discretize.base.BaseTensorMesh#

Inheritance diagram of BaseTensorMesh
class discretize.base.BaseTensorMesh(h, origin=None, **kwargs)[source]#

Base class for tensor-product style meshes

This class contains properites and methods that are common to Cartesian and cylindrical meshes. That is, meshes whose cell centers, nodes, faces and edges can be constructed with tensor-products of vectors.

Do not use this class directly! Practical tensor meshes supported in discretize will inherit this class; i.e. discretize.TensorMesh and CylindricalMesh. Inherit this class if you plan to develop a new tensor-style mesh class (e.g. a spherical mesh).

Parameters
h(dim) iterable of int, numpy.ndarray, or tuple

Defines the cell widths along each axis. The length of the iterable object is equal to the dimension of the mesh (1, 2 or 3). For a 3D mesh, the list would have the form [hx, hy, hz] .

Along each axis, the user has 3 choices for defining the cells widths:

  • int -> A unit interval is equally discretized into N cells.

  • numpy.ndarray -> The widths are explicity given for each cell

  • the widths are defined as a list of tuple of the form (dh, nc, [npad]) where dh is the cell width, nc is the number of cells, and npad (optional) is a padding factor denoting exponential increase/decrease in the cell width for each cell; e.g. [(2., 10, -1.3), (2., 50), (2., 10, 1.3)]

origin(dim) iterable, default: 0

Define the origin or ‘anchor point’ of the mesh; i.e. the bottom-left-frontmost corner. By default, the mesh is anchored such that its origin is at [0, 0, 0].

For each dimension (x, y or z), The user may set the origin 2 ways:

  • a scalar which explicitly defines origin along that dimension.

  • {‘0’, ‘C’, ‘N’} a str specifying whether the zero coordinate along each axis is the first node location (‘0’), in the center (‘C’) or the last node location (‘N’).

See also

utils.unpack_widths

The function used to expand a list or tuple to generate widths.

Attributes

area

area has been deprecated.

average_cell_to_edge

Averaging operator from cell centers to edges (scalar quantities).

average_cell_to_face

Averaging operator from cell centers to faces (scalar quantities).

average_cell_vector_to_face

Averaging operator from cell centers to faces (vector quantities).

average_edge_to_cell

Averaging operator from edges to cell centers (scalar quantities).

average_edge_to_cell_vector

Averaging operator from edges to cell centers (vector quantities).

average_edge_to_face_vector

Averaging operator from edges to faces (vector quantities).

average_face_to_cell

Averaging operator from faces to cell centers (scalar quantities).

average_face_to_cell_vector

Averaging operator from faces to cell centers (vector quantities).

average_node_to_cell

Averaging operator from nodes to cell centers (scalar quantities).

average_node_to_edge

Averaging operator from nodes to edges (scalar quantities).

average_node_to_face

Averaging operator from nodes to faces (scalar quantities).

axis_u

Deprecated since version 0.7.0.

axis_v

Deprecated since version 0.7.0.

axis_w

Deprecated since version 0.7.0.

boundary_edge_vector_integral

Represents the operation of integrating a vector function on the boundary

boundary_edges

Boundary edge locations

boundary_face_outward_normals

Outward normal vectors of boundary faces

boundary_face_scalar_integral

Represents the operation of integrating a scalar function on the boundary

boundary_faces

Boundary face locations

boundary_node_vector_integral

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

boundary_nodes

Boundary node locations

cell_centers

Return gridded cell center locations

cell_centers_x

Return x-coordinates of the cell centers along the x-direction

cell_centers_y

Return y-coordinates of the cell centers along the y-direction

cell_centers_z

Return z-coordinates of the cell centers along the z-direction

cell_volumes

Return cell volumes

dim

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

edge

edge has been deprecated.

edgeCurl

edgeCurl has been deprecated.

edge_curl

Edge curl operator (edges to faces)

edge_lengths

Returns the lengths of all edges in the mesh

edge_tangents

Unit tangent vectors for all mesh edges

edges

Gridded edge locations

edges_x

Gridded x-edge locations

edges_y

Gridded y-edge locations

edges_z

Gridded z-edge locations

faceDiv

faceDiv has been deprecated.

face_areas

Returns the areas of all faces in the mesh

face_divergence

Face divergence operator (faces to cell-centres)

face_normals

Unit normal vectors for all mesh faces

faces

Gridded face locations

faces_x

Gridded x-face locations

faces_y

Gridded y-face locations

faces_z

Gridded z-face locations

h

Cell widths along each axis direction

h_gridded

Return dimensions of all mesh cells as staggered grid.

hx

Width of cells in the x direction

hy

Width of cells in the y direction

hz

Width of cells in the z direction

n_cells

Total number of cells in the mesh.

n_edges

Total number of edges in the mesh

n_edges_per_direction

The number of edges in each direction

n_edges_x

Number of x-edges in the mesh

n_edges_y

Number of y-edges in the mesh

n_edges_z

Number of z-edges in the mesh

n_faces

Total number of faces in the mesh

n_faces_per_direction

The number of faces in each axis direction

n_faces_x

Number of x-faces in the mesh

n_faces_y

Number of y-faces in the mesh

n_faces_z

Number of z-faces in the mesh

n_nodes

Total number of nodes in the mesh

nodalGrad

nodalGrad has been deprecated.

nodalLaplacian

nodalLaplacian has been deprecated.

nodal_gradient

Nodal gradient operator (nodes to edges)

nodal_laplacian

Nodal scalar Laplacian operator (nodes to nodes)

nodes

Return gridded node locations

nodes_x

Return x-coordinates of the nodes along the x-direction

nodes_y

Return y-coordinates of the nodes along the y-direction

nodes_z

Return z-coordinates of the nodes along the z-direction

normals

normals has been deprecated.

orientation

Rotation matrix defining mesh axes relative to Cartesian

origin

Origin or 'anchor point' of the mesh

project_edge_to_boundary_edge

Projection matrix from all edges to boundary edges.

project_face_to_boundary_face

Projection matrix from all faces to boundary faces.

project_node_to_boundary_node

Projection matrix from all nodes to boundary nodes.

reference_is_rotated

Indicates whether mesh uses standard coordinate axes

reference_system

Coordinate reference system

rotation_matrix

Alias for orientation

shape_cells

The number of cells in each coordinate direction.

stencil_cell_gradient

Stencil for cell gradient operator (cell centers to faces)

tangents

tangents has been deprecated.

vectorCCx

vectorCCx has been deprecated.

vectorCCy

vectorCCy has been deprecated.

vectorCCz

vectorCCz has been deprecated.

vectorNx

vectorNx has been deprecated.

vectorNy

vectorNy has been deprecated.

vectorNz

vectorNz has been deprecated.

vol

vol has been deprecated.

x0

An alias for the origin

Methods

closest_points_index(locations[, grid_loc, ...])

Find the indicies for the nearest grid location for a set of points.

copy()

Make a copy of the current mesh

deserialize(items, **kwargs)

Create this mesh from a dictionary of attributes

equals(other_mesh)

Compares current mesh with another mesh to determine if they are identical

getEdgeInnerProduct(*args, **kwargs)

getEdgeInnerProduct has been deprecated.

getEdgeInnerProductDeriv(*args, **kwargs)

getEdgeInnerProductDeriv has been deprecated.

getFaceInnerProduct(*args, **kwargs)

getFaceInnerProduct has been deprecated.

getFaceInnerProductDeriv(*args, **kwargs)

getFaceInnerProductDeriv has been deprecated.

getInterpolationMat(*args, **kwargs)

getInterpolationMat has been deprecated.

getTensor(*args, **kwargs)

getTensor has been deprecated.

get_edge_inner_product([model, ...])

Generate the edge inner product matrix or its inverse.

get_edge_inner_product_deriv(model[, ...])

Function handle to multiply vector with derivative of edge inner product matrix (or its inverse).

get_face_inner_product([model, ...])

Generate the face inner product matrix or its inverse.

get_face_inner_product_deriv(model[, ...])

Function handle to multiply vector with derivative of face inner product matrix (or its inverse).

get_interpolation_matrix(loc[, ...])

Construct linear interpolation matrix from mesh

get_tensor(key)

Returns the base 1D arrays for a specified mesh tensor.

isInside(*args, **kwargs)

isInside has been deprecated.

is_inside(pts[, location_type])

Determine which points lie within the mesh

point2index(locs)

Finds cells that contain the given points.

projectEdgeVector(*args, **kwargs)

projectEdgeVector has been deprecated.

projectFaceVector(*args, **kwargs)

projectFaceVector has been deprecated.

project_edge_vector(edge_vectors)

Project vectors to the edges of the mesh.

project_face_vector(face_vectors)

Project vectors onto the faces of the mesh.

save([file_name, verbose])

Save the mesh to json

serialize()

An alias for to_dict()

to_dict()

Representation of the mesh's attributes as a dictionary

validate()

Return the validation state of the mesh

Galleries and Tutorials using discretize.base.BaseTensorMesh#