# discretize.CylindricalMesh¶

class discretize.CylindricalMesh(*args, **kwargs)[source]

Bases: discretize.base.base_tensor_mesh.BaseTensorMesh, discretize.base.base_mesh.BaseRectangularMesh, discretize.operators.inner_products.InnerProducts, discretize.operators.differential_operators.DiffOperators

CylindricalMesh is a mesh class for cylindrical problems. It supports both cylindrically symmetric and 3D cylindrical meshes that include an azimuthal discretization.

For a cylindrically symmetric mesh use h = [hx, 1, hz]. For example:

import discretize
from discretize import utils

cs, nc, npad = 20., 30, 8
mesh = discretize.CylindricalMesh([hx, 1, hz], origin=[0, 0, -hz.sum()/2])
mesh.plot_grid()


To create a 3D cylindrical mesh, we also include an azimuthal discretization

import discretize
from discretize import utils

cs, nc, npad = 20., 30, 8
nc_theta = 8
hy = 2 * np.pi/nc_theta * np.ones(nc_theta)
mesh = discretize.CylindricalMesh([hx, hy, hz], origin=[0, 0, -hz.sum()/2])
mesh.plot_grid()


Required Properties:

• axis_u (Vector3): Vector orientation of u-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: X

• axis_v (Vector3): Vector orientation of v-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: Y

• axis_w (Vector3): Vector orientation of w-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: Z

• cartesian_origin (Array): Cartesian origin of the mesh, a list or numpy array of <class ‘float’> with shape (*)

• h (a tuple of Array): h is a list containing the cell widths of the tensor mesh in each dimension., a tuple (each item is a list or numpy array of <class ‘float’> with shape (*)) with length between 1 and 3

• origin (Array): origin of the mesh (dim, ), a list or numpy array of <class ‘float’>, <class ‘int’> with shape (*)

• 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

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_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

averaging operator of edges to cell centers

average_edge_to_cell_vector

averaging operator of edges to a cell centered vector

average_edge_x_to_cell

averaging operator of x-edges (radial) to cell centers

average_edge_y_to_cell

averaging operator of y-edges (azimuthal) to cell centers

average_edge_z_to_cell

averaging operator of z-edges to cell centers

average_face_to_cell

averaging operator of faces to cell centers

average_face_to_cell_vector

averaging operator of x-faces (radial) to cell centered vectors

average_face_x_to_cell

averaging operator of x-faces (radial) to cell centers

average_face_y_to_cell

averaging operator of y-faces (azimuthal) to cell centers

average_face_z_to_cell

averaging operator of z-faces (vertical) 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

axis_u (Vector3): Vector orientation of u-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: X

axis_v

axis_v (Vector3): Vector orientation of v-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: Y

axis_w

axis_w (Vector3): Vector orientation of w-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: Z

cartesianOrigin

cartesianOrigin has been deprecated. See cartesian_origin for documentation

cartesian_origin

cartesian_origin (Array): Cartesian origin of the mesh, a list or numpy array of <class ‘float’> with shape (*)

cellGrad

cellGradBC

cellGradx

cellGrady

cellGradz

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_z

Cell centered Gradient in the x dimension.

cell_volumes

Volume of each cell

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

The edgeCurl (edges to faces)

edge_lengths

Edge lengths

edge_tangents

Edge Tangents

edge_x_lengths

x-edge lengths - these are the radial edges. Radial edges only exist

edge_y_lengths

y-edge lengths - these are the azimuthal edges. Azimuthal edges exist

edge_z_lengths

z-edge lengths - these are the vertical edges. Vertical edges only

edges_x

Edge staggered grid in the x direction.

edges_y

Grid of y-edges (azimuthal-faces) in cylindrical coordinates $$(r, \theta, z)$$.

edges_z

Grid of z-faces (vertical-faces) in cylindrical coordinates $$(r, \theta, z)$$.

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

Face areas

face_divergence

Construct divergence operator (faces to cell-centres).

face_normals

Face Normals

face_x_areas

Area of the x-faces (radial faces).

face_x_divergence

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

face_y_areas

Area of y-faces (Azimuthal faces).

face_y_divergence

Construct divergence operator in the y component (faces to cell-centres).

face_z_areas

Area of z-faces.

face_z_divergence

Construct divergence operator in the z component (faces to cell-centres).

faces_x

Grid of x-faces (radial-faces) in cylindrical coordinates $$(r, \theta, z)$$.

faces_y

Face staggered grid in the y direction.

faces_z

Face staggered grid in the z direction.

h

h (a tuple of Array): h is a list containing the cell widths of the tensor mesh in each dimension., a tuple (each item is a list or numpy array of <class ‘float’> with shape (*)) with length between 1 and 3

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

isSymmetric

isSymmetric has been deprecated. See is_symmetric for documentation

is_symmetric

Is the mesh cylindrically symmetric?

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

Returns

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

Returns

nodalGrad

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 in cylindrical coordinates $$(r, \theta, z)$$.

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

origin

origin (Array): origin of the mesh (dim, ), a list or numpy array of <class ‘float’>, <class ‘int’> with shape (*)

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: cartesian

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

Returns

shape_faces_x

Returns

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

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

 cartesianGrid(*args, **kwargs) cartesianGrid has been deprecated. cartesian_grid([location_type, theta_shift]) Takes a grid location (‘CC’, ‘N’, ‘Ex’, ‘Ey’, ‘Ez’, ‘Fx’, ‘Fy’, ‘Fz’) and returns that grid in cartesian coordinates Make a copy of the current mesh deserialize(value, **kwargs) Creates HasProperties instance from serialized dictionary equal(other) Determine if two HasProperties instances are equivalent 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. getInterpolationMatCartMesh(*args, **kwargs) getInterpolationMatCartMesh 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 interpolation matrix Takes a cartesian mesh and returns a projection to translate onto the cartesian grid. 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. 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 serialize([include_class, save_dynamic]) Serializes a HasProperties instance to dictionary setCellGradBC(*args, **kwargs) setCellGradBC has been deprecated. 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. Call all registered class validator methods writeVTK(file_name[, models, directory]) Makes and saves a VTK object from this mesh and given models write_vtk(file_name[, models, directory]) Makes and saves a VTK object from this mesh and given models
 check_cartesian_origin_shape

## Attributes¶

CylindricalMesh.area

area has been deprecated. See face_areas for documentation

CylindricalMesh.areaFx

areaFx has been deprecated. See face_x_areas for documentation

CylindricalMesh.areaFy

areaFy has been deprecated. See face_y_areas for documentation

CylindricalMesh.areaFz

areaFz has been deprecated. See face_z_areas for documentation

CylindricalMesh.average_cell_to_face

Construct the averaging operator on cell centers to faces.

CylindricalMesh.average_cell_vector_to_face

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

CylindricalMesh.average_edge_to_cell

averaging operator of edges to cell centers

Returns
scipy.sparse.csr_matrix

matrix that averages from edges to cell centers

CylindricalMesh.average_edge_to_cell_vector

averaging operator of edges to a cell centered vector

Returns
scipy.sparse.csr_matrix

matrix that averages from edges to cell centered vectors

CylindricalMesh.average_edge_x_to_cell

averaging operator of x-edges (radial) to cell centers

Returns
scipy.sparse.csr_matrix

matrix that averages from x-edges to cell centers

CylindricalMesh.average_edge_y_to_cell

averaging operator of y-edges (azimuthal) to cell centers

Returns
scipy.sparse.csr_matrix

matrix that averages from y-edges to cell centers

CylindricalMesh.average_edge_z_to_cell

averaging operator of z-edges to cell centers

Returns
scipy.sparse.csr_matrix

matrix that averages from z-edges to cell centers

CylindricalMesh.average_face_to_cell

averaging operator of faces to cell centers

Returns
scipy.sparse.csr_matrix

matrix that averages from faces to cell centers

CylindricalMesh.average_face_to_cell_vector

averaging operator of x-faces (radial) to cell centered vectors

Returns
scipy.sparse.csr_matrix

matrix that averages from faces to cell centered vectors

CylindricalMesh.average_face_x_to_cell

averaging operator of x-faces (radial) to cell centers

Returns
scipy.sparse.csr_matrix

matrix that averages from x-faces to cell centers

CylindricalMesh.average_face_y_to_cell

averaging operator of y-faces (azimuthal) to cell centers

Returns
scipy.sparse.csr_matrix

matrix that averages from y-faces to cell centers

CylindricalMesh.average_face_z_to_cell

averaging operator of z-faces (vertical) to cell centers

Returns
scipy.sparse.csr_matrix

matrix that averages from z-faces to cell centers

CylindricalMesh.average_node_to_cell

Construct the averaging operator on cell nodes to cell centers.

CylindricalMesh.average_node_to_edge

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

CylindricalMesh.average_node_to_face

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

CylindricalMesh.axis_u

axis_u (Vector3): Vector orientation of u-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: X

CylindricalMesh.axis_v

axis_v (Vector3): Vector orientation of v-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: Y

CylindricalMesh.axis_w

axis_w (Vector3): Vector orientation of w-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: Z

CylindricalMesh.cartesianOrigin

cartesianOrigin has been deprecated. See cartesian_origin for documentation

CylindricalMesh.cartesian_origin

cartesian_origin (Array): Cartesian origin of the mesh, a list or numpy array of <class ‘float’> with shape (*)

CylindricalMesh.cellGrad

CylindricalMesh.cellGradBC

CylindricalMesh.cellGradx

CylindricalMesh.cellGrady

CylindricalMesh.cellGradz

CylindricalMesh.cell_centers

Cell-centered grid.

CylindricalMesh.cell_centers_x

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

CylindricalMesh.cell_centers_y

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

CylindricalMesh.cell_centers_z

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

CylindricalMesh.cell_gradient
CylindricalMesh.cell_gradient_BC

The cell centered Gradient boundary condition matrix

CylindricalMesh.cell_gradient_x
CylindricalMesh.cell_gradient_y
CylindricalMesh.cell_gradient_z

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

CylindricalMesh.cell_volumes

Volume of each cell

Returns
numpy.ndarray

cell volumes

CylindricalMesh.dim

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

Returns
int

dimension of the mesh

CylindricalMesh.edge

edge has been deprecated. See edge_lengths for documentation

CylindricalMesh.edgeCurl

edgeCurl has been deprecated. See edge_curl for documentation

CylindricalMesh.edgeEx

edgeEx has been deprecated. See edge_x_lengths for documentation

CylindricalMesh.edgeEy

edgeEy has been deprecated. See edge_y_lengths for documentation

CylindricalMesh.edgeEz

edgeEz has been deprecated. See edge_z_lengths for documentation

CylindricalMesh.edge_curl

The edgeCurl (edges to faces)

Returns
scipy.sparse.csr_matrix

edge curl operator

CylindricalMesh.edge_lengths

Edge lengths

Returns
numpy.ndarray

vector of edge lengths $$(r, \theta, z)$$

CylindricalMesh.edge_tangents

Edge Tangents

Returns
numpy.ndarray

normals, (n_edges, dim)

CylindricalMesh.edge_x_lengths

x-edge lengths - these are the radial edges. Radial edges only exist for a 3D cyl mesh.

Returns
numpy.ndarray

CylindricalMesh.edge_y_lengths

y-edge lengths - these are the azimuthal edges. Azimuthal edges exist for all cylindrical meshes. These are arc-lengths ($$\theta r$$)

Returns
numpy.ndarray

vector of the azimuthal edges

CylindricalMesh.edge_z_lengths

z-edge lengths - these are the vertical edges. Vertical edges only exist for a 3D cyl mesh.

Returns
numpy.ndarray

vector of the vertical edges

CylindricalMesh.edges_x

Edge staggered grid in the x direction.

CylindricalMesh.edges_y

Grid of y-edges (azimuthal-faces) in cylindrical coordinates $$(r, \theta, z)$$.

Returns
numpy.ndarray

grid locations of azimuthal faces

CylindricalMesh.edges_z

Grid of z-faces (vertical-faces) in cylindrical coordinates $$(r, \theta, z)$$.

Returns
numpy.ndarray

CylindricalMesh.faceDiv

faceDiv has been deprecated. See face_divergence for documentation

CylindricalMesh.faceDivx

faceDivx has been deprecated. See face_x_divergence for documentation

CylindricalMesh.faceDivy

faceDivy has been deprecated. See face_y_divergence for documentation

CylindricalMesh.faceDivz

faceDivz has been deprecated. See face_z_divergence for documentation

CylindricalMesh.face_areas

Face areas

For a 3D cyl mesh: [radial, azimuthal, vertical], while a cylindrically symmetric mesh doesn’t have y-Faces, so it returns [radial, vertical]

Returns
numpy.ndarray

face areas

CylindricalMesh.face_divergence

Construct divergence operator (faces to cell-centres).

CylindricalMesh.face_normals

Face Normals

Returns
numpy.ndarray

normals, (n_faces, dim)

CylindricalMesh.face_x_areas

Area of the x-faces (radial faces). Radial faces exist on all cylindrical meshes

$A_x = r \theta h_z$
Returns
numpy.ndarray

area of x-faces

CylindricalMesh.face_x_divergence

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

CylindricalMesh.face_y_areas

Area of y-faces (Azimuthal faces). Azimuthal faces exist only on 3D cylindrical meshes.

$A_y = h_x h_z$
Returns
numpy.ndarray

area of y-faces

CylindricalMesh.face_y_divergence

Construct divergence operator in the y component (faces to cell-centres).

CylindricalMesh.face_z_areas

Area of z-faces.

$A_z = \frac{\theta}{2} (r_2^2 - r_1^2)z$
Returns
numpy.ndarray

area of the z-faces

CylindricalMesh.face_z_divergence

Construct divergence operator in the z component (faces to cell-centres).

CylindricalMesh.faces_x

Grid of x-faces (radial-faces) in cylindrical coordinates $$(r, \theta, z)$$.

Returns
numpy.ndarray

CylindricalMesh.faces_y

Face staggered grid in the y direction.

CylindricalMesh.faces_z

Face staggered grid in the z direction.

CylindricalMesh.h

h (a tuple of Array): h is a list containing the cell widths of the tensor mesh in each dimension., a tuple (each item is a list or numpy array of <class ‘float’> with shape (*)) with length between 1 and 3

CylindricalMesh.h_gridded

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

CylindricalMesh.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].

CylindricalMesh.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].

CylindricalMesh.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].

CylindricalMesh.isSymmetric

isSymmetric has been deprecated. See is_symmetric for documentation

CylindricalMesh.is_symmetric

Is the mesh cylindrically symmetric?

Returns
bool

True if the mesh is cylindrically symmetric, False otherwise

CylindricalMesh.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.

CylindricalMesh.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.

CylindricalMesh.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.

CylindricalMesh.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.

CylindricalMesh.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.

CylindricalMesh.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.

CylindricalMesh.n_cells
CylindricalMesh.n_edges

Total number of edges.

Returns
int

sum([n_edges_x, n_edges_y, n_edges_z])

Notes

Also accessible as nE.

CylindricalMesh.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)

CylindricalMesh.n_edges_x
CylindricalMesh.n_edges_y
CylindricalMesh.n_edges_z
Returns
int

Number of z-edges

CylindricalMesh.n_faces

Total number of faces.

Returns
int

sum([n_faces_x, n_faces_y, n_faces_z])

Notes

Also accessible as nF.

CylindricalMesh.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)

CylindricalMesh.n_faces_x
CylindricalMesh.n_faces_y
CylindricalMesh.n_faces_z
CylindricalMesh.n_nodes
Returns
int

Total number of nodes

CylindricalMesh.nodalGrad

CylindricalMesh.nodalLaplacian

nodalLaplacian has been deprecated. See nodal_laplacian for documentation

CylindricalMesh.nodal_gradient

Construct gradient operator (nodes to edges).

CylindricalMesh.nodal_laplacian

Construct laplacian operator (nodes to edges).

CylindricalMesh.nodes

Nodal grid in cylindrical coordinates $$(r, \theta, z)$$. Nodes do not exist in a cylindrically symmetric mesh.

Returns
numpy.ndarray

grid locations of nodes

CylindricalMesh.nodes_x

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

CylindricalMesh.nodes_y

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

CylindricalMesh.nodes_z

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

CylindricalMesh.normals

normals has been deprecated. See face_normals for documentation

CylindricalMesh.origin

origin (Array): origin of the mesh (dim, ), a list or numpy array of <class ‘float’>, <class ‘int’> with shape (*)

CylindricalMesh.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 $$(0,0,1)$$

CylindricalMesh.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

CylindricalMesh.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.

CylindricalMesh.shape_cells

The number of cells in each direction

Returns
tuple of ints

Notes

Also accessible as vnC.

CylindricalMesh.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.

CylindricalMesh.shape_edges_y

Number of y-edges in each direction

Returns
tuple of ints

vnEy or None if dim < 2, (dim, )

CylindricalMesh.shape_edges_z
Returns
tuple of ints

Number of z-edges in each direction or None if nCy > 1, (dim, )

CylindricalMesh.shape_faces_x
Returns
numpy.ndarray

Number of x-faces in each direction, (dim, )

CylindricalMesh.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.

CylindricalMesh.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.

CylindricalMesh.shape_nodes
CylindricalMesh.stencil_cell_gradient
CylindricalMesh.stencil_cell_gradient_x
CylindricalMesh.stencil_cell_gradient_y
CylindricalMesh.stencil_cell_gradient_z
CylindricalMesh.tangents

tangents has been deprecated. See edge_tangents for documentation

CylindricalMesh.vectorCCx

vectorCCx has been deprecated. See cell_centers_x for documentation

CylindricalMesh.vectorCCy

vectorCCy has been deprecated. See cell_centers_y for documentation

CylindricalMesh.vectorCCz

vectorCCz has been deprecated. See cell_centers_z for documentation

CylindricalMesh.vectorNx

vectorNx has been deprecated. See nodes_x for documentation

CylindricalMesh.vectorNy

vectorNy has been deprecated. See nodes_y for documentation

CylindricalMesh.vectorNz

vectorNz has been deprecated. See nodes_z for documentation

CylindricalMesh.vol

vol has been deprecated. See cell_volumes for documentation

CylindricalMesh.x0

## Methods¶

CylindricalMesh.cartesianGrid(*args, **kwargs)

cartesianGrid has been deprecated. See cartesian_grid for documentation

CylindricalMesh.cartesian_grid(location_type='cell_centers', theta_shift=None, **kwargs)[source]

Takes a grid location (‘CC’, ‘N’, ‘Ex’, ‘Ey’, ‘Ez’, ‘Fx’, ‘Fy’, ‘Fz’) and returns that grid in cartesian coordinates

Parameters
location_type{‘CC’, ‘N’, ‘Ex’, ‘Ey’, ‘Ez’, ‘Fx’, ‘Fy’, ‘Fz’}

grid location

theta_shiftfloat, optional

shift for theta

Returns
numpy.ndarray

cartesian coordinates for the cylindrical grid

CylindricalMesh.check_cartesian_origin_shape(change)[source]
CylindricalMesh.copy()

Make a copy of the current mesh

classmethod CylindricalMesh.deserialize(value, **kwargs)

Creates HasProperties instance from serialized dictionary

This uses the Property deserializers to deserialize all JSON-compatible 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.

CylindricalMesh.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 CylindricalMesh.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.

CylindricalMesh.getBCProjWF(*args, **kwargs)

getBCProjWF has been deprecated. See get_BC_projections for documentation

CylindricalMesh.getBCProjWF_simple(*args, **kwargs)

getBCProjWF_simple has been deprecated. See get_BC_projections_simple for documentation

CylindricalMesh.getEdgeInnerProduct(*args, **kwargs)

getEdgeInnerProduct has been deprecated. See get_edge_inner_product for documentation

CylindricalMesh.getEdgeInnerProductDeriv(*args, **kwargs)

getEdgeInnerProductDeriv has been deprecated. See get_edge_inner_product_deriv for documentation

CylindricalMesh.getFaceInnerProduct(*args, **kwargs)

getFaceInnerProduct has been deprecated. See get_face_inner_product for documentation

CylindricalMesh.getFaceInnerProductDeriv(*args, **kwargs)

getFaceInnerProductDeriv has been deprecated. See get_face_inner_product_deriv for documentation

CylindricalMesh.getInterpolationMat(*args, **kwargs)

getInterpolationMat has been deprecated. See get_interpolation_matrix for documentation

CylindricalMesh.getInterpolationMatCartMesh(*args, **kwargs)

getInterpolationMatCartMesh has been deprecated. See get_interpolation_matrix_cartesian_mesh for documentation

CylindricalMesh.getTensor(*args, **kwargs)

getTensor has been deprecated. See get_tensor for documentation

CylindricalMesh.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']

CylindricalMesh.get_BC_projections_simple(discretization='CC')

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

CylindricalMesh.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)

CylindricalMesh.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)

CylindricalMesh.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)

CylindricalMesh.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

CylindricalMesh.get_interpolation_matrix(loc, location_type='cell_centers', zeros_outside=False, **kwargs)[source]

Produces interpolation matrix

Parameters
locnumpy.ndarray

Location of points to interpolate to

location_typestr

What to interpolate 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

CylindricalMesh.get_interpolation_matrix_cartesian_mesh(Mrect, location_type='cell_centers', location_type_to=None, **kwargs)[source]

Takes a cartesian mesh and returns a projection to translate onto the cartesian grid.

Parameters
Mrectdiscretize.base.BaseMesh

the mesh to interpolate on to

location_type{‘CC’, ‘N’, ‘Ex’, ‘Ey’, ‘Ez’, ‘Fx’, ‘Fy’, ‘Fz’}

grid location

location_type_to{‘CC’, ‘N’, ‘Ex’, ‘Ey’, ‘Ez’, ‘Fx’, ‘Fy’, ‘Fz’}, or None, optional

grid location to interpolate to. If None, the same grid type as location_type will be assumed

Returns
scipy.sparse.csr_matrix

M, the interpolation matrix

CylindricalMesh.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.

CylindricalMesh.isInside(*args, **kwargs)

isInside has been deprecated. See is_inside for documentation

CylindricalMesh.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

CylindricalMesh.plotGrid(*args, **kwargs)

plotGrid has been deprecated. See plot_grid for documentation

CylindricalMesh.plotImage(*args, **kwargs)

plotImage has been deprecated. See plot_image for documentation

CylindricalMesh.plotSlice(*args, **kwargs)

plotSlice has been deprecated. See plot_slice for documentation

CylindricalMesh.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

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.

CylindricalMesh.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()


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)

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)

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)

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)

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)

CylindricalMesh.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()


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)

CylindricalMesh.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()


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)

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)

CylindricalMesh.projectEdgeVector(*args, **kwargs)

projectEdgeVector has been deprecated. See project_edge_vector for documentation

CylindricalMesh.projectFaceVector(*args, **kwargs)

projectFaceVector has been deprecated. See project_face_vector for documentation

CylindricalMesh.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, )

CylindricalMesh.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, )

CylindricalMesh.r(*args, **kwargs)

r has been deprecated. See reshape for documentation

CylindricalMesh.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.

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')

CylindricalMesh.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

CylindricalMesh.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 JSON-compatible 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.

CylindricalMesh.setCellGradBC(*args, **kwargs)

CylindricalMesh.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’]

CylindricalMesh.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

CylindricalMesh.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

CylindricalMesh.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

CylindricalMesh.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.

CylindricalMesh.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

CylindricalMesh.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