discretize.CurvilinearMesh#

Inheritance diagram of CurvilinearMesh
class discretize.CurvilinearMesh(node_list, **kwargs)[source]#

Curvilinear mesh class.

Curvilinear meshes are numerical grids whose cells are general quadrilaterals (2D) or cuboid (3D); unlike tensor meshes (see TensorMesh) whose cells are rectangles or rectangular prisms. That being said, the combinatorial structure (i.e. connectivity of mesh cells) of curvilinear meshes is the same as tensor meshes.

Parameters
node_listlist of array_like

List array_like containing the gridded x, y (and z) node locations.

  • For a 2D curvilinear mesh, node_list = [X, Y] where X and Y have shape (n_nodes_x, n_nodes_y)

  • For a 3D curvilinear mesh, node_list = [X, Y, Z] where X, Y and Z have shape (n_nodes_x, n_nodes_y, n_nodes_z)

Examples

Using the example_curvilinear_grid() utility, we provide an example of a curvilinear mesh.

>>> from discretize import CurvilinearMesh
>>> from discretize.utils import example_curvilinear_grid
>>> import matplotlib.pyplot as plt

The example grid slightly rotates the nodes in the center of the mesh,

>>> x, y = example_curvilinear_grid([10, 10], "rotate")
>>> x.shape
(11, 11)
>>> y.shape
(11, 11)
>>> curvilinear_mesh = CurvilinearMesh([x, y])
>>> curvilinear_mesh.shape_nodes
(11, 11)
>>> fig = plt.figure(figsize=(5,5))
>>> ax = fig.add_subplot(111)
>>> curvilinear_mesh.plot_grid(ax=ax)
>>> plt.show()

(Source code, png, pdf)

../../_images/discretize-CurvilinearMesh-1.png

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_edge_x_to_cell

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

average_edge_y_to_cell

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

average_edge_z_to_cell

Averaging operator from z-edges to cell centers (scalar 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_face_x_to_cell

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

average_face_y_to_cell

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

average_face_z_to_cell

Averaging operator from z-faces to cell centers (scalar 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

Orientation of the first axis.

axis_v

Orientation of the second axis.

axis_w

Orientation of the third axis.

boundary_edge_vector_integral

Integrate 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

Represent the operation of integrating a scalar function on the boundary.

boundary_faces

Boundary face locations.

boundary_node_vector_integral

Integrate a vector function dotted with the boundary normal.

boundary_nodes

Boundary node locations.

cellGrad

cellGrad has been deprecated.

cellGradBC

cellGradBC has been deprecated.

cellGradx

cellGradx has been deprecated.

cellGrady

cellGrady has been deprecated.

cellGradz

cellGradz has been deprecated.

cell_centers

Return gridded cell center locations.

cell_gradient

Cell gradient operator (cell centers to faces).

cell_gradient_BC

Boundary conditions matrix for the cell gradient operator (Deprecated).

cell_gradient_x

X-derivative operator (cell centers to x-faces).

cell_gradient_y

Y-derivative operator (cell centers to y-faces).

cell_gradient_z

Z-derivative operator (cell centers to z-faces).

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

Return 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 (staggered grid).

edges_y

Gridded y-edge locations (staggered grid).

edges_z

Gridded z-edge locations (staggered grid).

faceDiv

faceDiv has been deprecated.

faceDivx

faceDivx has been deprecated.

faceDivy

faceDivy has been deprecated.

faceDivz

faceDivz has been deprecated.

face_areas

Return 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.

face_x_divergence

X-derivative operator (x-faces to cell-centres).

face_y_divergence

Y-derivative operator (y-faces to cell-centres).

face_z_divergence

Z-derivative operator (z-faces to cell-centres).

faces

Gridded face locations.

faces_x

Gridded x-face locations (staggered grid).

faces_y

Gridded y-face locations (staggered grid).

faces_z

Gridded z-face locations (staggered grid).

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 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).

node_list

The gridded x, y (and z) node locations used to create the mesh.

nodes

Return gridded node locations.

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

Indicate whether mesh uses standard coordinate axes.

reference_system

Coordinate reference system.

rotation_matrix

Alias for orientation.

shape_cells

Number of cells in each coordinate direction.

shape_edges_x

Number of x-edges along each axis direction.

shape_edges_y

Number of y-edges along each axis direction.

shape_edges_z

Number of z-edges along each axis direction.

shape_faces_x

Number of x-faces along each axis direction.

shape_faces_y

Number of y-faces along each axis direction.

shape_faces_z

Number of z-faces along each axis direction.

shape_nodes

The number of nodes along each axis direction.

stencil_cell_gradient

Stencil for cell gradient operator (cell centers to faces).

stencil_cell_gradient_x

Differencing operator along x-direction (cell centers to x-faces).

stencil_cell_gradient_y

Differencing operator along y-direction (cell centers to y-faces).

stencil_cell_gradient_z

Differencing operator along z-direction (cell centers to z-faces).

tangents

tangents has been deprecated.

vol

vol has been deprecated.

x0

Alias for the origin.

Methods

cell_gradient_weak_form_robin([alpha, beta, ...])

Create Robin conditions pieces for weak form of the cell gradient operator (cell centers to faces).

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(value, **kwargs)

Create this mesh from a dictionary of attributes.

edge_divergence_weak_form_robin([alpha, ...])

Create Robin conditions pieces for weak form of the edge divergence operator (edges to nodes).

equals(other_mesh)

Compare the current mesh with another mesh to determine if they are identical.

from_omf(element)

Convert an omf object to a discretize mesh.

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.

get_BC_projections(BC[, discretization])

Create the weak form boundary condition projection matrices.

get_BC_projections_simple([discretization])

Create weak form boundary condition projection matrices for mixed boundary condition.

get_edge_inner_product([model, ...])

Generate the edge inner product matrix or its inverse.

get_edge_inner_product_deriv(model[, ...])

Get a 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[, ...])

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

get_interpolation_matrix(loc[, ...])

Construct a linear interpolation matrix from 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 grid for nodal, cell-centered and staggered grids.

plot_image(v[, v_type, grid, view, ax, ...])

Plot quantities defined on a given mesh.

plot_slice(v[, v_type, normal, ind, ...])

Plot a slice of fields on the given 3D mesh.

point2index(locs)

Find 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.

r(*args, **kwargs)

r has been deprecated.

reshape(x[, x_type, out_type, return_format])

Reshape tensor quantities.

save([file_name, verbose])

Save the mesh to json.

serialize()

Represent the mesh's attributes as a dictionary.

setCellGradBC(*args, **kwargs)

setCellGradBC has been deprecated.

set_cell_gradient_BC(BC)

Set boundary conditions for derivative operators acting on cell-centered quantities.

toVTK([models])

Convert mesh (and models) to corresponding VTK or PyVista data object.

to_dict()

Represent the mesh's attributes as a dictionary.

to_omf([models])

Convert to an omf data object.

to_vtk([models])

Convert mesh (and models) to corresponding VTK or PyVista data object.

validate()

Return the validation state of the mesh.

writeVTK(file_name[, models, directory])

Convert mesh (and models) to corresponding VTK or PyVista data object then writes to file.

write_vtk(file_name[, models, directory])

Convert mesh (and models) to corresponding VTK or PyVista data object then writes to file.

Galleries and Tutorials using discretize.CurvilinearMesh#

Basic Forward 2D DC Resistivity

Basic Forward 2D DC Resistivity

Basic Forward 2D DC Resistivity
Overview of Mesh Types

Overview of Mesh Types

Overview of Mesh Types