# 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’).

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. 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 An alias for to_dict() Representation of the mesh's attributes as a dictionary Return the validation state of the mesh

## Galleries and Tutorials using discretize.base.BaseTensorMesh# Operators: Cahn Hilliard

Operators: Cahn Hilliard Plot Mirrored Cylindrically Symmetric Model

Plot Mirrored Cylindrically Symmetric Model Basic Forward 2D DC Resistivity

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Basic: PlotImage   Plotting: Streamline thickness

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Overview of Mesh Types Tensor meshes

Tensor meshes Cylindrical meshes

Cylindrical meshes Tree Meshes

Tree Meshes Averaging Matricies

Averaging Matricies Differential Operators

Differential Operators Basic Inner Products

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Constitutive Relations Differential Operators

Differential Operators   