell centers with appropriate robin boundary conditions as:

>>> V = sp.diags(mesh.cell_volumes)
>>> D = mesh.face_divergence
>>> phi = np.sin(np.pi * mesh.cell_centers[:, 0]) * np.sin(np.pi * mesh.cell_centers[:, 1])
>>> phi_grad = (-D.T @ V + A) @ phi + b

(Source code)

TensorMesh.copy()

Make a copy of the current mesh

classmethod TensorMesh.deserialize(items, **kwargs)
TensorMesh.edge_divergence_weak_form_robin(alpha=0.0, beta=1.0, gamma=0.0)

Robin boundary condition for the weak formulation of the edge divergence

This function returns the necessary parts to form the full weak form of the edge divergence using the nodal gradient with appropriate boundary conditions.

The alpha, beta, and gamma parameters can be scalars, or arrays. If they are arrays, they can either be the same length as the number of boundary faces, or boundary nodes. If multiple parameters are arrays, they must all be the same length.

beta can not be 0.

It is assumed here that quantity that is approximated on the boundary is the gradient of another quantity. See the Notes section for explicit details.

Parameters
alpha, betascalar or array_like

Parameters for the Robin boundary condition. array_like must be defined on either boundary faces or boundary nodes.

gamma: scalar or array_like

right hand side boundary conditions. If this parameter is array like, it can be fed either a (n_boundary_XXX,) shape array or an (n_boundary_XXX, n_rhs) shape array if multiple systems have the same alpha and beta parameters.

Notes

For these returned operators, it is assumed that the quantity on the boundary is related to the gradient of some other quantity.

The weak form is obtained by multiplying the divergence by a (piecewise-constant) test function, and integrating over the cell, i.e.

(4)\[\int_V y \nabla \cdot \vec{u} \partial V\]

This equation can be transformed to reduce the differentiability requirement on \(\vec{u}\) to be,

(5)\[-\int_V \vec{u} \cdot (\nabla y) \partial V + \int_{dV} y \vec{u} \cdot \hat{n} \partial S.\]

Furthermore, when applying these types of transformations, the unknown vector \(\vec{u}\) is usually related to some scalar potential as:

(6)\[\vec{u} = \nabla \phi\]

Thus the robin conditions returned by these matrices apply to the quantity of \(\phi\).

\[ \begin{align}\begin{aligned}\alpha \phi + \beta \nabla \phi \cdot \hat{n} = \gamma\\\alpha \phi + \beta \vec{u} \cdot \hat{n} = \gamma\end{aligned}\end{align} \]

The returned operators cannot be used to impose a Dirichlet condition on \(\phi\).

TensorMesh.equals(other)
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(*args, **kwargs)

getBCProjWF has been deprecated. See get_BC_projections for documentation

TensorMesh.getBCProjWF_simple(*args, **kwargs)

getBCProjWF_simple has been deprecated. See get_BC_projections_simple for documentation

TensorMesh.getEdgeInnerProduct(*args, **kwargs)

getEdgeInnerProduct has been deprecated. See get_edge_inner_product for documentation

TensorMesh.getEdgeInnerProductDeriv(*args, **kwargs)

getEdgeInnerProductDeriv has been deprecated. See get_edge_inner_product_deriv for documentation

TensorMesh.getFaceInnerProduct(*args, **kwargs)

getFaceInnerProduct has been deprecated. See get_face_inner_product for documentation

TensorMesh.getFaceInnerProductDeriv(*args, **kwargs)

getFaceInnerProductDeriv has been deprecated. See get_face_inner_product_deriv for documentation

TensorMesh.getInterpolationMat(*args, **kwargs)

getInterpolationMat has been deprecated. See get_interpolation_matrix for documentation

TensorMesh.getTensor(*args, **kwargs)

getTensor has been deprecated. See get_tensor for documentation

TensorMesh.get_BC_projections(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.get_BC_projections_simple(discretization='CC')

The weak form boundary condition projection matrices when mixed boundary condition is used

TensorMesh.get_edge_inner_product(model=None, invert_model=False, invert_matrix=False, do_fast=True, **kwargs)

Generate the edge inner product matrix

Parameters
modelnumpy.ndarray

material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))

invert_modelbool

inverts the material property

invert_matrixbool

inverts the matrix

do_fastbool

do a faster implementation if available.

Returns
scipy.sparse.csr_matrix

M, the inner product matrix (nE, nE)

TensorMesh.get_edge_inner_product_deriv(model, do_fast=True, invert_model=False, invert_matrix=False, **kwargs)
Parameters
modelnumpy.ndarray

material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))

do_fastbool

do a faster implementation if available.

invert_modelbool

inverts the material property

invert_matrixbool

inverts the matrix

Returns
scipy.sparse.csr_matrix

dMdm, the derivative of the inner product matrix (nE, nC*nA)

TensorMesh.get_face_inner_product(model=None, invert_model=False, invert_matrix=False, do_fast=True, **kwargs)

Generate the face inner product matrix

Parameters
modelnumpy.ndarray

material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))

invert_modelbool

inverts the material property

invert_matrixbool

inverts the matrix

do_fastbool

do a faster implementation if available.

Returns
scipy.sparse.csr_matrix

M, the inner product matrix (nF, nF)

TensorMesh.get_face_inner_product_deriv(model, do_fast=True, invert_model=False, invert_matrix=False, **kwargs)
Parameters
modelnumpy.ndarray

material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))

do_fast :

bool do a faster implementation if available.

invert_modelbool

inverts the material property

invert_matrixbool

inverts the matrix

Returns
scipy.sparse.csr_matrix

dMdmu(u), the derivative of the inner product matrix for a certain u

TensorMesh.get_interpolation_matrix(loc, location_type='cell_centers', zeros_outside=False, **kwargs)

Produces linear interpolation matrix

Parameters
locnumpy.ndarray

Location of points to interpolate to

location_typestr

What to interpolate (see below)

location_type can be:

'Ex', 'edges_x'           -> x-component of field defined on x edges
'Ey', 'edges_y'           -> y-component of field defined on y edges
'Ez', 'edges_z'           -> z-component of field defined on z edges
'Fx', 'faces_x'           -> x-component of field defined on x faces
'Fy', 'faces_y'           -> y-component of field defined on y faces
'Fz', 'faces_z'           -> z-component of field defined on z faces
'N', 'nodes'              -> scalar field defined on nodes
'CC', 'cell_centers'      -> scalar field defined on cell centers
'CCVx', 'cell_centers_x'  -> x-component of vector field defined on cell centers
'CCVy', 'cell_centers_y'  -> y-component of vector field defined on cell centers
'CCVz', 'cell_centers_z'  -> z-component of vector field defined on cell centers
Returns
scipy.sparse.csr_matrix

M, the interpolation matrix

TensorMesh.get_tensor(key)

Returns a tensor list.

Parameters
keystr

Which tensor (see below)

key can be:

'CC', 'cell_centers' -> location of cell centers
'N', 'nodes'         -> location of nodes
'Fx', 'faces_x'      -> location of faces with an x normal
'Fy', 'faces_y'      -> location of faces with an y normal
'Fz', 'faces_z'      -> location of faces with an z normal
'Ex', 'edges_x'      -> location of edges with an x tangent
'Ey', 'edges_y'      -> location of edges with an y tangent
'Ez', 'edges_z'      -> location of edges with an z tangent
Returns
list

list of the tensors that make up the mesh.

TensorMesh.isInside(*args, **kwargs)

isInside has been deprecated. See is_inside for documentation

TensorMesh.is_inside(pts, location_type='nodes', **kwargs)

Determines if a set of points are inside a mesh.

Parameters

pts (numpy.ndarray) – Location of points to test

Return type

numpy.ndarray

Returns

inside, numpy array of booleans

TensorMesh.plotGrid(*args, **kwargs)

plotGrid has been deprecated. See plot_grid for documentation

TensorMesh.plotImage(*args, **kwargs)

plotImage has been deprecated. See plot_image for documentation

TensorMesh.plotSlice(*args, **kwargs)

plotSlice has been deprecated. See plot_slice for documentation

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.plot_grid(ax=None, nodes=False, faces=False, centers=False, edges=False, lines=True, show_it=False, **kwargs)

Plot the nodal, cell-centered and staggered grids.

Parameters
axmatplotlib.axes.Axes or None, optional

The axes to draw on. None produces a new Axes.

nodes, faces, centers, edges, linesbool, optional

Whether to plot the corresponding item

show_itbool, optional

whether to call plt.show()

colorColor or str, optional

If lines=True, the color of the lines, defaults to first color.

linewidthfloat, optional

If lines=True, the linewidth for the lines.

Returns
matplotlib.axes.Axes

Axes handle for the plot

Other Parameters
edges_x, edges_y, edges_z, faces_x, faces_y, faces_zbool, optional

When plotting a TreeMesh, these are also options to plot the individual component items.

cell_linebool, optional

When plotting a TreeMesh, you can also plot a line through the cell centers in order.

slice{‘both’, ‘theta’, ‘z’}

When plotting a CylindricalMesh, which dimension to slice over.

Notes

Excess arguments are passed on to plot

Examples

Plotting a 2D TensorMesh grid

>>> from matplotlib import pyplot as plt
>>> import discretize
>>> import numpy as np
>>> h1 = np.linspace(.1, .5, 3)
>>> h2 = np.linspace(.1, .5, 5)
>>> mesh = discretize.TensorMesh([h1, h2])
>>> mesh.plot_grid(nodes=True, faces=True, centers=True, lines=True)
>>> plt.show()

(Source code, png, pdf)

../../_images/discretize-TensorMesh-6_00_00.png

Plotting a 3D TensorMesh grid

>>> from matplotlib import pyplot as plt
>>> 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.plot_grid(nodes=True, faces=True, centers=True, lines=True)
>>> plt.show()

(png, pdf)

../../_images/discretize-TensorMesh-6_01_00.png

Plotting a 2D CurvilinearMesh

>>> from matplotlib import pyplot as plt
>>> import discretize
>>> X, Y = discretize.utils.exampleLrmGrid([10, 10], 'rotate')
>>> M = discretize.CurvilinearMesh([X, Y])
>>> M.plot_grid()
>>> plt.show()

(png, pdf)

../../_images/discretize-TensorMesh-6_02_00.png

Plotting a 3D CurvilinearMesh

>>> from matplotlib import pyplot as plt
>>> import discretize
>>> X, Y, Z = discretize.utils.exampleLrmGrid([5, 5, 5], 'rotate')
>>> M = discretize.CurvilinearMesh([X, Y, Z])
>>> M.plot_grid()
>>> plt.show()

(png, pdf)

../../_images/discretize-TensorMesh-6_03_00.png

Plotting a 2D TreeMesh

>>> from matplotlib import pyplot as plt
>>> import discretize
>>> M = discretize.TreeMesh([32, 32])
>>> M.insert_cells([[0.25, 0.25]], [4])
>>> M.plot_grid()
>>> plt.show()

(png, pdf)

../../_images/discretize-TensorMesh-6_04_00.png

Plotting a 3D TreeMesh

>>> from matplotlib import pyplot as plt
>>> import discretize
>>> M = discretize.TreeMesh([32, 32, 32])
>>> M.insert_cells([[0.3, 0.75, 0.22]], [4])
>>> M.plot_grid()
>>> plt.show()

(png, pdf)

../../_images/discretize-TensorMesh-6_05_00.png
TensorMesh.plot_image(v, v_type='CC', 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_thickness=None, stream_threshold=None, **kwargs)

Plots fields on the given mesh.

Parameters
vnumpy.ndarray

values to plot

v_type{‘CC’,’CCV’, ‘N’, ‘F’, ‘Fx’, ‘Fy’, ‘Fz’, ‘E’, ‘Ex’, ‘Ey’, ‘Ez’}

Where the values of v are defined.

view{‘real’, ‘imag’, ‘abs’, ‘vec’}

How to view the array.

axmatplotlib.axes.Axes, optional

The axes to draw on. None produces a new Axes.

climtuple of float, optional

length 2 tuple of (vmin, vmax) for the color limits

range_x, range_ytuple of float, optional

length 2 tuple of (min, max) for the bounds of the plot axes.

pcolor_optsdict, optional

Arguments passed on to pcolormesh

gridbool, optional

Whether to plot the edges of the mesh cells.

grid_optsdict, optional

If grid is true, arguments passed on to plot for grid

sample_gridtuple of numpy.ndarray, optional

If view == ‘vec’, mesh cell widths (hx, hy) to interpolate onto for vector plotting

stream_optsdict, optional

If view == ‘vec’, arguments passed on to streamplot

stream_thicknessfloat, optional

If view == ‘vec’, linewidth for streamplot

stream_thresholdfloat, optional

If view == ‘vec’, only plots vectors with magnitude above this threshold

show_itbool, optional

Whether to call plt.show()

numberingbool, optional

For 3D TensorMesh only, show the numbering of the slices

annotation_colorColor or str, optional

For 3D TensorMesh only, color of the annotation

Examples

2D TensorMesh plotting

>>> from matplotlib import pyplot as plt
>>> 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.plot_image(v)
>>> plt.show()

(Source code, png, pdf)

../../_images/discretize-TensorMesh-7_00_00.png

3D TensorMesh plotting

>>> 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.plot_image(v, annotation_color='k')
>>> plt.show()

(png, pdf)

../../_images/discretize-TensorMesh-7_01_00.png
TensorMesh.plot_slice(v, v_type='CC', normal='Z', ind=None, slice_loc=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 slice of fields on the given 3D mesh.

Parameters
vnumpy.ndarray

values to plot

v_type{‘CC’,’CCV’, ‘N’, ‘F’, ‘Fx’, ‘Fy’, ‘Fz’, ‘E’, ‘Ex’, ‘Ey’, ‘Ez’}, or tuple of these options

Where the values of v are defined.

normal{‘Z’, ‘X’, ‘Y’}

Normal direction of slicing plane.

indNone, optional

index along dimension of slice. Defaults to the center index.

slice_locNone, optional

Value along dimension of slice. Defaults to the center of the mesh.

view{‘real’, ‘imag’, ‘abs’, ‘vec’}

How to view the array.

axmatplotlib.axes.Axes, optional

The axes to draw on. None produces a new Axes. Must be None if v_type is a tuple.

climtuple of float, optional

length 2 tuple of (vmin, vmax) for the color limits

range_x, range_ytuple of float, optional

length 2 tuple of (min, max) for the bounds of the plot axes.

pcolor_optsdict, optional

Arguments passed on to pcolormesh

gridbool, optional

Whether to plot the edges of the mesh cells.

grid_optsdict, optional

If grid is true, arguments passed on to plot for the edges

sample_gridtuple of numpy.ndarray, optional

If view == ‘vec’, mesh cell widths (hx, hy) to interpolate onto for vector plotting

stream_optsdict, optional

If view == ‘vec’, arguments passed on to streamplot

stream_thicknessfloat, optional

If view == ‘vec’, linewidth for streamplot

stream_thresholdfloat, optional

If view == ‘vec’, only plots vectors with magnitude above this threshold

show_itbool, optional

Whether to call plt.show()

Examples

Plot a slice of a 3D TensorMesh solution to a Laplace’s equaiton.

First build the mesh:

>>> from matplotlib import pyplot as plt
>>> import discretize
>>> from pymatsolver import Solver
>>> 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])

then build the necessary parts of the PDE:

>>> q = np.zeros(M.vnC)
>>> q[[4, 4], [4, 4], [2, 6]]=[-1, 1]
>>> q = discretize.utils.mkvc(q)
>>> A = M.face_divergence * M.cell_gradient
>>> b = Solver(A) * (q)

and finaly, plot the vector values of the result, which are defined on faces

>>> M.plot_slice(M.cell_gradient*b, 'F', view='vec', grid=True, pcolor_opts={'alpha':0.8})
>>> plt.show()

(Source code, png, pdf)

../../_images/discretize-TensorMesh-8_00_00.png

We can use the slice_loc kwarg to tell `plot_slice where to slice the mesh. Let’s create a mesh with a random model and plot slice of it. The slice_loc kwarg automatically determines the indices for slicing the mesh along a plane with the given normal.

>>> M = discretize.TensorMesh([32, 32, 32])
>>> v = discretize.utils.random_model(M.vnC, seed=789).reshape(-1, order='F')
>>> x_slice, y_slice, z_slice = 0.75, 0.25, 0.9
>>> plt.figure(figsize=(7.5, 3))
>>> ax = plt.subplot(131)
>>> M.plot_slice(v, normal='X', slice_loc=x_slice, ax=ax)
>>> ax = plt.subplot(132)
>>> M.plot_slice(v, normal='Y', slice_loc=y_slice, ax=ax)
>>> ax = plt.subplot(133)
>>> M.plot_slice(v, normal='Z', slice_loc=z_slice, ax=ax)
>>> plt.tight_layout()
>>> plt.show()

(png, pdf)

../../_images/discretize-TensorMesh-8_01_00.png

This also works for TreeMesh. We create a mesh here that is refined within three boxes, along with a base level of refinement.

>>> TM = discretize.TreeMesh([32, 32, 32])
>>> TM.refine(3, finalize=False)
>>> BSW = [[0.25, 0.25, 0.25], [0.15, 0.15, 0.15], [0.1, 0.1, 0.1]]
>>> TNE = [[0.75, 0.75, 0.75], [0.85, 0.85, 0.85], [0.9, 0.9, 0.9]]
>>> levels = [6, 5, 4]
>>> TM.refine_box(BSW, TNE, levels)
>>> v_TM = discretize.utils.volume_average(M, TM, v)
>>> plt.figure(figsize=(7.5, 3))
>>> ax = plt.subplot(131)
>>> TM.plot_slice(v_TM, normal='X', slice_loc=x_slice, ax=ax)
>>> ax = plt.subplot(132)
>>> TM.plot_slice(v_TM, normal='Y', slice_loc=y_slice, ax=ax)
>>> ax = plt.subplot(133)
>>> TM.plot_slice(v_TM, normal='Z', slice_loc=z_slice, ax=ax)
>>> plt.tight_layout()
>>> plt.show()

(png, pdf)

../../_images/discretize-TensorMesh-8_02_00.png
TensorMesh.projectEdgeVector(*args, **kwargs)

projectEdgeVector has been deprecated. See project_edge_vector for documentation

TensorMesh.projectFaceVector(*args, **kwargs)

projectFaceVector has been deprecated. See project_face_vector for documentation

TensorMesh.project_edge_vector(edge_vector)

Project vectors onto the edges of the mesh

Given a vector, edge_vector, in cartesian coordinates, this will project it onto the mesh using the tangents

Parameters
edge_vectornumpy.ndarray

edge vector with shape (n_edges, dim)

Returns
numpy.ndarray

projected edge vector, (n_edges, )

TensorMesh.project_face_vector(face_vector)

Project vectors onto the faces of the mesh.

Given a vector, face_vector, in cartesian coordinates, this will project it onto the mesh using the normals

Parameters
face_vectornumpy.ndarray

face vector with shape (n_faces, dim)

Returns
numpy.ndarray

projected face vector, (n_faces, )

TensorMesh.r(*args, **kwargs)

r has been deprecated. See reshape for documentation

TensorMesh.readModelUBC(*args, **kwargs)

readModelUBC has been deprecated. See read_model_UBC for documentation

classmethod TensorMesh.readUBC(file_name, directory='')
classmethod TensorMesh.readVTK(file_name, directory='')

Read VTK Rectilinear (vtr xml file) and return Tensor mesh and model

Parameters
file_namestr

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_UBC(file_name, directory='')

Wrapper to Read UBC GIF 2D and 3D tensor mesh and generate same dimension TensorMesh.

Input: :param str file_name: 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 file_name.

TensorMesh.read_model_UBC(file_name, directory='')
Read UBC 2D or 3D Tensor mesh model

and generate Tensor mesh model

Input: :param str file_name: 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.read_vtk(file_name, directory='')

Read VTK Rectilinear (vtr xml file) and return Tensor mesh and model

Parameters
file_namestr

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.reshape(x, x_type='cell_centers', out_type='cell_centers', format='V', **kwargs)

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.

reshape can fulfil your dreams:

mesh.reshape(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.save(file_name='mesh.json', verbose=False, **kwargs)

Save the mesh to json :param str file: file_name for saving the casing properties :param str directory: working directory for saving the file

TensorMesh.serialize()
TensorMesh.setCellGradBC(*args, **kwargs)

setCellGradBC has been deprecated. See set_cell_gradient_BC for documentation

TensorMesh.set_cell_gradient_BC(BC)

Function that sets the boundary conditions for cell-centred 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_dict()
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()

Every object will be valid upon initialization

classmethod TensorMesh.vtk_to_tensor_mesh(vtrGrid)

Converts a vtkRectilinearGrid or pyvista.RectilinearGrid to a discretize.TensorMesh object.

TensorMesh.writeModelUBC(*args, **kwargs)

writeModelUBC has been deprecated. See write_model_UBC for documentation

TensorMesh.writeUBC(*args, **kwargs)

writeUBC has been deprecated. See write_UBC for documentation

TensorMesh.writeVTK(file_name, models=None, directory='')

Makes and saves a VTK object from this mesh and given models

Parameters
file_namestr

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_UBC(file_name, models=None, directory='', comment_lines='')

Writes a TensorMesh to a UBC-GIF format mesh file.

Input: :param str file_name: 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.write_model_UBC(file_name, model, directory='')

Writes a model associated with a TensorMesh to a UBC-GIF format model file.

Input: :param str file_name: 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.write_vtk(file_name, models=None, directory='')

Makes and saves a VTK object from this mesh and given models

Parameters
file_namestr

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