discretize.base.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