discretize.CurvilinearMesh

class discretize.CurvilinearMesh(node_list, **kwargs)

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)

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	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	Gridded boundary edge locations
boundary_face_outward_normals	Outward normals of boundary faces
boundary_face_scalar_integral	Represents the operation of integrating a scalar function on the boundary
boundary_faces	Gridded locations of non-hanging x-faces
boundary_node_vector_integral	Represents the operation of integrating a vector function dotted with the boundary normal
boundary_nodes	Gridded 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	Gridded cell center locations (staggered grid)
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	Returns the lengths of all edges in the mesh
edge_tangents	Gridded edge tangents directions for all mesh edges
edges	Gridded edge locations (staggered grid)
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	Returns the areas of all faces in the mesh
face_divergence	Face divergence operator (faces to cell-centres)
face_normals	Gridded average face normals 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 (staggered grid)
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	Returns the gridded x, y (and z) node locations used to create the mesh.
nodes	Gridded node locations (staggered grid)
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.
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	Returns 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	An alias for the origin

Methods

cell_gradient_weak_form_robin([alpha, beta, ...])	Robin conditions for weak form of the cell gradient operator (cell centers to faces)
copy()	Make a copy of the current mesh
deserialize(value, **kwargs)
edge_divergence_weak_form_robin([alpha, ...])	Robin conditions for weak form of the edge divergence operator (edges to nodes)
equals(other_mesh)	Compares current mesh with another mesh to determine if they are identical
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 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).
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, ...])	Plots quantities defined on a given mesh.
plot_slice(v[, v_type, normal, ind, ...])	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_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, format])	General reshape method for tensor quantities
save([file_name, verbose])	Save the mesh to json
serialize()	An alias for to_dict()
setCellGradBC(*args, **kwargs)	setCellGradBC has been deprecated.
set_cell_gradient_BC(BC)	Set zero Dirichlet/Neumann boundary conditions for derivative operators acting on cell-centered quantities.
toVTK([models])	toVTK has been deprecated and replaced by to_vtk
to_dict()	Representation of the mesh's attributes as a dictionary
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 mesh (and models) to corresponding VTK or PyVista data object
validate()	Return the validation state of the mesh
writeVTK(file_name[, models, directory])	writeVTK has been deprecated and replaced by write_vtk
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

Overview of Mesh Types

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