# discretize.CurvilinearMesh¶

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

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

CurvilinearMesh is a mesh class that deals with curvilinear meshes.

Example of a curvilinear mesh:

import discretize
X, Y = discretize.utils.exampleLrmGrid([3,3],'rotate')
mesh = discretize.CurvilinearMesh([X, Y])
mesh.plot_grid(show_it=True)


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

• node_list (a list of Array): List of arrays describing the node locations, a list (each item is a list or numpy array of <class ‘float’>, <class ‘int’> with shape (*, *) or (*, *, *)) with length between 2 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

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_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

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

cellGrad

cellGradBC

cellGradx

cellGrady

cellGradz

cell_centers

Cell-centered grid

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

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

edge_curl

Construct the 3D curl operator.

edge_lengths

Edge lengths

edge_tangents

Edge tangents

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.

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

Area of the faces

face_divergence

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

face_normals

Face normals: calling this will average the computed normals so that there is one per face.

face_x_divergence

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

face_y_divergence
face_z_divergence

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

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 y 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

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).

node_list

node_list (a list of Array): List of arrays describing the node locations, a list (each item is a list or numpy array of <class ‘float’>, <class ‘int’> with shape (*, *) or (*, *, *)) with length between 2 and 3

nodes

Nodal grid.

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

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

tangents

tangents has been deprecated. See edge_tangents for documentation

vol

vol has been deprecated. See cell_volumes for documentation

x0

Methods

 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. 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 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, grid, …]) 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

## Attributes¶

CurvilinearMesh.area

area has been deprecated. See face_areas for documentation

CurvilinearMesh.average_cell_to_face

Construct the averaging operator on cell centers to faces.

CurvilinearMesh.average_cell_vector_to_face

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

CurvilinearMesh.average_edge_to_cell

Construct the averaging operator on cell edges to cell centers.

CurvilinearMesh.average_edge_to_cell_vector

Construct the averaging operator on cell edges to cell centers.

CurvilinearMesh.average_edge_x_to_cell

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

CurvilinearMesh.average_edge_y_to_cell

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

CurvilinearMesh.average_edge_z_to_cell

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

CurvilinearMesh.average_face_to_cell

Construct the averaging operator on cell faces to cell centers.

CurvilinearMesh.average_face_to_cell_vector

Construct the averaging operator on cell faces to cell centers.

CurvilinearMesh.average_face_x_to_cell

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

CurvilinearMesh.average_face_y_to_cell

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

CurvilinearMesh.average_face_z_to_cell

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

CurvilinearMesh.average_node_to_cell

Construct the averaging operator on cell nodes to cell centers.

CurvilinearMesh.average_node_to_edge

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

CurvilinearMesh.average_node_to_face

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

CurvilinearMesh.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

CurvilinearMesh.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

CurvilinearMesh.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

CurvilinearMesh.cellGrad

CurvilinearMesh.cellGradBC

CurvilinearMesh.cellGradx

CurvilinearMesh.cellGrady

CurvilinearMesh.cellGradz

CurvilinearMesh.cell_centers

Cell-centered grid

CurvilinearMesh.cell_gradient

The cell centered Gradient, takes you to cell faces.

CurvilinearMesh.cell_gradient_BC

The cell centered Gradient boundary condition matrix

CurvilinearMesh.cell_gradient_x

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

CurvilinearMesh.cell_gradient_y
CurvilinearMesh.cell_gradient_z

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

CurvilinearMesh.cell_volumes

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

CurvilinearMesh.dim

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

Returns
int

dimension of the mesh

CurvilinearMesh.edge

edge has been deprecated. See edge_lengths for documentation

CurvilinearMesh.edgeCurl

edgeCurl has been deprecated. See edge_curl for documentation

CurvilinearMesh.edge_curl

Construct the 3D curl operator.

CurvilinearMesh.edge_lengths

Edge lengths

CurvilinearMesh.edge_tangents

Edge tangents

CurvilinearMesh.edges_x

Edge staggered grid in the x direction.

CurvilinearMesh.edges_y

Edge staggered grid in the y direction.

CurvilinearMesh.edges_z

Edge staggered grid in the z direction.

CurvilinearMesh.faceDiv

faceDiv has been deprecated. See face_divergence for documentation

CurvilinearMesh.faceDivx

faceDivx has been deprecated. See face_x_divergence for documentation

CurvilinearMesh.faceDivy

faceDivy has been deprecated. See face_y_divergence for documentation

CurvilinearMesh.faceDivz

faceDivz has been deprecated. See face_z_divergence for documentation

CurvilinearMesh.face_areas

Area of the faces

CurvilinearMesh.face_divergence

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

CurvilinearMesh.face_normals

Face normals: calling this will average the computed normals so that there is one per face. This is especially relevant in 3D, as there are up to 4 different normals for each face that will be different.

To reshape the normals into a matrix and get the y component:

NyX, NyY, NyZ = M.reshape(M.face_normals, 'F', 'Fy', 'M')

CurvilinearMesh.face_x_divergence

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

CurvilinearMesh.face_y_divergence
CurvilinearMesh.face_z_divergence

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

CurvilinearMesh.faces_x

Face staggered grid in the x direction.

CurvilinearMesh.faces_y

Face staggered grid in the y direction.

CurvilinearMesh.faces_z

Face staggered grid in the y direction.

CurvilinearMesh.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.

CurvilinearMesh.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.

CurvilinearMesh.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.

CurvilinearMesh.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.

CurvilinearMesh.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.

CurvilinearMesh.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.

CurvilinearMesh.n_cells
CurvilinearMesh.n_edges

Total number of edges.

Returns
int

sum([n_edges_x, n_edges_y, n_edges_z])

Notes

Also accessible as nE.

CurvilinearMesh.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)

CurvilinearMesh.n_edges_x
CurvilinearMesh.n_edges_y
CurvilinearMesh.n_edges_z
CurvilinearMesh.n_faces

Total number of faces.

Returns
int

sum([n_faces_x, n_faces_y, n_faces_z])

Notes

Also accessible as nF.

CurvilinearMesh.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)

CurvilinearMesh.n_faces_x
CurvilinearMesh.n_faces_y
CurvilinearMesh.n_faces_z
CurvilinearMesh.n_nodes
CurvilinearMesh.nodalGrad

CurvilinearMesh.nodalLaplacian

nodalLaplacian has been deprecated. See nodal_laplacian for documentation

CurvilinearMesh.nodal_gradient

Construct gradient operator (nodes to edges).

CurvilinearMesh.nodal_laplacian

Construct laplacian operator (nodes to edges).

CurvilinearMesh.node_list

node_list (a list of Array): List of arrays describing the node locations, a list (each item is a list or numpy array of <class ‘float’>, <class ‘int’> with shape (*, *) or (*, *, *)) with length between 2 and 3

CurvilinearMesh.nodes

Nodal grid.

CurvilinearMesh.normals

normals has been deprecated. See face_normals for documentation

CurvilinearMesh.origin

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

CurvilinearMesh.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 $$(0,0,1)$$

CurvilinearMesh.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

CurvilinearMesh.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.

CurvilinearMesh.shape_cells

The number of cells in each direction

Returns
tuple of ints

Notes

Also accessible as vnC.

CurvilinearMesh.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.

CurvilinearMesh.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.

CurvilinearMesh.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.

CurvilinearMesh.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.

CurvilinearMesh.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.

CurvilinearMesh.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.

CurvilinearMesh.shape_nodes

Number of nodes in each direction

Returns
tuple of int

Notes

Also accessible as vnN.

CurvilinearMesh.stencil_cell_gradient
CurvilinearMesh.stencil_cell_gradient_x
CurvilinearMesh.stencil_cell_gradient_y
CurvilinearMesh.stencil_cell_gradient_z
CurvilinearMesh.tangents

tangents has been deprecated. See edge_tangents for documentation

CurvilinearMesh.vol

vol has been deprecated. See cell_volumes for documentation

CurvilinearMesh.x0

## Methods¶

CurvilinearMesh.copy()

Make a copy of the current mesh

classmethod CurvilinearMesh.deserialize(value, **kwargs)[source]

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.

CurvilinearMesh.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 CurvilinearMesh.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.

CurvilinearMesh.getBCProjWF(*args, **kwargs)

getBCProjWF has been deprecated. See get_BC_projections for documentation

CurvilinearMesh.getBCProjWF_simple(*args, **kwargs)

getBCProjWF_simple has been deprecated. See get_BC_projections_simple for documentation

CurvilinearMesh.getEdgeInnerProduct(*args, **kwargs)

getEdgeInnerProduct has been deprecated. See get_edge_inner_product for documentation

CurvilinearMesh.getEdgeInnerProductDeriv(*args, **kwargs)

getEdgeInnerProductDeriv has been deprecated. See get_edge_inner_product_deriv for documentation

CurvilinearMesh.getFaceInnerProduct(*args, **kwargs)

getFaceInnerProduct has been deprecated. See get_face_inner_product for documentation

CurvilinearMesh.getFaceInnerProductDeriv(*args, **kwargs)

getFaceInnerProductDeriv has been deprecated. See get_face_inner_product_deriv for documentation

CurvilinearMesh.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']

CurvilinearMesh.get_BC_projections_simple(discretization='CC')

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

CurvilinearMesh.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)

CurvilinearMesh.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)

CurvilinearMesh.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)

CurvilinearMesh.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

CurvilinearMesh.plotGrid(*args, **kwargs)

plotGrid has been deprecated. See plot_grid for documentation

CurvilinearMesh.plotImage(*args, **kwargs)

plotImage has been deprecated. See plot_image for documentation

CurvilinearMesh.plotSlice(*args, **kwargs)

plotSlice has been deprecated. See plot_slice for documentation

CurvilinearMesh.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.

CurvilinearMesh.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)

CurvilinearMesh.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)

CurvilinearMesh.plot_slice(v, v_type='CC', normal='Z', ind=None, grid=False, view='real', ax=None, clim=None, show_it=False, pcolor_opts=None, stream_opts=None, grid_opts=None, range_x=None, range_y=None, sample_grid=None, stream_threshold=None, stream_thickness=None, **kwargs)

Plots 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.

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
>>> import numpy as np
>>> hx = [(5, 2, -1.3), (2, 4), (5, 2, 1.3)]
>>> hy = [(2, 2, -1.3), (2, 6), (2, 2, 1.3)]
>>> hz = [(2, 2, -1.3), (2, 6), (2, 2, 1.3)]
>>> M = discretize.TensorMesh([hx, hy, hz])


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()

CurvilinearMesh.projectEdgeVector(*args, **kwargs)

projectEdgeVector has been deprecated. See project_edge_vector for documentation

CurvilinearMesh.projectFaceVector(*args, **kwargs)

projectFaceVector has been deprecated. See project_face_vector for documentation

CurvilinearMesh.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, )

CurvilinearMesh.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, )

CurvilinearMesh.r(*args, **kwargs)

r has been deprecated. See reshape for documentation

CurvilinearMesh.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')

CurvilinearMesh.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

CurvilinearMesh.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.

CurvilinearMesh.setCellGradBC(*args, **kwargs)

CurvilinearMesh.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’]

CurvilinearMesh.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

CurvilinearMesh.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

CurvilinearMesh.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

CurvilinearMesh.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.

CurvilinearMesh.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

CurvilinearMesh.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